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FOTD 12-08-03 (Space Station [7])
by Jim Muth 12 Aug '03

12 Aug '03

FOTD -- August 12, 2003 (Rating 7) Fractal visionaries and enthusiasts: I try to convince myself that the public media is a fair and unbiased source of information, but it is becoming very hard to keep up the self-delusion. Every time I turn on the fractal TV, it seems I see dramatic fear-inspiring stories of record- breaking heat, drought, and fires in Europe and the western U.S. The assumption is that global warming has arrived, and we are ready to run out of water and be wiped out by heat exhaustion, wildfires, flooded coastal cities, and mass starvation. But where are the stories about the ongoing record-breaking cool, rainy summer in the Eastern part of the U.S., or the cold wave in Europe this past April, or the current record-cold weather in Australia? And finally, why are most professional meteorologists more concerned about an ice age than global warming? Those living in the Fractal Central area are already more worried about the next ice age than global warming. The local farmers (in addition to the local cats) are actually praying for dry weather. Yesterday was the 22nd consecutive day with at least some rain here at F.C. While I have been searching for an unbiased news source, I have also been searching for fractals. For today's image I returned to my favorite fractal rectangle -- the one in the Z^(2.003)+C Julia set at C=-1.7435,0.0 and Z=0.00019,0.07388. This object is shaped like a rectangle only when sliced in the Julia direction. Any deviation from that direction quickly distorts the rectangle. In today's image, we deviate only one degree toward the Parabolic direction, but even that small deviation turns the rectangle into a kind of table-top sitting on a platform, creating a convenient landing place for a space ship. I have named the image "Space Station". The image needed a little help to reveal its full potential. The surface of the table top, as well as most of the platform consist of inside material made visible by the 'fmod' option. When this was done, the result was an image worthy of a rating of 7. Changing the imag(p1) parameter even slightly totally changes the image. If imag(p1) is reduced to 80, the effect is more of a cut-away view of a volcano. When the parameter is reduced beyond that, the image stretches horizontally until, by the time the Parabolic direction is reached, it becomes little more than a series of horizontal bands. Four minutes is a fast-enough time for the attached parameter file. And as always, the completely finished image is available in good old-fashioned GIF format on the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather on Monday here at Fractal Central would have been near perfect if a heavy thunder-shower had not arrived and dropped 0.8 inches or 2cm of rain just as the dynamic duo were finishing their near-perfect day in the yard. Had it not been for the rain, the temperature of 81F 27C would have been ideal. The rain did one good thing however -- it hurried the duo indoors without urging from me. When they were safely inside, I gave them a small treat of tuna to assure their continued good moods. Today is scheduled to be a repeat. Things will be all right if the rain holds off until 5pm. I'll be all right if the work goes smoothly and the next fractal is a good one. Until that next fractal arrives, take care, and where is the heat one expects in this part of the world at this time of year? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Space_Station { ; time=0:04:10.07--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=flip/ident passes=1 center-mag=-0.0058071/1.00614e-016/58.884\ 49/1/90/-1.23373533611470521e-014 params=90/89/2.0\ 03/0/0.00019/0.07388/-1.7435/0 float=y maxiter=1200 inside=fmod proximity=0.0333 periodicity=10 colors=000oT8qS8tQA000wNAyLCzKCzICzGDzFDzDDzCFzAFz\ AGz8Fz8Dz7Cz7Cz5Az58z38z37z25y25w03v02v02t00r00q00\ o00m00l00j00i00g00zwzlazzczjKzzmziazzzziazzqziizii\ zA30C50D70D70F80FA0GC0GC0ID0KF0KG0LG0LI0MJ0NK0OL0Q\ M0QO0SQ0SQ0TS0VT0VV0XV0XX0YY0__0__0aa0ab0bd0bd0de0\ eg0ei0gi0gl0io0jr0qt0yw0zz0zz0zz0zz0zz0zy0ww0wt0vr\ 2to2rm3rj5rj5ri7ri7rg8tg8teAteCtdCvdDvbDvbFvaFwaGw\ _Gw_IwYKwYKyXLyXLyVNyVNzTOzTQzSQzSSzQSzQTzOTzOVzQT\ zOVzOVwNXvNXrNYqLYmL_lL_iK_gKadKabIb_IbYIdVGdTGeQG\ eOFeLFgKDgGDiFDiCCjACj7Cl5Al2Al0Am08m08o08o07q07q0\ 5o07q08q0Ar0Cr0Dt0Ft0Gt0Iv0Kv3Kw5Lw7Ny8OyAQyDSzFTz\ GVzIXzKXzIVzIVzGTzGTzFSzFSzDQzDQzCOzCOzDNzDLzDLzDK\ zFIzFIzFGzFFzGFzGDyGCwGCvIArI8qI8oI7mK5jK5iK3gK2e0\ QCK2dLDQNODO_0Oi0Oj0Oj0Ol0Ol0Ol3Om7OmAOoDOoGOoKOqN\ OqQOqTOrYOraOtdOtgOtjOvmOvqOwtOwwOwzOyzOyzOyzSwzTv\ zXtzYrydb5ea5i_7jY7lX7mV8 } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 11-08-03 (Disconnected Midget [5])
by Jim Muth 11 Aug '03

11 Aug '03

FOTD -- August 11, 2003 (Rating 5) Fractal visionaries and enthusiasts: I spent too much effort being lazy all day Sunday, so the fractal I eventually found rates only a 5. But after all, even an average fractal is worth seeing. Some fractals, such as the well-known Mandelbrot set, are connected. This means that every apparently disconnected midget is actually connected to the main bay by an infinitely thin filament. Other fractals, such as the parent of today's image, are not connected, and contain areas totally cut off from the main body of the fractal. Today's midget lies in one of these areas that is cut off from the main body of the parent fractal, which appears as a slightly distorted M-set. This is why I named it "Disconnected Midget". I rendered the image with the outside set to 'tdis' to emphasize the disconnected nature of the scene. The 'tdis' outside also makes a better picture. The short render time of a nice neat 0:02:02.02 is pleasant enough, though not quite as much fun as downloading the already- completed GIF image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Sunday was an unusually pleasant day here at Fractal Central. The rain held off and the temperature reached 84F 29C, which made the cats happy, and I got through the day without finding work that needed to be done, which made me happy. Hopefully, today will be a repeat, but there is still a bit of work to be finished first. Until next time, take care, and stay connected. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ DisconnectedMidget { ; time=0:02:02.02--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-1.83854548477051500/+0.410334133501795\ 70/4.195225e+007/1/85/-3.35216519486980502e-007 params=1/3/2/-0.5/0/0 float=y maxiter=500 inside=0 outside=tdis periodicity=10 colors=000vPnyOuqSrjWpc_nXblQfiJjgCne5qc4sj3uq3wwA\ nxGeyNXyTOzZFz`JvbNrdQnfUkhYgj`cld_mgXkXWiMWgCWbEV\ ZGUUITQKTMHOIEKEBGB8C758324M8bK9fPAnUAuYJtaRteZtig\ tmotqwtntpkqmhnjekgbhd`faVa_PXYJTWDOU7JS1FQ2IR3LR3\ OR4QR5TS5WS6ZS6`S8_Q9ZOBZMCYKEXIFXGHWEIWCJ`IKdOKiT\ LmZLqck4eT2SA1FH3MN5SU7Y_8cfAilCorDusCotCiuBcvBYwA\ SxANt8Op7Pl5Ph4Qd2Q`1RY0RnTMfXUZ_`RbhKeoNciQacT_YW\ YSZWMaUGdTAiWUmZlnbmnfmojnonnornpshqsbrsXstRttLutF\ ut9lf6dU4XH2P40S30U30X30Z30`30c30e30g30`49V5HP6PI7\ XC8d69l09tmO4gTHaYUWbfRfsSiwSkzXrmayaXuhTrnOotKlz_\ 96`CAaFDbIHcLKdONeRRfUUgWXfYbe_gd`mcbrccwahx`lyZpz\ Ytz_jt``naSigYjlbkqglvllonhipdcraXtYRvVLxRFzOKpJOf\ ESY9VXJYXT`XbcXlfXvhVqiUmkShlRdmQ`8H8FJPMLeSMvc8O`\ IZYSiWatbSpiJlp9hv0dpGbjWaek``kaWkaSkaQjYOjUNiQLiM\ JhIIhEGgAFg7IiDKjJMkPOlVQm`SnfUolWprUomTnhRncQmZPm\ VYUMXOOWIPgYFjWMmUTpT`sRg } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 10-08-03 (A Fractal in Nirvana [7])
by Jim Muth 10 Aug '03

10 Aug '03

FOTD -- August 10, 2003 (Rating 7) Fractal visionaries and enthusiasts: Years ago there was a small deli restaurant in the Fractal Central neighborhood, run by a Korean immigrant. The merchant has long since moved away, but I still remember the conversa- tions he and I used to have on slow days. He was a Buddhist who was eager to talk about religion, particu- larly his idea of Buddhism. He often told me that the goal of Buddhists is to escape the constant reincarnations on earth and enter Nirvana. He expressed amusement at the simplicity of our two main western beliefs -- that we go to heaven when we die, to be perfectly happy for all eternity, or that we simply cease to exist, eliminating the need to concern ourselves with the topic. When I asked him to describe the Nirvana that Buddhists believe in, he told me that it is hard to put into words, but that Nirvana is like a mixture of heaven and non-existence. We cease to exist when we enter Nirvana, which is the ultimate peace, yet somehow we can enjoy the ultimate peace of not existing. When I asked him what it is that does the enjoying, he simply shrugged and said that one must enter Nirvana before they can understand it. Nirvana is an oxymoron. Today's image is also an oxymoron. It consists of as much inside material as outside material, yet it is impossible to tell one from the other. I named it "A Fractal in Nirvana" when the etheric blues reminded me of the conversations about transcendental things that I once had at that small restaurant. The parent fractal is the same as the parent of yesterday's 'Wonderland' image, though instead of going to 'East valley' to explore, I went to one of the numerous tiny valleys on the west shore of the main bay. The 'inside' parts of the image have been made visible by the 'bof60' inside fill. This fill normally creates mostly bubbles, though the bubbles are not very apparent in today's image. The image is notably better that yesterday's hasty achievement, and IMO rates an honest 7. And the 9-minute render time allows ample time to ponder the mysteries of the beyond. Those more concerned with the here and the now may bypass the pondering by downloading the completed GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The rain on Saturday amounted to only a few sprinkles here at Fractal Central, but even that was enough to wet the grass and dampen the spirits of the dynamic duo. Due to the high humid- ity, the temperature of 80F 27C felt more like 90F 32C. I have little hope for improvement, because today promises to be more of the same. For the cats, the day will be questionable. For me it's going to be a lazy day -- that is if I can get through it without finding any work that needs to be done. Until next FOTD, take care, and walk in the peace of eternal fractal oneness. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_In_Nirvana { ; time=0:09:09.69--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+1.55913935558906900/+0.103410051541293\ 70/709229.8/1/-170/-1.28612687166906881e-009 params=2/3/-2/0.05/0/0 float=y maxiter=1200 inside=bof60 periodicity=10 colors=000cCA_DAVFAQGBMHBHJBCKB8LBCNFFQIJUMMXPQXST\ _WWaZ_cabfe020ijkMrQOqUPoYRnaSmeUkiWjmXhqZgu_fxXXm\ VObSESQ5IR9KSDMTHNTLPUPRVTSVWUW_WXcXYgZYk`Zoa_sc_v\ dWscSpbPnbLkaHh`Ef`Ac_7a_8Z`8Xa8Ua8Sb8Pc8Nc8Kd8Ie8\ Fe8Df8Ag88gGLZNYRVjIavA621954C76FA8ICALECOHFRJHUMJ\ XOL_QNbTQeVShYUk_WmaYk_WjYUhWSgUQeSOdRMbPKaNJ`LHZJ\ AYIFWGKVEPTCUSAZR9cUFhXKmZPraUwd_wfdwiiwknweoz`jwW\ frQcmL_hG`cJafMchK`iJZjIXkHVlGTmFRmDOnCMoBKpAIq9Gr\ 8ErGLjOSbWZVceNklFzr7wq6tp6po6mn5im5el5bk4_k4Xj4Ti\ 3Oh3Ig3Ff2Ce29e2Dc5Gb8JaBM`EP_HTZKWYNZXQaVTdUWhTZk\ SanRdqQgtPjwOmpJbjESc9HY57Z6AZ7DZ8FZ9IZALZBNZCQZDS\ ZEVZFYZG_ZHbZHdUF`PDXKBUF9QA7M56J49N4CQ4FT4IW4LZ4O\ a4Rd4Tg8UeBVdFVcIWbMWaPX`TY_WYZ_ZYbZXf_Wi`Vm`UpaTs\ aSpYPnUMlRJiNHgKEeGBbC9`96Z53X21P95IF8BMB4SE9QCDPB\ IOAMN9QM8VL7ZK6cJ5gI4kH3pG2tF1xE0vI4tL7sOBqREoVHnY\ Ll`OkcRttimoegja`eZV`VKtM } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 09-08-03 (Mandel Wonderland [5])
by Jim Muth 09 Aug '03

09 Aug '03

FOTD -- August 09, 2003 (Rating 5) Fractal visionaries and enthusiasts: This will be a short discussion because it's getting late and today's FOTD is far overdue. Today's pot-luck fractal, which was found in 10 minutes and rendered in 11, rates a 5. It is a scene in the East Valley area of the fractal that results when 2 parts of Z^0.05 are subtracted from two parts of Z^3. The parent fractal somewhat resembles the mouth of a crying clown turned on its side. I named the image "Mandel Wonderland", though it is a fairly routine, generic scene that might appear in almost any valley. The parent fractal almost certainly holds far more interesting scenes. I'll post one of these as tomorrow's FOTD. As always, the completed GIF image is available on the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The numerous showers somehow all bypassed Fractal Central on Friday, and the temperature reached 86F 30C, giving the dynamic fractal cats several dry hours in the yard. Their moods were accordingly pleasant. The day ended with them sleeping peace- fully together in their favorite overstuffed chair. Today is overcast with heavy rain forecast, but the rain has so far failed to appear. The cats are currently romping in the yard. Hopefully, their good luck will continue for the rest of the day. We will know for sure in 18 hours, when the next FOTD appears. Until then, take care, and is the meaning of fractals the same as the meaning of life? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Mandel_Wonderland { ; time=0:11.41.14--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+2.19230087842847400/-0.000225004562220\ 96/1.734486e+011/1/-126.5/-0.00001734773581692533 params=2/3/-2/0.05/0/0 float=y maxiter=1300 inside=0 logmap=222 periodicity=10 colors=000GKPHJNIHLJGJKEHLDFMBDNABN99OFCPLEPRHQXJQ\ aMRgORmRSsTSxVRtWQqWQnWPkXOhXOdXNaXMZYMWYLTYLQYJW_\ Ia`HfbFlcEreDwf5xn4qi3ke2da2ZY1SU0MQ0GM9OKHWIQcHYk\ FesEatGZuHWuITvJQvKMwMJwNGxODxPAyQ7yR9xSAwTBvUDuVE\ tVFsWGrXIrYJqZKpZLo_Nn`OmaPlbQlbdLNaRK_XHYbEVhBTn8\ Rt5PuANuFLuKJuPHuUFuZDucBuhAumCoiEieFcbHZZITWKNSLI\ POLRROTURUWUWZXXa_Zca_fdaigbkjdnmeqpgsrhtmcuh_vcWv\ ZRwVNxQJxLEyGAzB6z72tA6oDAjGEeJI`MM_KP_JS_IV_HY_G`\ _FcZEfZDiZClZBoZArZ9tPRmFgf6x_9rZBlYDfXFaWHWVJQULL\ TMMRMMPMMONNMNNKNNJOOHOOFOOEPPCPPAPP9QQ7QQ5QQ4NRGL\ SRITbGTmMPrRMwTQtUTrVWpWZnWZnX_nX_otB1qE2nH3kJ4iM5\ fP6cR7`U8ZW9SbIMhQFoY9ueBtcDsbFr`Hq_JpYLoXNnVPnURm\ TTlRVkQXjOZiN`hLbgKdgJnYLwPNvMMvKLvHKvFJvDJpB5k9Al\ FFmLKnRPnXUobZphcpnhrnmqjrqgwqczq`zpXzpUzpQzqNzrKz\ sJztJzuJzvJzwIzxIzyIzzIzzHzzHzzHzzHzzGzzGzzGzzGzzP\ zzHzz9zz1zz3zz4zzPzzNzzMz } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD for Aug 09 delayed
by Jim Muth 09 Aug '03

09 Aug '03

Fractal enthusiasts: Due to an unexpected rush job, the FOTD for Aug. 09 will be delayed several hours. -- Sorry! Jim M.

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Nautibroids
by Russell Walsmith 08 Aug '03

08 Aug '03

I still can hardly believe that I'm seeing this stuff... here are more fibrot/nautibroid images: -------------------------startparfile----------------------------- The_Jungle { ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=dcls4.frm formulaname=Fibrot1 passes=3 center-mag=1.32611/-0.0253659/7.041667 params=0/2/1/0 float=y maxiter=300 colors=000ruonsjQdrLdtblU<3>Mb8<3>LQ8KM8KJ8<2>I88H44G00<3>TA5WD6\ ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5z\ P5zL6zI6zE6wE6tD6<6>vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW4E<2>_4\ H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>u1mt1ns1o\ r2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6Zc7`c7aa7c_7eY<3>F\ cgHciJbl<3>S_v<3>civflvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8X\ a<3>8JP8FL8CI<4>XCAaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<6>UXAW`BYcC<3\ >hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi_5fc0ce7_jFRoNIzb0zj0000zr1\ zz1zzC<2>zzzvxu } --------------------------endparfile------------------------------ The Jungle reuses the Lee Skinner map I borrowed earlier. Great map Lee, but I'll be glad when I"ve got a grip on the pallet tools... is there a tutorial for that anywhere? La Concha uses a throughly generalized formula, the MandelbroidG. The frm3 option was intended to toggle from 'ident' to 'abs' so to view the 'naked' fractal (i.e., absent the field lines), but of course it turns out to offer a bit more than that... Let p4=2; then p1=p2=p3=1 and fm1=fm2=fm3=ident generates the Mset. -------------------------startparfile----------------------------- La_Concha { ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=dcls4.frm formulaname=NautibroidG function=conj/cabs/ident passes=3 center-mag=-0.843279/0.34679/0.51358 params=5/1/3/1/-1/0/2.618/0 float=y maxiter=300 outside=imag colors=653xwulHICXNwuIDCTjCRATl653xwulHICXNwuIDCTjCRATlccc<238>c\ cc } --------------------------endparfile------------------------------ It still blows my socks off to realize that just a few tweaks ago La_Concha was the Mandelbrot set!!! Finally, there's the device of putting d=pixel^2 into the M-set iteration loop like so: z=z^2 + c + p1*d. This induces the Mset's shy twin to fly in from infinity. It works in the MetaNaut formula as well: -------------------------startparfile----------------------------- Hummingbrot { ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=dcls4.frm formulaname=metanaut passes=1 center-mag=-2.77783/-1.41777/0.1529238 params=4/1/0.707/0.707/2/0 float=y maxiter=300 colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0W } --------------------------endparfile------------------------------ -------------------------startfrmfile----------------------------- frm:Fibrot1 { z = 0, c = pixel, j=0, k=1: a = p2*j + p1*k j = k k = a z = z^k + c z < 1000 } frm:NautibroidG { z = 0, c = pixel, k=p4, j=p3: j=p3*j k=p1*fn1(k)*j z = z^k + c j=p3*j k=p2*fn2(k)*j z = z^k + c fn3(z) < 1000 } frm:MetaNaut { z = 0, c = pixel, d = pixel^2, k=p3: k=p1*k z = z^k + c + p2*d z < 1000 } fn3(z) < 1000 } ---------------------------endfrmfile-----------------------------

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FOTD 08-08-03 (No Luck Today [4])
by Jim Muth 08 Aug '03

08 Aug '03

FOTD -- August 08, 2003 (Rating 4) Fractal visionaries and enthusiasts: Sometimes fractal luck, like any other luck, can turn bad. This happened to me during my fractal explorations on Thursday evening, when I was tracking today's scene. Today's scene is a slow one, and I had already been on its track for over an hour when I started calculating the final frame, fully expecting to find a midget at the center. But I had been fooled. Today's image is not one of a midget, it is another of those 'dry lakes' that from a distance look like the basin surrounding a midget but up close prove to be nothing more than an area of symmetry. Normally, I discard such failures, but I had put so much time and effort into today's image that I decided to declare it the FOTD for 8-8-03 despite the lack of a midget. (Also, even without the standard midget, it is an interesting scene.) Actually, I never had a chance of finding a midget even if one were at the center of the basin. The image as it appears is of such a great magnitude that it is already showing signs of resolution breakdown. If a midget were at the center, I would never be able to reach it. This excessive magnitude is the reason I included the 'mathtolerance' entry in the parameter file. I named the final result "No Luck Today" and rated it at a below- average 4. The unusually slow render time of almost an hour is admittedly excessive for such a mediocre image. I advise letting Paul and Scott render the image, and then picking it up from one of their FOTD web sites. The URL of Paul's site is: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's site is: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The clouds and occasional light rain prevailed all day Thursday here at Fractal Central. The temperature of 79F 26C was comfortable enough, but the wet grass kept the fractal cats confined to within a few feet of the porch. When they came indoors, their moods were so sour that a squabble broke out and a few punches were thrown before a treat of tuna eased their frustration. Today is forecast to be another showery day. Hopefully, the duo will weather any rain better than they did yesterday. I'm going to spend the day finishing the modicum of work still waiting to be done, and then I'll search for a better fractal. Until tomorrow, when that better fractal will appear as the FOTD, take care, and don't get run down by a DUI fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ No_Luck_Today { ; time=0:55:52.48--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-1.628689612431902/+0.00008782771078793\ /2.832453e+013/1/90/3.88578058618804789e-016 params=2/0.05/2/3/0/0 float=y maxiter=12000 periodicity=10 mathtolerance=/1 colors=000nTqpTqqXnq_lqbjqehncekaci_afYZcXXaVVZTSW\ RQUPOROLOMJMKHJIEGGCDE9EFAFGAFGAGHAHHAHIAIJAIJAJKA\ KKBKLBLMBMMBMNBNNBNOBOOBPPBPQBQQCRRCRRCSSCSTCTTCUU\ CUUCVVCVVCUWDTXESXFRYFQZGPZHO_HN_IM`JLaJKaKJbLNfKJ\ bLG_MDXNAUO7RPDUUJWYPZaU`f_cjeenomwjgrfbnaYiYTeTO`\ PJXKESG9OC4KE6LF8LG9LHBMIDMJEMKGNLINMJNNLOOMOPOOQQ\ PRRPSTPUVQVWQWYQX_RY`RZbR_cS`eSagSbhTcjTdlTemUfoUg\ pUkr_otesvkwxqqvpktoero_pnUnnOlmEjtJkmOkgTlaYlVamP\ fmJknCpn6tn0pi3me6i`9fXCcSF_OIXJLUFNVHMWILWJKXKJXL\ IYMHYNGZOF`ODZPEYPEXQEWQEVREURETRESSERSEQTEPTEOTEN\ UEMUELVEKVEIVFHWFGWFFXFEXFDXFCYFBYFAZF9ZF8ZF7_F6_F\ 5`F4`F1cC3`F5YH7VJ9TLBQNDNPFLSHIUJFWLDYNA_P7aQ5cT4\ dV4dX3eZ3ea2fc2fe2fg1gj1gl0hn0hp0ho1in1in1im1jl1jl\ 1jk1kj1kj1ki1kh2lh2lg2lf2mf2me2me2md2nc2nc2nb3oa3o\ a3o`3o_3p_3pZ3pY3qY3qX3qY2rX3qX4pW4oW5nW5mV6lV6kU7\ jU7iU8hT9gT9fTAehTqjTqlTq } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 07-08-03 (Mantis Cases [7])
by Jim Muth 07 Aug '03

07 Aug '03

FOTD -- August 07, 2003 (Rating 7) Fractal visionaries and enthusiasts: Is nothing sacred? When I opened my e-mail box this morning, I found two letters from the Fractint programmers list. This is unusual, since normally, the list is considered active if it has one letter per month. But I was soon disappointed. The subject of the first letter was 'hey wgtjvjh...' This letter contained total gibberish and was likely posted only to determine if it would actually be sent out to list members. The second letter, which was sent from the same address a short time later, directed the reader to a web site selling 4-percent mortgages. I didn't bother visiting the web site. I'm sure the 'list member' who sent the spam will soon be deleted from the list. Today's unusually brilliant image rates a 7, but most of the rating is due to program features, not to an exceptional scene that I discovered and rendered. The feature that made the image is the 'fmod' inside fill option of Fractint, which was used to render the 'inside' parts of the image. This option produces an effect of overlapping bubbles. A good part of today's scene consists of trapped 'inside' points, and it is these areas that create the frothy, bubbly effect. The frothy areas of the image remind me of the egg case of a praying mantis, which is the reason for the name "Mantis Cases". The parent fractal, which was created by subtracting Z^(0.2) from 2 parts of Z^3, is so convoluted that it is impossible to describe. But it does have a 'Mandelbrot Molecule', or midget, at its northern extremity. The 'East Valley' of this midget is split into two parts. Today's scene is located in a spiral on the shoreline of the western branch of the split. Those who suspect that the colors of today's image are not quite natural are correct. I gave the original bland color palette a huge boost in contrast in a separate graphics program. This is no cause for concern, because when I run Fractint images through a separate program, I always make sure the changes can be encoded accurately into a parameter file. Running today's attached parameter file will take 10 minutes and will reproduce the enhanced image as it appears on my screen. Not all fractalists enjoy sitting back and watching images slowly appear on their screens. Those who desire instant fractal satisfaction can find it on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Wednesday was fair enough here at Fractal Central, with lots of sun and a temperature of 81F 27C. The problem was that a brief but heavy shower passed over at 1pm and again made things too wet in the holly thicket for the intrepid duo. They spent the afternoon on the porch, their moods questionable. Today is starting cloudy and threatening to bring more showers, so the moods of the duo have yet to be determined. I've got a bit of work to do and some fractals to find. Until the next FOTD appears, take care, and retain your enthusiasm. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Mantis_Cases { ; time=0:10:55.81--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.45558038289711040/+0.654666421634426\ 80/7.187779e+009/1/32.5/-7.89103793002315923e-006 params=-1/0.2/2/3/0/0 float=y maxiter=1200 inside=fmod proximity=0.1375 periodicity=10 colors=0000Rr0Nr0Kr3HrUKz6Hr0HH0H00000H00D00D00D0A\ DARDRkAhzAyzAzzAzzAzz6zz3zz0zz0zz0zz0zz0zz0zz0zz0u\ z0rz0kz0hz0dy0Yu0Ur0Nn0Kk0Dh0Ak000000K00kH0za0zu0z\ z0zz0zu0zn0zh0zR0zAHz0Yz0nz0zz0zz0zz0zz0zz0zz6zzRz\ zkzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzyzzuzz\ rzzkzzhzydzyazyYzyYzyUzuUzuRzuRzuNzrNzrKzrz0zKzraz\ dnzRzzDzh0zK0z00z00z00z00z00z00z00z00z30z60zA0zD0z\ K0zN0zR0zY0za0yd0uh0na0kY0hR0dN0aK0YD0UA0R66N0DK0N\ H0UD0aA0k60r30y00z00z00z00z00z00z00z03z0Az0Dz0Kz0N\ z0Uz0Yz0az0hz0kz0rz0uz0uz0yz0zz0zz0zz3zzAzzDzzHzzK\ zzNzzRzzYzzazzdzzhzzkyznvzrrzrnzugzu_yuVnyTdyURz0H\ v06s00m03d06U0DH0H63K0DR0RU0dY0nd0zh0zk0zy00aDKKAA\ U00X00_00b00e00h00k00m03o03r06t0Pv3Uw0Zx0cy0hz0myR\ rzzzkzynzuryruzzzzzzzzzzzzyzzxzzwzzuzzszzqzzozzmzz\ kzzizzgzzezzczzazz_zzXzzUzzDzz0zz0zz0zz0zu0zn0yr0u\ r0rr0nr0kr0hr0dr0ar0Yr0Ur } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 05-08-03 (Fractal Wilderness [5])
by Jim Muth 06 Aug '03

06 Aug '03

FOTD -- August 05, 2003 (Rating 5) Fractal visionaries and enthusiasts: Sometimes I like to ponder questions that would never be considered by a sensible person. Of course, this is no handicap, because I have never claimed to be, nor do I make an effort to be, a completely sensible person. (I find such individuals a bit boring.) And even if I tried my best to be sensible, we would need total agreement on what constitutes sensible thought. (For example, is it sensible to believe in precognition when one has personally and unambiguously experienced it?) My current ponderings are somewhat more sensible than experiencing the future before it happens. I am pondering the Mandelbrot set. Is the set an objective thing, a subjective thing, or something in between, as ghosts are supposed to be? Would the Mandelbrot set exist if the universe were empty of intelligent life? And as far as that goes, did it exist before the 20th century? The answers, if such things as answers exist, depend on abstractions such as the much-debated nature of reality. We could state that the M-set (or at least the potential for the M-set) always existed, but the set itself was not discovered (or was it created?) until the latter part of the 20th century. We can also debate whether today's image is a real fractal, since it has no dividing line that separates trapped points from points that tend to infinity. In fact, it has no escaping points. The points, which are all trapped, are colored by the bof61 inside fill according to which iteration comes closest to the origin. The result is curious, but too chaotic to hold long-term interest. Today's image will be the last in the present series of Mystic2 images. Like the previous images in this series, it is filled with many potential proto-themes, but none of them are sufficiently developed, giving an effect of untamed Fractal Wilderness, which in fact is what I named it. Studying the image, I see many spots that promise interesting zooms. Some of these spots may indeed hold images worthy of being declared FOTD's. Others likely lead to fractal dead ends. This tendency is probably why the formula never became a favorite of mine, as the MandelbrotMix4 formula did. As a result of the disorganization in today's image, I can rate it no higher than a 5 -- an average effort. But the render time of 4 minutes is fast enough to make seeing the average scene reasonably convenient. And as always, the pre-rendered image is available on the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The on and off showers continued into the afternoon Monday here at Fractal Central, spoiling the cats' day. The sun appeared by 3pm and raised the temperature to 84F 29C, but by then the duo were already sulking. Luckily, the tuna treat made things right. Today is again starting showery, so I had best have more tuna ready. The day's work load is average. But the next FOTD, which will appear in 24 hours, will be far from average. Until then, take care, and go ahead and be silly. Fractals are fun, and is the world not little more than a cosmic joke? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Wilderness { ; time=0:04:23.48--SF5 on a p200 reset=2002 type=formula formulafile=jim.frm formulaname=Mystic2 function=cotan passes=1 center-mag=-0.06074811025606387/-0.993573573575838\ 00/1425.244/1/-25/1.08651629360245749e-011 params=3.4/6/-9/3.8/6.1/-2.4 float=y maxiter=95 inside=bof61 logmap=yes periodicity=0 colors=000mfWqqQrpZsogtnpumxmkueirYgpQemIcjAbhJU`S\ QT`QLRHDcI5cTBobHnlNnvTiwYewaawefwbkq_piXuaUyVRj8w\ iAuiBtiCriDqiEoiFncOiZWeUdaPlYKtULuSMvRNvQOwOPwNQw\ LRwKSwJTwHUwGVwEWwDXwCYwAZw9_w7`w6aw5dwAfwFhvKkrPm\ oUolZrhctehvbmx_qvZptYprXpqWpoVpmUpkTpjSphRpfQpeQp\ PJpcPpaOp_NpZMpXLpVKpTJpSIpQHpOGpAahB_iCYjDXjEVkFU\ kGSlHRlIPmJNnKMnLKoMJoNHpwhltfmrdmobmm`njZnhXneVnc\ To`RoZPoWNoULpRJpPHpxwNruSmnWgg_b`dXUhSNlDPWFN`HLd\ JJhLHlBKoEJpGIpJHpLGpHw_It`IraIobJmcJjdJheKefKcgKa\ hLZiLXjLUkMSlMPmMNnNKoNIpwCOuDQsDRrDSpDToDVmDWlEXj\ EYiEZgE`fEadEbbFcaFd_FfZFgXFhWFiUGjTGlRGmQGnOGo8hg\ 9fhAehBciBbiCajD_jDZjEXkFWkGVlGTlHSmIRmIPmJOnKMnLL\ oLKoMIpNHpD`8FWHHSQJOZLKg7pE9lIBhMCdQEaUFYYHUaJReK\ NiMJmGwWHuXHsYHqZIo_Im`IkaJibJgcJedKceKafK_gLYhLWi\ LUjMSkMQlMOmNMnNKoNIp8JCAIGBIKDIOEHRFHVHHZIHbJGeLG\ iMGmtqprnpplpnjplhpjfphdp } frm:Mystic2 {; Jim Muth a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), k=real(p3), f=imag(p3), g=pixel, z=(pixel)^a+(b*(pixel))^c: z=(fn1(z)+(d*(g)))^k+(f*(cos(g))) g=sqr(g), LastSqr <= 100 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 06-08-03 (Spots and Spotlets [5])
by Jim Muth 06 Aug '03

06 Aug '03

FOTD -- August 06, 2003 (Rating 5) Fractal visionaries and enthusiasts: At the end of yesterday's discussion I stated that today's image would be a much better one. Actually, today's image is another perfectly average 5-rated one. I apologize for any bitter disappointment. The parent fractal of today's image was created by adding 0.018 part of Z^3 to Z^2, then adding 1/C instead of straight C, and increasing the bailout radius to 40000. It is a tiny Mandeloid, barely visible at the center of the default screen, shaped like a classic M-set with a greatly amplified negative stem. Instead of being a mere stick, the stem has broken apart into a new open area shaped much like a Julia set. But this area is not a Julia set, because it has Mandeloid buds and midgets on its border. One of the valleys holds today's scene. When studying the image for a name, I noticed the multitude of red-orange spots, and decided to name the image "Spots and Spotlets". The image is a pleasant one to view, especially on a video-tube monitor in subdued light, even though it rates only mediocre. Perhaps the image's greatest drawback is the 21 minutes required to render it from the attached parameter file. But that draw- back can be avoided by downloading the finished GIF image from Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The version of Fractint used by Scott on his site has been recently having trouble correctly rendering the images created with the 'Mystic2' formula. However, today's image returns to the 'MandelbrotMix4' formula, which has always worked properly, so Scott's site will have the correct image. A heavy thunder-shower at noon totally spoiled the cats' day Monday here at Fractal Central. When the sun appeared at 1pm, the yard was a puddle of mud and the holly trees were dripping, making it unfit for the delicate paws and ears of the dynamic duo, who spent the afternoon sulking on the porch. At least the temperature of 81F 27C was within their comfort zone. This morning is actually starting sunny, but more heavy rain fell during the night, and even more rain is forecast for this afternoon. Will things dry out in time for the duo to have a pleasant day? Find out in 24 hours, when the next FOTD will appear. Until then, take care, and pray for the rain to stop. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Spots_and_Spotlets { ; time=0:21:35.86--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.02416004980605908/+0.000316771873493\ 02/4.86578e+012/1/142.503194220881852/-0.009630602\ 08333854639 params=1/2/0.018/3/-0.9/40000 float=y maxiter=1600 inside=bof61 logmap=207 periodicity=10 colors=000MH`PHcRHgTHkWHoYHs_HvVMjQRZLWNJYOI_PH`QG\ bRFcREeSDfTBhUAiV9kV8lW7nX6oY5qZ4rZ7kW9eUCZSETQGRR\ IPRKNRMLROKRQIRSGRUERWCRXBRZAU_9X`8_a7bb6ec6g`AdZD\ bXH`VKYTOWRRUPVSNYPLaNJdLHhJFkGDoEBrC9uAAqBBmCCiDD\ eDEbEFZFGVFHRGINHJKIKGILCJM8KM5KR4JV4I_4Hc3Gh3Fl3E\ p3Dq2Bq2Aq29q28q27q26q25q24q23q22k95eG8_MAUTDOZGIe\ ICkL6rO0xQ4tO8qNBmMFjKJfJMcIOaKQ_MSYOUWQVUSXSUZQV`\ OXaMZcK`eIbgGdhEekA`n7Xq3Tt0Ps1Us1Zs1cs1hq2co3Zn4V\ l5QzcLz_HzWCzC7wD3sC2oB2kB2gA2cA2c92b91b91b91a91a9\ 1a91ZD6XHAVLFTPJRSOPWSN_XLc`JfdLefMegNehOeiPejRelS\ emTdnUdoVdpXdrYdsZdt_du`dvY`uVYuSVtPRtMOsJUsHYsgcn\ kgdndVqVMnXQlZUi`Ygbaddebfi_hmYjqWkt_lkcmcfnW`kUWi\ TRgSMdRGaPBZO6WN1TM5UO8UPCWRFYSJ`UMbVPdXTfYWh__j`b\ kbflcimelnfhoadoX`oTXpOTpJPpFLqAHq5Eq1FmBFiLFiVGkd\ GmnGowEqqCtkBwe9z_8zV6zP4zJ3zD1z70z24z48z5Bz7Fz8Jz\ AMzBQzDUzEXzG`zHdzJgzKKzX } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] FOTD irregularities & Jim Muth's Mystic2 formula
by Jim Muth 05 Aug '03

05 Aug '03

At 08:38 AM 8/5/03 -0500, Scott Boyd wrote: >Hi all, > >I was looking at Jim's .par files for the last four days to try to see why two >out of the four days, the FOTD did not generate properly on my Linux >computer. The only difference I see, is that the days it didn't generate >correctly, Jim used the 'cos' function. (Aug. 2 & Aug. 4) Strangely enough, >the 'cosxx' function that Jim used Aug. 3rd, did work correctly. And this is >the function that Jim says has an error in it! (The Aug. 1 .par file >generated correctly, but Jim used the 'atanh' function that day.) > >So it's possible that the 'cos' function is broke in Xfractint.... I doubt that this is so. If it were, none of the Mystic2 images would generate correctly. A 'cos' function is hard-coded into the fifth line of the formula. Jim M.

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FOTD irregularities & Jim Muth's Mystic2 formula
by Scott D. Boyd 05 Aug '03

05 Aug '03

Hi all, I was looking at Jim's .par files for the last four days to try to see why two out of the four days, the FOTD did not generate properly on my Linux computer. The only difference I see, is that the days it didn't generate correctly, Jim used the 'cos' function. (Aug. 2 & Aug. 4) Strangely enough, the 'cosxx' function that Jim used Aug. 3rd, did work correctly. And this is the function that Jim says has an error in it! (The Aug. 1 .par file generated correctly, but Jim used the 'atanh' function that day.) So it's possible that the 'cos' function is broke in Xfractint.... Scott Boyd -- sdboyd56(a)swbell.net http://sdboyd.dyndns.org --------------------------------------- No Microsoft or other proprietary products were used in the creation of this email.

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Re: [Fractint] Sucess
by nick.grasso＠hrads.com 04 Aug '03

04 Aug '03

Andrew Coppin wrote: >>>For several months I have been utterly unable to sent messages to this list... I have now discovered the cause of this devistating problem: I typed the address wrong in my address book. (Even that is not beyond doubt - there was a single letter missing. It may simply be that I have a malfunctioning keyboard!)<<< Welcome back Andrew, but you (or your keyboard) also dropped a single letter from 'success' ;o) Sorry, I couldn't resist that. Nick

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FOTD 04-08-03 (Cosine-Square [6])
by Jim Muth 04 Aug '03

04 Aug '03

FOTD -- August 04, 2003 (Rating 6) Fractal visionaries and enthusiasts: A number of years ago, a local auto dealer ran a series of ads proclaiming that nobody has better cars and nobody sells them for less. The ads worked great until a second auto dealer started calling himself Mr. Nobody. and took advantage of the first dealer's advertising. The clever second dealer won the day by making something of nothing. Today's image, which was created by the Mystic2 formula, consists entirely of blank inside space, which in traditional fractal rendering is nothing. But that nothing has been turned into something by the bof61 inside fill. Like that clever auto dealer, (and true mystics), I have turned nothing into something. I named the image "Cosine-Square" simply because those two functions are used in its creation. It is an unusually complex image for one that consists only of inside stuff. The 4-way symmetry almost gives the impression that a Mandelbrot midget lies at the center. But don't bother looking. At a slightly deeper level, the apparent 4-8-16-way symmetry breaks down into an awkward figure with 13 lobes, and then the entire image goes flat blank. Considering the image's assets and faults, I decided that a rating of 6 would be best for it. Its chief asset is the render time, which is only a bit over one minute. One of its faults is the color palette, which uses only a few of the 256 available GIF colors, and gives a rather muddy overall effect. As always, those who choose not to render may pick up the finished GIF image at one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Sunday turned questionable in a hurry. The temperature reached only 83F 28C, but just after noon a series of thunder-showers moved in. The rain was not unusually heavy, but it persisted until sunset, and was enough to keep the fractal cats confined to the indoors, sulking about their confinement and skittish about the prolonged rumbling. The evening treat of tuna eased their nerves and disappointment. Today is starting even worse than Sunday. It's raining already. As a result, I expect another sulky cat day. Between showers, I'll accomplish a few other tasks and find a few fractals, one of which will appear as the next FOTD. Until 24 hours from now, take care, and don't get caught in a square cosine. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Cosine-Square { ; time=0:01:20.53--SF5 on a p200 reset=2002 type=formula formulafile=jim.frm formulaname=Mystic2 function=cos passes=1 center-mag=0/0/8.226655 params=-6.3/9.2/-3.4/-1.4\ /-7.1/6.2 float=y maxiter=95 inside=bof61 logmap=yes periodicity=10 colors=000UoroMGgaZ7F5HSLRU`iAzfLwdWuafrzzzXcmcmkw\ clcpzcvBJNBSbW7KXHWcAAjChrKkqSnpMX_Tgh_3icrGbqQaqZ\ `qgSlZVndYpjIvfooUgpeklmeooVSvXZtYdsZkq84iSvJVtVYr\ eLYjTgmsY8ldNeka3Lir`2meFhiScmd8kSMnda`AfsHMULTe`m\ WhfflwBmqMnkXoegpr4PhTbv0ZcknOPRUccdkZangFhcadJQ8z\ VVu5nNLpaPguTksXnq60sEErLRqTdpXUmZeo7Iaus8mrNfqapa\ LkeTgi`cmhx6NqIVkUaeeiU0zXRuXZ9YeOZkbl_KfdQciZamgY\ m7ZoU7ZwHetRkrvnIpoRjp_dqhB5eKMiSamDuILsUTreXmSZod\ IGPOTZUegO4fRHiUTkXenmRRfdcUYMXgahRIYMoZUpZap_ipq`\ vTq7hd459488XMVf_wk_tnSW6WfUTUuOmDRnNUoXXpfNWgRajU\ flXlnV9xXLvYWtZfr7_FFdPMhYTmgG_3NeKUk`oAiiPldcnmlC\ DWJJP2FREBTQ8VaDcfIlkei8SbFEXMOZRX_Wfa`oberUitMmvE\ q_VcDjQJmTPpVVsY_u_t8Yz_wsdulhsemqFBcQXjhADIJYNSbR\ `gWilawD`tXohtikrdnqje6ghIdkUanesV0aOE`bYG38LGKQTV\ VeeNdWRhaUkfXnk_yD_vR_scnq`iqfdqkzrMs_bndfihidmmYE\ rZSq_dpm9ZhOdcbj9hyGkvNmt } frm:Mystic2 {; Jim Muth a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), k=real(p3), f=imag(p3), g=pixel, z=(pixel)^a+(b*(pixel))^c: z=(fn1(z)+(d*(g)))^k+(f*(cos(g))) g=sqr(g), LastSqr <= 100 } END 20.0 PAR-FORMULA FILE==================================

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Sucess
by Andrew Coppin 03 Aug '03

03 Aug '03

Hi folks. For several months I have been utterly unable to sent messages to this list... I have now discovered the cause of this devistating problem: I typed the address wrong in my address book. (Even that is not beyond doubt - there was a single letter missing. It may simply be that I have a malfunctioning keyboard!) But anyway... I'm back! Yay!! I've just been doing some stuff with the good old cubic function f(z) = z^3 - 3(a^2)z + b. This formula has (IIRC) several critical points, but all bar 2 of them are always within the basin of attraction to infinity. (Corrections, anyone?) The two that (sometimes) aren't are +A and -A. (If I'm not mistaken, 0 is NOT critical for this mapping...) Now, the cubic Mandelbrot is defined as being the set of points (A, B) for which for orbits of Z[0] = +A *and* Z[0] = -A remain bounded. (Compare the classic quadratic Mandelbrot: this is the set of all C such that Z[0] = 0 remains bounded.) Thus, the set M+ is defined as the set of (A, B) for which Z[0] = +A remains bounded, and M- is defined as the set of (A, B) for which Z[0] = -A remains bounded. (I have a feeling the two sets are mirror images or something... not entirely sure.) Then the M set itself is simply the intersection of M- and M+. (Try telling that to fractint!!!) I've got a number of formulas that attempt to draw the cubic M, but none of them seem to work entirely properly. They do, however, draw some rather fabulouse images! Of course, having to navigate a 4-dimensional M set that is really the intersection of the mirror-image M+ and M- sets (which, therefore, are also 4-D) is somewhat confusing to say the least! But the results are well worth it... Out of interest, I would rather like to know 1) if the statements I've made thus far are actually correct, 2) what the "generalised form" for a 4th order polynomial looks like... Hey - keep fractalling ;-) Thanks. Andrew. PS. I've heard it said that z^3 - 3(a^2)z + b is more complex than needed, and z^3 + az + b will work. My reason for using the former is that it draws a much nicer image. (Oh, and finding the critical points is easier ;-)

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FOTD 03-08-03 (Fractal Explosion [7])
by Jim Muth 03 Aug '03

03 Aug '03

FOTD -- August 03, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal image comes on with a bang. Or at least it appears to. It is another of those 'anything can happen' images produced by my little-used 'Mystic2' formula. Curiously enough, in today's image, the function that produces the best picture is the function with an error in it -- the 'cosxx' function. Since the image consists entirely of 'inside' material, an active inside fill is needed to reveal the details. Today's image uses the 'bof61' inside fill, though several other fills work almost as well. When I saw the explosive nature of the image, I immediately named it "Fractal Explosion". I rather like the image, so I rated it a 7. The render time of 4 minutes can be avoided by downloading the completed GIF file from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> But when downloading, be cautious. I have seen a report that the version of Fractint that Scott is using might draw incorrect images with the 'Mystic2' formula, which creates images that consist entirely of inside fill. If so, this is an unusual situation. Scott's images are almost always correct. Saturday was warm and muggy enough. The temperature reached 86F 30C, but it did not rain, and the cats had an enjoyable several hours in the yard. Today is starting exactly the same, so there is no reason to expect anything other than happy cats. For me, it's a lazy day. I think I'll simply read some thought- provoking articles in the magazines piled on the shelf, and see if I can provoke some thoughts. Later, I'll turn to fractals. Until next time, which will be in 24 hours, take care, and think deep thoughts. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Explosion { ; time=0:04:27.60--SF5 on a P200 reset=2002 type=formula formulafile=jim.frm formulaname=Mystic2 function=cosxx passes=1 center-mag=+0.00401393777775/-0.9968332050329/347.\ 2512 params=1.1/3.6/2.6/-3.1/-0.6/-0.4 float=y maxiter=100 inside=bof61 logmap=yes periodicity=10 colors=000DEABC8000NqTMnRLlQKjPJhOJeNR7MVRLQMJGXIF\ VHETGDRFDOECMDBKBAIAAF99D88B7796ObuSZtWVq`RndNkhJh\ lFeWouXqpYrkZse_t``uVavQekPi`OlQOaZNSgMIpMJqRKqVLq\ ZMrcNrgOrkOroQpmSnlUlkVmgWmcXm_YmWZmS_mOWjSThVQfZN\ daKadH_hEYkBWnAgbAsRAzGIuIPkJWaLbSM`QVZOcXMlVKuUIu\ zwurvqjvkcueWuZOtTHtNLnTOiZSdcVZiZUnaPtdKuaZd_lLYi\ KWfJUcIS`HQZFOWEMTDKQCINBGLAEI9CF87FIAC7896zTmxQhq\ OcjLZcJUYGPREKKBFD9ApuudhhUWWIJIDu9Cn8Bh8Aa7AW79Q6\ 8J67D5RlsOfkL`dIVYFPQCJJ9DCsugnocij_deW_`SVWOQRKLM\ GGHCBC8veirben_bjX_fVXbSUZPRVNNRKKNHHJFEFCBB98GeVE\ _QDUMBOIAID8C9jaSg_QeYPcWOaVMZTLXRKVPJTOHRMGOKFMJD\ KHCIFBFDADC8BA7986V_rUYoTXmSWkRViQTgPSeORcNQaMP_LN\ YKMWJLUIKRHJPGHNFGLEFJDEHCDFBBDAAB999887z`uyZqvXnr\ VkoThkSehQbdO_aMXYLTVJQRHNOFKKEHHCEDABA88Vq9Pe8JU7\ DI6VzHRpFNgDJZBFP9BG7nwgkteiqcgoael_cjYagW_eVYbTW`\ RUYPRWNPTLNRJLOIJMGHJEFHC } frm:Mystic2 {; Jim Muth a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), k=real(p3), f=imag(p3), g=pixel, z=(pixel)^a+(b*(pixel))^c: z=(fn1(z)+(d*(g)))^k+(f*(cos(g))) g=sqr(g), LastSqr <= 100 } END 20.0 PAR-FORMULA FILE==================================

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Re: Correction! etc.
by JackOTradez 03 Aug '03

03 Aug '03

Whomever may be affected: In last post I mentioned Russ Walsmith was making an error in his PAR file posts. Wrong! The error is mine! Russ - there is nothing wrong. Don't change anything! I confused a couple things myself and typed before I thought about it. Sorry ... <sg> As for Golden Ratio - anyone who has downloaded / used any of my programs (like the Fractint Animators) might notice that they open up in a window with the Golden Ratio. Actually, noone has noticed it yet. It is the ratio of adjacent Fibonacci numbers as the sequence is taken to infinity. Or, as the Ancients knew, it simply looks cool. The rectangle is not "too fat" or "too long" etc., it looks "Just Right". The Nautibrot4 animation is posted on my web site now (shortened version); the full viddie is over 400 MEG! The Cornucopia animation is almost done - it is way cool, the best of them yet. JoTz

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Re: [Fractint] Re: L'Escargot
by Russell Walsmith 02 Aug '03

02 Aug '03

-- --------- Original Message --------- DATE: Thu, 31 Jul 2003 14:07:21 From: "JackOTradez" <JackOTradez(a)email.msn.com> To: <fractint(a)mailman.xmission.com> Cc: > >BTW, I have just animated the L'Escargot (Nautibrot4) over 3000 frames at >1024x768, set to the tune "Green Onions", by Booker-T & MG's (anyone >remember that one?). In-f'n-credible! Yeah, that's a cool tune. Green Onions and L'Escargot... sounds savory, I gotta check it out. Let me know what I can do to expedite acquiring a copy. Thanx. > >Russ - you are not posting your files correctly. Those (like me) who know >the rite way can fix it, but others may have a problem, and will not see >your fantastic images. > >In the PAR, there is a line like "formulafile=next.frm". It is wrong. >Instead of "next" you should have the name of the specific formula, in this >case "Nautibrot4". Ok, I'll try it, but I think it's maybe more complicated than that. E.g., the guys who post a lot of pars (J.M., L.S., A.N. ...) use all sorts of filename assignments, and I gathered from that that it's arbitrary. What might have gone wrong is that I changed the assignment AFTER saving the par; as I now recall from earlier experience, that's a no-no. > >These images are incredible - how do you find these things??? Hey, I'm glad you like them. These formulas are so rich that finding compelling images is no problem. In fact, it's probably more difficult to find parameter values that DON'T make nice graphics. For example, consider the par below (which I will also repost as per your suggestion); ---------------------------StartParfile--------------------------- La_Tropicana { ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=dcls4.frm formulaname=Nautibrot6 function=ident passes=3 center-mag=0.0996911/0.234681/1.103753 params=1.618033989/1.618033989/1/0 float=y maxiter=200 colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0W } -----------------------------EndParfile--------------------------- This is about as basic as it gets, save that p1 is complex with the phi constant in both the real and imag values... So there's lots of bang for the buck in this par, and it takes off from there. Since at this point it's all new, images essentially find themselves in this context. The larger question then is, "How do I find the formulas?" Well, they find themselves too. It all started years ago when I was trying to figure out to play 5-string banjo... I was pretty agressive sometimes in pestering the accomplished pickers for the logic behind the long cascades of notes that seemed to spill effortlessly from their instruments. Musicians, btw, were a subset of a greater artistic community that included writers, painters, sculptors and etc., and hell, I wasn't proud; I'd pick anyone's brain if I thought it would afford me some insights into the creative process. And it was all very maddening, because the more accomplished the artist, the more likely they were to tell me, "Logic? I don't need no stinkin' logic, man..." It took me a while to recognize the limits of logical processes, but once I did, I was able to also perceive the value of balancing the mind with the intuition. Ever since, Virtually everything becomes progressively easier as I attend to that focus, and I expect that even posting par files will be a piece of cake pretty soon... > >I will now try to animate Cornucopia; me and ((( 5^(1/2)) + 1) / 2 ) >"Golden Ratio" go back a long way . . .. ... ..... ........ I'd like to hear sometime about the contexts in which you've explored the GR. As for Cornucopia, that looks like a tough'n to animate, but good luck! I'm not now as infatuated with that image as I was a few days ago... I've just discovered a new one, and I think I'm in love... ---------------------------StartParfile--------------------------- Las_Conchitas { ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=dcls4.frm formulaname=Nautibroid function=conj/cabs passes=3 center-mag=-0.899316/0.230079/0.4862158 params=5/1/3/1/-1/0 float=y maxiter=1000 colors=653xwulHICXNwuIDCTjCRATl653xwulHICXNwuIDCTjCRATlccc<238>c\ cc } -----------------------------EndParfile--------------------------- Isn't she pretty? I am enthralled with the graceful lines of this image and the exquisite necklace of shells from whence is taken the name. The formula 'Nautibroid' incorporates the 'Dynamic Coefficients' concept into nautibrot6. (This idea is explored more extensively at http://fibonacci-arrays.com) ---------------------------StartFrmfile--------------------------- frm:Nautibroid {; by Russ Walsmith z = 0, c = pixel, k=1, j=p3: j=p3*j k=p1*fn1(k)*j z = z^k + c j=p3*j k=p2*fn2(k)*j z = z^k + c z < 1000 } frm:Nautibrot6 {; by Russ Walsmith z = 0, c = pixel, k=1, j=p2: j=p2*j k=p1*fn1(k)*j z = z^k + c z < 1000 } -----------------------------EndFrmfile--------------------------- Still Amazed, Russell Alternate parfile versions: ---------------------------StartParfile--------------------------- La_Tropicana { ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=Nautibrot6.frm formulaname=Nautibrot6 function=ident passes=3 center-mag=0.0996911/0.234681/1.103753 params=1.618033989/1.618033989/1/0 float=y maxiter=200 colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0W } Las_Conchitas { ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=Nautibroid.frm formulaname=Nautibroid function=conj/cabs passes=3 center-mag=-0.899316/0.230079/0.4862158 params=5/1/3/1/-1/0 float=y maxiter=1000 colors=653xwulHICXNwuIDCTjCRATl653xwulHICXNwuIDCTjCRATlccc<238>c\ cc } -----------------------------EndParfile---------------------------

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Re: FOTD 02-08-03 (Neo-Fractal [5])
by Paul N. Lee 02 Aug '03

02 Aug '03

Lee H. Skinner wrote: > > The FOTD pictured on S.D. Boyd's website > today is very different from the image > generated by Jim's par! > Yes, I noticed that as well. I do not remember this happening since the first few weeks when Scott first started hosting Jim's FOTD. Do not recall what caused the problem then, and how it was resolved, but maybe I can look back on some old postings to see if there was an explanation. Sincerely, P.N.L. ------------------------------------------------- http://home.att.net/~Paul.N.Lee/PNL_Fractals.html http://www.Nahee.com/Fractals/

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Shear Amazement
by Russell Walsmith 02 Aug '03

02 Aug '03

In a recent perusal of Bradley Beacham's "AN INTRODUCTION TO THE FRACTINT FORMULA PARSER" (the FRMTUTOR.TXT file in Fractint) I came across the 'fibo-A' formula. This .frm introduces Fibonacci-type recursions to the Mset formula, and it inspired me to investigate this idea further. I thus came up with the 'Fibrot' formula, presented (in a generalized version) below: ------------------------------parfile----------------------------- Nautiloid { ; July 23, '03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=next.frm formulaname=Fibrot1 passes=3 center-mag=-6.42033/2.44459/0.04984424 params=-5/-1/1/0 float=y maxiter=300 colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0W } ------------------------------frmfile----------------------------- frm:Fibrot1 { z = 0, c = pixel, j=0, k=1: a = p2*j + p1*k j = k k = a z = z^k + c z < 1000 } -------------------------------endpar----------------------------- Soon thereafter, Jack O'TradeZ used this .frm to render the 'Mosaic' viddie now playing at: http://www.sonic.net/~jot/ufvp.html Both the 'stills' and the video demonstrate that complex parameter values in 'Fibrot' induce a shear factor along the real axis that warps circular shapes into nautiloids. It occurred to me that a variant formula might give more insight into this effect, and this led to a series of 'Nautibrot' formulas, some of which are presented below: ------------------------------parfile----------------------------- Nautilii { ; July 23, '03 ; Version 2002 Patchlevel 5 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=next.frm formulaname=Nautibrot2 passes=3 center-mag=-6.84262/0/0.04783259 params=5/1 float=y maxiter=300 colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0W } ------------------------------frmfile----------------------------- frm:Nautibrot2 { z = 0, c = pixel, k=1, j=-1: j=j*(-1) k=p1*k*j z = z^k + c z < 1000 } -------------------------------endpar----------------------------- Another variant introduces i-axis shear: ------------------------------parfile----------------------------- ShearMadness { ; July 23, '03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=next.frm formulaname=Nautibrot3 passes=3 center-mag=0/0/0.6666667 params=-1/1 float=y maxiter=300 colors=00000j0j0jj0j00j0j0jjkkkkrkdmwW000W0WW000WW0W0WWFNF<4>rNF\ zNFFVF<4>rVFzVFFbF<4>rbFzbFFjF<4>rjFzjFFrF<4>rrFzrFFzF<4>rzFzzFF\ FN<4>rFNzFNFNN<4>rNNzNNFVN<4>rVNzVNFbN<4>rbNzbNFjN<4>rjNzjNFrN<4\ >rrNzrNFzN<4>rzNzzNFFV<4>rFVzFVFNV<4>rNVzNVFVV<4>rVVzVVFbV<4>rbV\ zbVFjV<4>rjVzjVFrV<4>rrVzrVFzV<4>rzVzzVFFb<4>rFbzFbFNb<4>rNbzNbF\ Vb<4>rVbzVbFbb<4>rbbzbbFjb<4>rjbzjbFrb<4>rrbzrbFzb<4>rzbzzbFFj<4\ >rFjzFjFNj<4>rNjzNjFVj<4>rVjzVjFbj<4>rbjzbjFjj<4>rjjzjjFrj<4>rrj\ zywccdWWWz000z0zz000zz0z0zzzzz } ------------------------------frmfile----------------------------- frm:Nautibrot3 { z = 0, c = pixel, k=1: k=p1*conj(k) z = z^k + c z < 1000 } -------------------------------endpar----------------------------- Finally, in these "Not-a-Brot" calculations, 2 + 3 = 4: ------------------------------parfile----------------------------- L'escagot { ; July 23, '03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=next.frm formulaname=Nautibrot4 passes=3 center-mag=-0.58651/0.281617/0.6666667 params=4/1 float=y maxiter=300 colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0W } ------------------------------frmfile----------------------------- frm:Nautibrot4 { z = 0, c = pixel, k=1, j=-1: j=j*(-1) k=p1*conj(k)*j z = z^k + c z < 1000 } -------------------------------endpar----------------------------- A generalized nautibrot is: ------------------------------frmfile----------------------------- Nautibrot5 { z = 0, c = pixel, k=p2: k=p1*fn1(k) z = z^k + c z < 1000 } -------------------------------endpar----------------------------- That's about the gist of it... I suspect that these efforts haven't been all for 'naut', for there are perhaps many other patterns that will emerge in this context. I hope that list members will find something of interest here, but hey, it got me all in a state of sheer amazement and that's the bottom line... Ciao, Russell (PS: I think I have this .par file thing down, but if they fail to render correctly,lemme know.)

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FOTD 02-08-03 (Neo-Fractal [5])
by Jim Muth 02 Aug '03

02 Aug '03

FOTD -- August 02, 2003 (Rating 5) Fractal visionaries and enthusiasts: This discussion will have to be brief. We have unexpected work waiting to be done here at F.C. and a customer who wants his job before he brings in the material. Some fractals simply defy logic. Today's image, which was created by the 'Mystic2' formula, is one of these. It has more themes than a Mexican TV-novella, any one of which could have served as the basis for a fractal. (Any theme, that is. I don't think I've ever seen a fractal based on a soap-opera.) There is so much that could be discussed in today's image that discussion is nearly useless. The only thing to do is to study the image, sit back and mutter, "Oh my!". The image is so mixed up in fact that it almost appears to have been constructed by hand from many different fractals. The image certainly is something new, which is why I named it "Neo-Fractal". I think that the mixture of unrelated themes actually goes too far, and this holds the rating to an average 5. The render time of 4 minutes can be avoided by downloading the finished image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Friday was cloudy and exceptionally humid here at Fractal Central. The temperature of 81F 27C was fair enough, but a two-hour period of light rain in the afternoon spoiled the cats' day in the yard. A treat of tuna was needed to restore their good moods. Today promises to be more of the same. I expect the same response from the dynamic duo. In 24 hours I shall return with the next fractal. Until then, take care, and when searching for truth, be sure you recognize it when you find it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Neo-Fractal { ; time=0:04:20.02--SF5 on a P200 reset=2002 type=formula formulafile=jim.frm formulaname=Mystic2 function=cos passes=1 center-mag=-0.001194479/-0.968563902/222.9189/1/22\ .5/8.944234242e-014 params=4.18/3.94/3.99/-4.27/2.\ 37/-2.66 float=y maxiter=95 inside=bof61 logmap=yes periodicity=0 colors=000mNWoSTqWPs_LudIwhEylBpeAhZ\ AXRuSKAKGALIAYUASPAVSAXVAWYEW_IWbMWdQVgUViXVk`VndU\ phUslUupUwsVrtVmtWhtWctXZtXVtXQuYLuYGuZBuZ6uZ2uY7s\ YCqXHoXMnXRlWVjW_hWdgVieVncVrbZq_apYdoWgoTjnRnmPqm\ MtlKwkIzkGwfHtbHqYHnUIkPIhLIeGJbCJ_8J`8Ib8Hc8He8Gf\ 8Fg8FdBHbDJ`FLZIMXKOVMQTPSRRTPTVNWXLYZJ__HbaFdcDfe\ BhfAdcA``AYZAUWAQT9NR9JO9FL9CJ98G95E88H7BK7DN6GP6J\ S5LV5OX4Q_3Tb3Wd2Yg2`j1cl1eo0hr0jt1kq1kn1ll1li2mf2\ md2na2n_3oX3oU3pS3pP4qM4qK4rH4rF6nH7jI9fJAbKC_LDWM\ FSNGOOIKPJHQLDRM9SO5TP2ULJQHZMM_JQ`GRZGSYGTXGTVGUU\ GVTGWRGWQGXPGYNGZMGZLG_JG`IGaHGaGGbHHcHIdIJdIKeJLf\ JMfKNgKOhKPhLQiLRjMSjMTkNUlNVlNWhQYeS_aUaZXbWZdS`f\ PbgMeiIgkFimCln8np5pr2rs3no3kl3hi3ef3bc3Z`3WY3TV3Q\ S3NP3JM3GJ3DG3AD37A347768A89D99GBAJDANEBQGBTHCWJDZ\ LDbMEeOEhQFkRFnTGqUGmVIjVJgVKcVL`VMYVNVVORVPOVQLVR\ IVSNTVSQYXO`aLceJfQA_B1TI7UODVUIV_OWkJ_ } frm:Mystic2 {; Jim Muth a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), k=real(p3), f=imag(p3), g=pixel, z=(pixel)^a+(b*(pixel))^c: z=(fn1(z)+(d*(g)))^k+(f*(cos(g))) g=sqr(g), LastSqr <= 100 } END 20.0 PAR-FORMULA FILE==================================

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Re: L'Escargot
by JackOTradez 02 Aug '03

02 Aug '03

Yea - I figured the typo. It does look like a snail. Those weird people across the pond actually eat the disgusting things - raw! BTW, I have just animated the L'Escargot (Nautibrot4) over 3000 frames at 1024x768, set to the tune "Green Onions", by Booker-T & MG's (anyone remember that one?). In-f'n-credible! Russ - you are not posting your files correctly. Those (like me) who know the rite way can fix it, but others may have a problem, and will not see your fantastic images. In the PAR, there is a line like "formulafile=next.frm". It is wrong. Instead of "next" you should have the name of the specific formula, in this case "Nautibrot4". These images are incredible - how do you find these things??? I will now try to animate Cornucopia; me and ((( 5^(1/2)) + 1) / 2 ) "Golden Ratio" go back a long way . . .. ... ..... ........ Stay Amazed, JoTz

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FOTD 01-08-03 (The Dance of Life [7])
by Jim Muth 01 Aug '03

01 Aug '03

FOTD -- August 01, 2003 (Rating 7) Fractal visionaries and enthusiasts: Fractals are mysterious, and I enjoy mysteries. At the present moment, I have on the shelf beside my desk the July issues of both 'Fate' magazine and 'Skeptical Inquirer' magazine, two publications that are the antithesis of each other. This is notable because, by coincidence, the covers of both magazines feature the same thing -- pictures of supposed lake monsters. And the corresponding articles both report that, though sightings of such monsters are often claimed, the monsters have never been found. I have read both magazines for many years. Both concern them- selves with the paranormal, 'Fate' assuming that the paranormal likely does exist, 'Skeptical Inquirer' pointing out that so- called paranormal happenings can almost always be explained by natural means. Both magazines also have flaws. The anecdotal reports and the articles in 'Fate' often cannot be verified, and 'Skeptical Inquirer' has an agenda to uphold -- the promotion of the materialistic philosophies. IMO, the magazines do a nearly equal job in the promotion of their views, and reading one cancels the effect of reading the other. As a result, the mysteries are still there. They still remain unsolved, and therefore fascinating. The formula that created today's image is named Mystic2. This formula also is a kind of mystery. It draws only empty circles, but when this emptiness is given definition by an active inside fill, it takes on almost infinite variety. Keeping with the theme of the mysterious, I have named today's image "The Dance of Life". The emergence of life is still one of the greatest mysteries of science. The rating of a 7 might be a bit excessive, but I'm satisfied with it. The location of today's image is at the very southern extremity of the parent empty circle, the edge of which is visible near the bottom of the frame. The image vaguely resembles an alien landscape, though what might be going on in the sky is anybody's guess. To see the mysterious activity, it is necessary to run the attached parameter file for 2 minutes. The activity may also be seen by downloading the completed GIF file from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The cloudy weather here at Fractal Central on Thursday did not deter the dynamic cats. The temperature reached only 81F 27C, but it remained dry, and that was all the duo needed to give them an enjoyable afternoon in the yard. Today is again starting cloudy and cool. It remains to be seen if the rain will hold off. Regardless of the weather, I will return in 24 hours with the next amazing fractal. To be amazed, check back here at that time. Until then, take care, and see you in the mysterious Fractal Land. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Dance_of_Life { ; time=0:02:49.06--SF5 on a p200 reset=2002 type=formula formulafile=jim.frm formulaname=Mystic2 function=atanh passes=1 center-mag=+0.00112210713120296/-0.999985554468765\ 70/64027.68 params=-1.6/2.08/1.27/1.58/-2.52/0.23 float=y maxiter=95 inside=bof61 periodicity=10 colors=000qW4nYBl_Hi`NgbTecZQj2ESE2AP5BN8CMADLDDJ0\ 00IFHLGFNGEQHDSIBVJAXJ9VM8TR8SS7QX7O_6Nb6Lc5Kf5Ii4\ Gl4Fo3Dr3Cu3PvC`wKmwSyy_xpYxmWwhUxbSuYRwSPtNNwHLqC\ KtHMqLNnQPkUQhYRebTbfU_jVXimUimRimOimLhmIhmFhmChm9\ ga6gb3gc0gc3fb6fa9f`Cf_FfZHfYKfXNfWQfVTfUVfTYfS`fR\ cfQffPhfPi_VjU`kOelIkmCqn6vl8tjArhCpfEndFlbHj`Jh_L\ fYNdWObUQ`SSZQUXOWVNXUMYXLY_LYbOZ`Q_ZS`XVaVXbTZcSa\ dQceOefMhgKjhJliHojFqkDslBumAlhHccOVZUMU`DQfETjFWn\ FYrJVsNSsQPsUMsXJt`GtcDtgAtj8tlErnKppQnrVlt`jvfhxl\ fzqesk`leXe_T_VPTPLMJHGEDojJlfIjcIg_HeXHbUH`QGYNGW\ JFTGFRDFe_DtvCrWWq6on5mk4lh4je3ib3g_2fX2dU1cR1bW9f\ _HjcPmbQnaQo`Qp_QpZQqYRrXRsXRsWRtVRuUSvTSvSSwRSxRS\ xPWvNZuLatKdsIgrGjpFmoDpnBsmAvlKUVT1DR2EP2EN2EM2EK\ 3FI3FG3FF3FD4GB4G94G84G65H45H25H15Hd4RmTZvqewhbw``\ xSZxKXzLXqO_iRaaTcUWeMZgE`iLVkSPmZKoeEql8sr3tr9brF\ MrL5iQF`VOS_XJdeZHcZEbhNL } frm:Mystic2 {; Jim Muth a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), k=real(p3), f=imag(p3), g=pixel, z=(pixel)^a+(b*(pixel))^c: z=(fn1(z)+(d*(g)))^k+(f*(cos(g))) g=sqr(g), LastSqr <= 100 } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] Shear Amazement
by Russell Walsmith 31 Jul '03

31 Jul '03

The nautibrot6 formula in the .frm file below is evidently of sufficient generality to generate all of the various nautibrot(x) images that were previously posted. So the first thing I want to do is get L'Escargot entered right. ------------------------------parfile----------------------------- L'Escargot { ; July 31, '03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=next.par formulaname=nautibrot6 function=conj passes=b center-mag=-0.83436/0.180208/0.611899 params=4/1/-1/0 float=y colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0W } -------------------------------endpar----------------------------- This next image REALLY blows my mind... It's astonishing to me that patterns so strongly associated with the Fibonacci sequence and the golden mean should become utterly predominant, evidently, in a milieu where Feigenbaum's constant usually reigns. Has the former ratio actually entirely supplanted the latter, or do they exert a sort of shared influence, with the fractal perhaps somehow splitting differences between the two? Whatever the case, I about lost track of my time spent cycling diverse color maps through this rather elegant object; the one chosen here is from a recent Lee Skinner par. ------------------------------parfile----------------------------- Cornucopia { ; July 31, '03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=next.frm formulaname=nautibrot6 function=exp passes=t center-mag=-0.86844/0.124809/0.611899 params=3/-2/-1/0 float=y colors=000000zr1zz1zzC<2>zzz<2>nsjQdrLdtblU<3>Mb8<3>LQ8KM8KJ8<2>\ I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz3<\ 4>zj4zg4zc4<3>zS5zP5zL6zI6zE6wE6tD6<6>vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5\ _<3>f5Ma5IW4E<2>_4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0f\ z0gy0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6\ Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvlqvotvsww<2>zzz<3>rw\ zovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<3>SCCXCAaB9<3>uA2zA0xA0<12>SA1QA\ 1NA1<3>D92<6>UXAW`BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi_5f\ c0ce7_jFRoNIzb0zj0 } -------------------------------endpar----------------------------- The 'Radiance' image shows that a surprising symmetry is present when a purely imaginary value is assigned to the parameter p1. ------------------------------parfile----------------------------- Radiance { ; July 31, '03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=next.frm formulaname=nautibrot6 function=conj passes=b center-mag=-2.39562/0.928852/0.2594452 params=0/4/-1/0 float=y colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0W } -------------------------------endpar----------------------------- This next is a bit whimsical: Save the image as a gif, open it in a small window and drag it about the screen; with the right settings (e.g., 'Show window contents while dragging') and a decent graphics card, you should see some very cool moire effects. This works for most of the others as well. ------------------------------parfile----------------------------- L'tl_L'es { ; July 31, '03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=next.par formulaname=nautibrot6 function=conj passes=b center-mag=-0.83436/0.180208/0.611899 params=2/1/-1/0 float=y colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0W } -------------------------------endpar----------------------------- I could not for some reason get this next one to render exactly in the #6 formula, so nautibrot4 is included. (Truly the 'naughtybrots' is what they should be called, since they don't behave at all like proper fractals.) So, OK, go ahead, color-cycle the Hypnoid... I dare ya! (but don't press "Enter" if you do...) ------------------------------parfile----------------------------- Hypnoid { ; July 31, '03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=next.par formulaname=nautibrot4 passes=3 center-mag=+0.98456120553466000/+0.17373634109460730/163.4115 params=4/1 float=y maxiter=1000 inside=0 outside=fmod colors=000CTT<3>8QR7PQ6PP5OP4NO<2>3OO3OP4OP<133>MvpMvpMvq<2>MwqM\ wqNvp<99>cWc } -------------------------------endpar----------------------------- ------------------------------frmfile----------------------------- frm:Nautibrot6 {;by Russ Walsmith z = 0, c = pixel, k=1, j=p2: j=j*(p2) k=p1*fn1(k)*j z = z^k + c z < 1000 } frm:Nautibrot4 { z = 0, c = pixel, k=1, j=-1: j=j*(-1) k=p1*conj(k)*j z = z^k + c z < 1000 } -------------------------------endfrms----------------------------

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FOTD 31-07-03 (Harlequin [5])
by Jim Muth 31 Jul '03

31 Jul '03

FOTD -- July 31, 2003 (Rating 5) Fractal visionaries and enthusiasts: The brilliant colors in today's image, which was produced by adding Z to Z^4, remind me of a harlequin's costume. I therefore named the image "Harlequin". The parent fractal is a Mandeloid with a lot of extra activity around the East Valley area. Today's scene is located deep in this activity. The image consists of a mixture of inside and outside material. The outside parts have been rendered in the traditional equal- iteration method; the inside however has been decorated with the 'fmod' inside fill. Since I had only limited time to find and color the image, I could not rate it at anything above average, though I did manage to give it a rating of a perfectly average 5. The render time of 10 minutes can be bypassed by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Wednesday featured a 2-1/2 hour power failure in the afternoon that put me behind in the work and kept it from being a perfect day. A man down the next block who thought he was a professional tree-trimmer turned out to be a total amateur. The partly sunny skies and temperature of 79F 26C were very comfortable for the hottest time of year. The cats were happy enough, since with the power off they had lots of supervised time in the yard. Today is starting cloudy and cool, with rain threatening. It remains to be seen how the rest of the day will go, but the best way I know to have a perfect day would be to find a perfect fractal. Will tomorrow be the day? Most likely not, but check to see how close it comes. Until then, take care, and as far as I know, the reality of fractals has never been determined. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Harlequin { ; time=0:10:34.39--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.04541673116753506/+0.062824240203421\ 91/1.00776e+012/1/-97.498923096774547/0.0005200442\ 07848097129 params=1/1/1/4/0/0 float=y maxiter=1000 inside=fmod symmetry=none periodicity=10 colors=000RaXTaYVaZXa`Zaa`abbacdadfaehagjahlainajp\ akqalsgetlZvrSwwLxzFvyHuvJtsLsqNrnPpkRohTnfVmcXl`Z\ kZ`iWbhTdgQffOheLjcIlbFnaDp`Ar_7tZ5uY7tX8rW9pWAnVB\ lUCjUDhTEgSGeSHcRIaQJ_QKYPLWONUOOTQQSSSRTUQVVPXWOY\ XN_YMaZLb`KdbJfdIgfHihGkjFlkEnmDpoCqpBsrAut9vu8xw7\ zy6zz6zr8yj9xbBwWCvOEuGFt9GuAHuBIuCJvCJvDKvELwELwF\ MwGNxGNxHOxIPyIPyJQyKRzKRzLSzMTzMTzNUzOVzOVxPWvQXs\ QYqRZnSZlS_iT`gUaeUacVcaWe`XgZYiXYkWZmU_oS`qRasPau\ NbwMcyKdzJdzRqtTpuUovWnvXmwYmw_lx`kxbjycjzGbRGSSGT\ TGUUGWVGVWGXXGXYGYZHY_IZ`J_aK`bL`cM_dNYgNWjNUlORoO\ PqOMtPJwPHyPEzPCzRFzTHyVJwWMtYOr_QpaSnbVkdXifZgg`e\ icbke`mgZnjWplUrnStpQusNwuLywJzyHyxIxxIwxJvxJuxKtw\ KswLrwLqwMpwMpwMovNnvNmvOlvOkvPjuPiuQhuQguRfuRfuRb\ sVZqYVoaSmdRlfQkhPjjOhmMgoLfqKesJcvIbxHazG`zJbxMct\ OdpRflTghWhdYia`kYclUemQhoMjpImqEorBr_CtHDdHOQHZBH\ hsKNnJPjJRfJSbIUZIWVIXRHZ } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 30-07-03 (Deep-Sea Scene [7])
by Jim Muth 30 Jul '03

30 Jul '03

FOTD -- July 30, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today might be the first time I have ever used the 'epsiloncross' inside fill in a FOTD fractal. This fill colors the points according to how close they come to the X and Y axes in their orbits. For some reason, this inside fill spreads into the outside areas as the proximity is raised. It has done this in today's image, where it has produced the fish-bone effect that inspired the name. The parent fractal was produced by taking plain Z and adding 1/20 part of Z^10 to it, then adding C. This parent resembles a M-set rotated 200 degrees, with a convergence of 9 valleys where its single East Valley should be. Today's scene is located in the fourth valley counting clockwise. While studying the image in search of a name, I at first could think of nothing. Then something in the picture reminded me of an underwater scene, and the 'epsiloncross' features started to look like fish skeletons. I named the image "Deep-Sea Scene" though it more closely resembles things that might be seen in shallow water. The rating of 7 is perhaps a bit high, but this is one of the few times, if not the only time I have used the 'epsiloncross' inside fill in a FOTD image, and that fact alone makes the image unique, or at least nearly so. The render time of 3 minutes is un-irritatingly short -- a real bargain for the time spent. Downloading the completed GIF image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> is equally efficient, assuming that the internet is not having one of its occasional bad days. Tuesday featured perfect weather and perfect cats here at Fractal Central. The blue skies were decorated with only a few angel-hair cirrus and cottonpuff cumulus clouds. The winds were light from the north, and the temperature reached only 81F 27C, at a time of year when near 90F 32C is normal. The cats spent several hours in the yard, meditating on whatever topic cats meditate on. Today's weather should be perfect once again. I expect the cats will be perfect also. Expect no surprises (other than the fractal) when the next FOTD appears in 24 hours. Until then, take care, and seek tranquility. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Deep-Sea_Scene { ; time=0:03:09.11--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.14224236936/-0.01022168581/35770.29/\ 1/-22.5/-2.3535721982437e-011 params=1/1/0.05/10/0\ /0 float=y maxiter=500 inside=epsiloncross proximity=0.0225 logmap=39 periodicity=10 colors=000K03zSCzNLsHUpMakJfgGo`DsYAvW8wTByQSzNXzK\ QzHNsEQhBUV8_PMjS_yVZqUZiUZaTZYTZWSZYSYWRYSRYSQYRP\ YRPXQOXQOXPNXPNXOMXOMZPP`QSbRUdSXmTZhUajVclWfnXhpY\ krYmF`3EV3CP2BJ2FM3IP4MR5PU6SW7WZ8Za9bcAefBhhC_l8R\ o5Jr2Kn8KkDLgILdNL`SMYYMUbNRgNNzNKqMJoLJmKIkJIiIHg\ HHeGGcFGaEF_DFYCEWBEUADS9DQ9DOCGLFJJILHLOFORDRTBUW\ 9WY7OdEHjL9qS2wZ3n_4f`5Z`6Ra6Ja6M`6P`6R`6U_6W_6Z_6\ `_6cZ6eZ6hZ6jZ6mY6oY6rY6tYAsWErUHqTLpROpPSoOVnMZmK\ amJXqVSueOxpGp_HqcIrfJsiJtlKupLvsMwvc4hKc1La5M`8N_\ BOYEPXHQWKRVNSTRTSUURXVQ_WObXNeYMhYLk_Qk`Vka_kbdkd\ ikenkfskgxkeyidzgczebzdazb`z`_zZZzYYzWXzUWzSVzRUzP\ TzNSzMWzSZzXazaRzJGz1NzCUzM`zWgzenzotzyuzvuzsuzpvz\ mvzkvzhwzewzbwz`xzYxzVxzSxzQizWWz`IzeMzdPzcTzbWza_\ z`bz_czddzidzmezrezvjzonziszbwzXvzYuzYtzYszZszZrzZ\ qzZpz_oz_oz_nz`mz`lz`lz`mzYnzWnzTozRpzOpzMqzJrzHrz\ EszCtz9KzSIzNGzJEzF000Az7 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 29-07-03 (Totally Ravishing [6])
by Jim Muth 29 Jul '03

29 Jul '03

FOTD -- July 29, 2003 (Rating 6) Fractal visionaries and enthusiasts: I was told that today's image is totally ravishing, which according to my dictionary means that viewing it causes indescribable delight. Well, I'm not fully convinced that my delight in viewing the image is indescribable, but the image is at least far enough above average to earn it a 6, so that's how I rated it. The name "Totally Ravishing" is an intentional exaggeration. The image is an evaporated one, with the inside activity made visible by the bof61 inside fill. The parent fractal in its un-evaporated form appears as a multi-bayed Mandeloid, its filaments leading to terminating rings. Today's scene is located in a cut-off feature close to a zig-zagging filament that runs down the center of a prominent valley. Although the resulting image was called 'totally ravishing', to me it appears to lack something. The colors, though brilliant, are not pure. A certain muddiness spoils things. And the elements have too many disquieting sharp points. The rating of 6 appears justified. The 5-minute render time is brief enough, but those with more pressing things to finish may save a few minutes by downloading the finished image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The rain held off until after 3pm Monday here at Fractal Central, giving the cat duo time enough in the yard to make them happy before things got wet. The temperature of 82F 28C was no problem. Today is starting cool and sunny -- just the conditions to keep the duo happy. And the work shelf is piled just high enough to keep me busy until 2pm or so -- the conditions that keep me happy. It actually looks like a good day might be coming. Another FOTD is also coming, and it will appear in 24 hours. Until then, take care, and be of good cheer. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Totally_Ravishing { ; time=0:05:29.44--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.26428153306016700/+1.055502538839018\ 00/254505.2/1/70/8.99066862625197416e-010 params=7/-1.3/0.7/-13/0/1e+100 float=y maxiter=500 inside=bof61 outside=tdis periodicity=10 colors=000o`b6um0zo0zqzzzzsuz`XzVbxPgmLk`GqPCuE6z2\ 2zA0zH0zP0zX0zd0zk0zs0zz0zgCzRbz8zz0zz0zm0oP0X00G0\ 08CE0iL0`T0T`0Je0Cm02u00z00q00gC6`PER`NHmXAxd0zm0z\ u6zvHzvVzvezxszxzzxovz`mzNdz8Tz0Jz0A_08z06g06e04V2\ 4L8EHENGJXEPdCVmA`v8ez6VxNJsdAmu0gz0dz0so0zC0z00x0\ 0k40JH00X00i00e4Ed8VbGXVLXNTZGZZAb`8e`6gb6kb4od2qd\ 2ue0ve0zd0z`0zZ0zX0z`0zd0zg0zk0vGGV8bXAbXCdZEdZEe`\ GebHgbJgdLgdLieNigPkgRkiRmiTmkVokXomZooZqo`qqbsqds\ qdssduueuuguvivvkvxkxxmxzozzqzzqzzszzuzzvzzxzzxzzz\ zzzzzzzz82zC6zEAzHCzJGzNJzPLzRPzVTzXVz`Zzb`zddzggz\ iizmmzoqzqszuvzvzzzzzzzzZ0z`2z`4zb6zb8zdAzdCzdEzeG\ zeGzgHzgJzgLziNziPzkRzkTzkTzmVzmXzoZzo`zobzqdzqezs\ gzsgzsizukzumzvozvqzvszxuzxuzzvzzxzzzzzzzzzzzzzzzG\ 0zH2zJ4zL6zN8zPAzRCzTEzVGzVHzXJzZLz`NzbPzdRzeTzgVz\ iXziZzk`zmbzodzqezsgzuizvkzxmzxozzqzzszzuzzvzzxzzz\ zzzzG00L00R46VAE`HJdNRiTX } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 28-07-03 (The Quantum [7])
by Jim Muth 29 Jul '03

29 Jul '03

FOTD -- July 28, 2003 (Rating 7) Fractal visionaries and enthusiasts: For today's FOTD we return to a formula that has not been used for over a year. This formula, which draws nothing but empty circles, is named 'Mystic2'. I gave it this name because it is a near miracle that worthwhile fractals can come from it. But miracles sometimes do happen, and when we look at today's image, we are seeing a miracle in progress. The empty interiors produced by the Mystic2 formula are filled with unseen activity, which can be made visible by active inside fills such as the 'bof61' used in today's image. So today's image consists of nothing but inside material. There is nothing new in this -- the 'evaporated' images that I some- times post consist of all-inside material also. But at least, those 'evaporated' images were once real inside-outside images. Today's image never was real. It has no connection at all to fractal reality, whatever that is. Today's image, with its vaguely-defined, all-seeing eye, is all fuzziness, all uncertainty. It has no sharp edges. It reminds me of existence at the quantum level, where nothing is certain but uncertainty itself, and from some of the things I read, even the uncertainty is uncertain. I see probability clouds, where electrons might or might not exist at any point, and I see atoms, which are more real, but still far from the type of reality we think of when we observe the 'real' world around us. Thinking of how our oh-so-solid real world is built of less-than- solid blocks, I named today's image "The Quantum". I then rated it at an above-average 7. Of course, I am uncertain that this is the most correct rating. The 'Mystic2' formula creates far more than the simple fuzziness seen in today's image. It can create images indistinguishable from the normal equal-iteration-band pictures. It can create images like nothing seen before. I have no idea why I use it so rarely. Maybe I'll devote a month to 'Mystic2' images in the not-too-distant future. Today's image renders in 9 minutes, which is a bit slow. The download from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> will speed things quite a bit. Sunday was hot enough here at Fractal Central to satisfy the most ardent fan of high temperatures. The high temperature of 92F 33C set no record, but combined with the high humidity, it kept the dynamic fractal cats confined to the air conditioned indoors. They did venture outside briefly just before sunset, but the sound of a can of tuna being opened brought them scur- rying inside to eat. Today brings a threat of much rain and unhappy cats, so we'll have to see how it goes, and we'll need to have more tuna ready for distribution. Until next FOTD, which will appear as usual in 24 hours, take care, and live in your entire self. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Quantum { ; time=0:09:05.52--SF5 on a P200 reset=2002 type=formula formulafile=jim.frm formulaname=Mystic2 function=ident passes=1 center-mag=0.0540916/0.744129/30.70416 params=1.6/1.4/-0.1/-1.1/-1.6/-0.4 float=y maxiter=255 inside=bof61 logmap=yes periodicity=10 colors=000LH6LI6LI6LI6LJ6LJ6LK6MK5MK5RhzML5cVUdWUe\ XUfYUf_Vg`VhaVibVidVjeWkfWlgWliWmjWnkXolkonXptXqpX\ zsYrrXqqXqqWppWppVooVooUnnUnnTmmTmmSllSkkRkkRjjQjj\ QioPiiPwhPhhOggOggNffNeeMeeMddLddLccKccKbbJbbJaaIa\ aI``H__H__GZZGZZGYYFYYFXXEXXEWWDWWDVVCUUCUUBTTBTTA\ SSASS9RR9RR8QQ8PR7QQ8QQ8RQ9RQ9SQASPATPBTPBTPCUPCUO\ DVODVOEWOEWOFWOFXNGXNGYNHYNHZNIZMI_MJ_MJ_MK`MK`LLa\ LLaLMbLMbLNbLNcKOcKOdKPdKPeKQeJQfJRfJRfJSgJSgIThIT\ hIUiIUiIViIVjHWjHWkHXkHXlHYlGYmGZmGZmG_nG_nF`oF`oF\ apFapFbpFbqEcqEcrEdrEdsEesDetDftDftDguDguChvChvCiw\ CiwCjwCoxClwCjuChtCfrCdqCapC_nCYmCWkCUjCSiCPgCNfCL\ dCJcCHbCFcDHcDIcDKdDLdDNdDOdDPeDReDSeDUeDVfDWfDYfD\ ZgD`gDagDbgDdhDehDghDhpHtlFnhDidBd`9ZX8UT6PP4JL2EH\ 0AI19I19I29I29I29I39I39I49I49I49I59I59J68J68J68J78\ J78J88J88J88J98J98JA8JA8KA7KB7KB7KC7KC7KC7KD7KD7KE\ 7KE7KE7KF7LF6LG6LG6LG6LH6 } frm:Mystic2 {; Jim Muth a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), k=real(p3), f=imag(p3), g=pixel, z=(pixel)^a+(b*(pixel))^c: z=(fn1(z)+(d*(g)))^k+(f*(cos(g))) g=sqr(g), LastSqr <= 100 } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] Shear Amazement
by Russell Walsmith 28 Jul '03

28 Jul '03

Among other typos, L'escagot is supposed to be l'escargot... -- >L'escagot { ; July 23, '03 > ; Version 2002 Patchlevel 5 > reset=2002 type=formula formulafile=next.frm > formulaname=Nautibrot4 passes=3 > center-mag=-0.58651/0.281617/0.6666667 params=4/1 float=y > maxiter=300 > colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ > zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ > 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ > zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ > zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ > 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ > zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ > zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ > 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ > zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ > zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ > 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ > zk0kW0W > } > >------------------------------frmfile----------------------------- > >frm:Nautibrot4 { > z = 0, c = pixel, k=1, j=-1: > j=j*(-1) > k=p1*conj(k)*j > z = z^k + c > z < 1000 } > >-------------------------------endpar-----------------------------

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[Fractint] Re: I knew I had seen this before: Striking resemblance ; )
by JackOTradez 28 Jul '03

28 Jul '03

Yes! A hyper-velocity bullet on a mission of destruction. http://www.rumble.org/trans/trans6-21.jpg Ya gotta love it! Now we in my turf here. BTW, the extended (3 minute) version of the "Mosaic" viddie is unbelievable. Doesn't even look like fractals - loox like a 1970's time warp throwback. (Anyone remember Gold Windowpane or Blue Blotter ?) It is too big to post on the site - only for CD. Now lemme see what I can do with Russ' new formulas . . .. ... ..... ........ Stay Amazed. JoTz

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FOTD 27-07-03 (Nothing in Sight [5])
by Jim Muth 27 Jul '03

27 Jul '03

FOTD -- July 27, 2003 (Rating 5) Fractal visionaries and enthusiasts: Today's fractal is a different kind of thing. It is so different in fact that I don't know what to call it. It is like nothing I have seen before, and this is why I named it "Nothing in Sight". I realize that this could raise the philosophical puzzle of whether nothing is actually something, but this is not really a puzzle at all. When a fish sees a gas bubble rising to the surface, it does not see an absence of water, it sees a real object that, assuming fish understand gravity, defies gravity. For that fish, nothing has literally become something. And is not a positron nothing more than the lack of a negative charge? In today's fractal, we are once again in the vicinity of the blazing rectangle of the past two FOTD's. But we have rotated a full 90 degrees from the Julia direction and are viewing the scene in the Rectangular direction, where imag(z) and imag(c) are displayed on the screen. The image has been rotated and unrotated, stretched and unstretched, skewed and unskewed so far that I have lost track of its undistorted appearance. Actually, the undistorted image is the distorted view, and the stretching, etc. is necessary to undistort it. The appearance of X-axis symmetry is illusory. A close inspection will reveal subtle differences. The image is more a curiosity than a work of art, and as such can be rated no higher than a rating of an average 5. (With all the average ratings I give my images, I would make a very poor salesperson.) The render time of 5 minutes is within reason. Downloading the completed image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> is also quite reasonable. A hot day Saturday brought out the laziness in the fractal cats. Of course, it takes very little to bring out laziness in old cats. When the temperature hit 90F 32C, they hit their beds, and stayed there most of the afternoon. They didn't get active until the sun was gone from the yard, when they took a short stroll to the holly thicket. Today is supposed to be even hotter, though to me it seems to be starting cooler. It remains to be seen how the duo will adjust. I'm going to adjust by doing as little as possible, except in the world of fractals that is. Until next FOTD, take care, and I do not believe that physical aliens from space are visiting earth, but why then does it concern me so much when I see others who do believe we are being visited? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Nothing_in_Sight { ; time=0:05:28.89--SF5 on a P200 reset=2002 type=formula formulafile=julibrot.frm formulaname=SliceJB-new passes=1 center-mag=-0.000\ 01046291457683/+0.02511627776549527/1353.851/0.065\ 63/89.9392475138482297/0.0607524861518090667 params=0.5/0.5/0/0.5/2.003/0/-1.7435/0/0.00019/0.0\ 7388 float=y maxiter=1000 inside=bof61 logmap=51 periodicity=10 colors=000GADIAFJAHKAJMALNANPAPQARSBTTBVUBXWBZXC`Z\ Cb_Cd`CfbChcDjeDlfDngDpiErjEtlEvmExnEzoGzpIzpKzqMz\ qOzrQzrSzsUzsWztYzt_wubtueqvhnvklwnjwqhytgywhzwhzw\ hzmczjfzgizdczaYzZTzWNzTHzQCyN6xK1wJ5uI9sHDqGHoFLm\ FOkESiDWgC_eBccBfaAj_9nY8rW7vU7yS9wQAuOBsMCqKDoKEm\ MFkOGjQHhSIfTJdVKbXL`ZMZ`NYbOWcPUeQSgRQiSOkTMlULhS\ MdQM`OMXMMTKMPIMLGMHEMDCM9AM59MF8MO7MX6Me6Mc7La8L`\ 9KZAKXBKWCJUDJTEJRFIPGIOIHMKHKMHJOGHQGGSGEUFCWFBYE\ 9_E7aE6cD4eD3gD6iE8kFBmGDnHGnIImJLlKNkLPjMSiNUhOXg\ PZfQaeRcdSecTd`SdYRdWQdTPcQOcONcLMcILcGKbHNaIP`JSZ\ KVYLXXM_WMaUNdTOgSPiRQlPRoOSqNTtLSwMTvMTvMTvMTvNTv\ NTvNTvNTvNUvOUvOUvOUvOUvPUvPUvPUvPVuRVuQVuUVuQVuXV\ uRVu_VuRWubWuRWueWuSWuhWuSWukYvSXunWuTVtqVtUUttTsU\ SswSsVRrzQrWPrzPqXOqzOqYQpzSpZUozWo_Yoz_n_anzcn`em\ zgmaimzklbmlzopaqnzslcukzwiezhzzfgzdzzcizazz`kzZzz\ YlzWzzUnzTzzRpzQzzODzfzza } frm:SliceJB-new {; by John R. H. Goering, July 1999 pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1), b=pi*imag(p1), g=pi*real(p2), d=pi*imag(p2), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+(p4), z=r+flip(s)+(p5): z=z^(p3)+c |z|<=9 } END 20.0 PAR-FORMULA FILE==================================

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RE: Four Dimensional Scene
by harrybissell 26 Jul '03

26 Jul '03

<delurk mode> its an 8 for sure. beautiful piece <relurk mode> H^) harry

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FOTD 26-07-03 (Blazing Rectangle-2 [5])
by Jim Muth 26 Jul '03

26 Jul '03

FOTD -- July 26, 2003 (Rating 5) Fractal visionaries and enthusiasts: In today's image we take another look at the rectangle that caught fire in yesterday's image. That rectangle, which is located in the Z^2.003+C Julia set with a C-value of -1.7435, at the Z-coordinates of 0.00019,0.07388 and at a magnitude of 100, is one of the most curious things I have yet discovered in the world of fractals. When viewed as a Julia set, it is as perfect a rectangle as one will find in any random fractal. But the slightest deviation from the Julia orientation has a devastating effect on it. A rotational deviation of as much as 1 degree totally destroys the perfection of the rectangular shape and produces a curvilinear quadrilateral such as we have in today's image. Changing the imaginary part of the C-value even the slightest distance from zero has an even more devastating effect. The entire rectangle rapidly falls apart into fractal debris and vanishes into the fractal ether. Since today's image is another sequel, I have named it "Blazing Rectangle-2". As an FOTD, it rates an average 5, but hey, the average FOTD is nothing to be sneezed at. And the render time of 5 minutes is fast enough to make the attached parameter file a near-joy to run. Those who prefer the acquisition of their fractals to be total ecstasy may download the completed GIF image file from one of the two FOTD web sites: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Friday, with its brilliant sun and temperature of 86F 30C, turned out to be one of those rare perfect summer days here at Fractal Central. The fractal cats were in one or their rare near-perfect moods as they passed the afternoon in the yard. My mood was a bit less than perfect as the work piled up faster than I could accomplish it. Today's weather is promising to be less than perfect, but still quite pleasant. If I can finish the modicum of work by noon, I'll have a pleasant enough day. And I'm certain to find an interesting fractal before the day ends. To see that interes- ting fractal, check back here in 24 hours. Until then, take care, and is truth a fractal? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ BlazingRectangle-2 { ; time=0:04:59.97--SF5 on a P200 reset=2002 type=formula formulafile=julibrot.frm formulaname=SliceJB-new passes=1 center-mag=+0.004\ 99268009490636/-0.00325779513771971/76.89922 params=0.5076/0.5037/0.49256/0.49876/2.003/0/-1.74\ 35/0/0.00019/0.07388 float=y maxiter=1000 inside=bof61 logmap=51 periodicity=10 colors=000GADIAFJAHKAJMALNANPAPQARSBTTBVUBXWBZXC`Z\ Cb_Cd`CfbChcDjeDlfDngDpiErjEtlEvmExnEzoGzpIzpKzqMz\ qOzrQzrSzsUzsWztYzt_wubtueqvhnvklwnjwqhytgywhzwhzw\ hzmczjfzgizdczaYzZTzWNzTHzQCyN6xK1wJ5uI9sHDqGHoFLm\ FOkESiDWgC_eBccBfaAj_9nY8rW7vU7yS9wQAuOBsMCqKDoKEm\ MFkOGjQHhSIfTJdVKbXL`ZMZ`NYbOWcPUeQSgRQiSOkTMlULhS\ MdQM`OMXMMTKMPIMLGMHEMDCM9AM59MF8MO7MX6Me6Mc7La8L`\ 9KZAKXBKWCJUDJTEJRFIPGIOIHMKHKMHJOGHQGGSGEUFCWFBYE\ 9_E7aE6cD4eD3gD6iE8kFBmGDnHGnIImJLlKNkLPjMSiNUhOXg\ PZfQaeRcdSecTd`SdYRdWQdTPcQOcONcLMcILcGKbHNaIP`JSZ\ KVYLXXM_WMaUNdTOgSPiRQlPRoOSqNTtLSwMTvMTvMTvMTvNTv\ NTvNTvNTvNUvOUvOUvOUvOUvPUvPUvPUvPVuRVuQVuUVuQVuXV\ uRVu_VuRWubWuRWueWuSWuhWuSWukYvSXunWuTVtqVtUUttTsU\ SswSsVRrzQrWPrzPqXOqzOqYQpzSpZUozWo_Yoz_n_anzcn`em\ zgmaimzklbmlzopaqnzslcukzwiezhzzfgzdzzcizazz`kzZzz\ YlzWzzUnzTzzRpzQzzODzfzza } frm:SliceJB-new {; by John R. H. Goering, July 1999 pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1), b=pi*imag(p1), g=pi*real(p2), d=pi*imag(p2), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+(p4), z=r+flip(s)+(p5): z=z^(p3)+c |z|<=9 } END 20.0 PAR-FORMULA FILE==================================

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Multifractal_7
by Albrecht.Niekamp＠t-online.de 26 Jul '03

26 Jul '03

Hi, the new multifractal edition now has 8 formulas to choose, a phoenix type is now available and a spider type. The maximum now has been reached concerning the structure of the formula and the possible amount of inputs. Another fundamental improvement is that the "warp-effect" now is used in two different ways: If reset is checked "z" is set to the basic value and the effect, if enabled, is applied to the input. If reset is not checked the effect, if enabled, is applied to "z" which generates a different image, of course. This means a whole lot of new possibilities and is especially useful in case of sensitive inputs such as Julia, Spider, Phoenix. So there are four different ways to control each in/out part of the image, with or without reset and with or without thw warp-effect, which by itself can be modified in many ways. Fractal greetings, Al --------------------------------start-frm---------------------- FRM:Multifractal_7 { ; Albrecht Niekamp 240703 ;p1 (spider)julia-seed ;real(p2) 5digits: frm-use: shape, outside, inside1, inside2, inside3 ; 0_off 1_secant/mand 2_bees/jul 3_m_mods/phoen 4_newt/spider +5_reset ; input2 : 2digits_many-mods 2digits_phoenix 2digits_spider ; 5digits_secondary frm use : 0_no 1_yes +5_warp ;imag(p2)(-) 2-4digits : quasinewton input (max 2000) ; 1digit : no many_mods multipl. 1_out 2_in1 3_in2 4_all ; 1digit : iter-reset 1_out 2_in1 3_in2 4_all ; input2 : 4digits(-)_mand/jul 2digits_secant 4digits_bees ;real(p3) many_mods bailout, bailout ;imag(p3) shape : factor (fn1), outside : border-in (5digits+fract) ;real(p4) outside : factor (fn2), border-out (5digits+fract) ;imag(p4) inside1 : maxiter1, 5digits_factor1 (fn2) ;real(p5) inside2 : maxiter2, 5digits_factor2 (fn3) ;imag(p5) inside3 : maxiter3, 5digits_factor3 (fn4) ;fn(1) is shared by many_mods, bees da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 d=trunc(dd/10000) t=d>5 dd=dd-d*10000 d=d-5*t d3=(d==2)+(d==4) d4=(d3==0) vb=(d==3)+(d==4) d=trunc(dd/1000) ex1=d>0 dd=dd-d*1000 rs1=d>5 d=d-5*rs1 v1m=(d==3) v1j=(d==4) dd1=(d==2)+(d==4) d=trunc(dd/100) ex2=d>0 dd=dd-d*100 rs2=d>5 d=d-5*rs2 v2m=(d==3) v2j=(d==4) dd2=(d==2)+(d==4) d=trunc(dd/10) ex3=d>0 dd=dd-d*10 rs3=d>5 d=d-5*rs3 v3m=(d==3) v3j=(d==4) dd3=(d==2)+(d==4) ex4=dd>0 rs4=dd>5 dd=dd-rs4*5 v4m=(dd==3) v4j=(dd==4) dd4=(dd==2)+(dd==4) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 ab=(d==2)+(d==7) da=da-d*10000 d=trunc(da/1000) w1=d>4 ab1=(d==2)+(d==7) da=da-d*1000 d=trunc(da/100) w2=d>4 ab2=(d==2)+(d==7) da=da-d*100 d=trunc(da/10) w3=d>4 ab3=(d==2)+(d==7) d=round(da-d*10) w4=d>4 ab4=(d==2)+(d==7) tt=ex0+ex1+ex2+ex3+ex4 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) d=round((d-dd)*10000000000) pp=trunc(dd/100)/10 dd=dd-1000*pp da=trunc(dd/10) so1=((da==1)+(da==4)==0) so2=((da==2)+(da==4)==0) so3=((da==3)+(da==4)==0) dd=dd-10*da ir1=(dd==1)+(dd==4) ir2=(dd==2)+(dd==4) ir3=(dd==3)+(dd==4) ; p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=real(p3) mb=trunc(d) ba=(d-mb)*100000 ; d=imag(p3) sfac=trunc(d) b1=(d-sfac)*100000 b0=b1/2 ; d=real(p4) ofac=trunc(d) b2=(d-ofac)*100000 ; d=imag(p4) mi1=trunc(d) fac1=(d-mi1)*100000 ; d=real(p5) mi2=trunc(d) fac2=(d-mi2)*100000 ; d=imag(p5) mi3=trunc(d) fac3=(d-mi3)*100000 ; mo=vb>ab mo1=v1m>ab1 mo2=v2m>ab2 mo3=v3m>ab3 mo4=v4m>ab4 ; sc=((ab+vb)==0) sc1=((ab1+v1m)==0) sc2=((ab2+v2m)==0) sc3=((ab3+v3m)==0) sc4=((ab4+v4m)==0) ; px=((ab+vb)==2) px1=((ab1+v1m)==2) px2=((ab2+v2m)==2) px3=((ab3+v3m)==2) px4=((ab4+v4m)==2) ; if (d4) z=0 if (vb) if (mo) c=0.4*log(sqr(pixel^mm)) else c=pixel z=pixel endif else c=pixel z=pixel*sc endif else c=p1 z=pixel endif t=0 u=d3 bo=z p=pp z0=p7 zold=(0.0,0.0) cb=p9 : If (tt) t=t+1 if ((ex0) && bo>b0) u=2*(fn1(t/sfac)) if (d4) z=z*u if (mo) c=0.4*log(sqr(pixel^mm)) ba=mb else c=pixel endif else z=pixel cb=p9*u c=p1*u p=pp*u endif ex0=0 tt=tt-1 elseif ((ex1) && bo>b1 && bo<b2) if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif rs=rs1 ab=ab1 if (dd1) if (rs) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif vb=v1j d3=1 else d3=0 if (rs) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v1m if (mo1) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir1) t=0 endif ex1=0 tt=tt-1 elseif ((ex2) && t>mi1) if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif rs=rs2 ab=ab2 if (dd2) if (rs) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif vb=v2j d3=1 else d3=0 if (rs) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v2m if (mo2) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir2) t=0 endif ex2=0 tt=tt-1 elseif ((ex3) && t>mi2) if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif ab=ab3 rs=rs3 if (dd3) if (rs) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif vb=v3j d3=1 else d3=0 if (rs) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) if (so3) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir3) t=0 endif ex3=0 tt=tt-1 elseif ((ex4) && t>mi3) if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif ab=ab4 rs=rs4 if (dd4) if (rs) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif vb=v4j d3=1 else d3=0 if (rs) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v4m if (mo4) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif ex4=0 tt=tt-1 endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Qusinewton Pusk s Istv n z2=p*z*z z=z-z1/z2 endif elseif (ab) zt=z*z+ph-0.5*zold ;Phoenix Mike Wareman zold=z z=zt else z2=fn1(z)+c ;Many_mods Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (d3) if (ab) z2=z*z ;Julia Pusk s Istv n z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) z2=z*z ;Mandel Pusk s Istv n z=z2*z2+p6*z2+c-p0 else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<=ba } -------------------------------------------start-par--------------------- downmix { ; inside spider-newton-phoenix ; Albrecht Niekamp July, 03 ; ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_7 function=cos/exp/exp/exp passes=t center-mag=0.453671/1.33227e-015/1.323725/1/-90/3.88578058618804789e-016 params=-0.02237006744590594/-0.07473982970671712/10498.32595010101/5000.\ 0608020602/2048.04084/384.0000045/384.00024/256.0076800000001/512.007680\ 0000001/768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200677<21>hiijkkkll<3>rss<21>HIIFGGEFF<3>677455344122000<25>0bo0d\ q0es<3>0kz<25>09C08A068<2>022000111<24>niQpjRrlS<3>ysX<25>BB7996775<3>00\ 0<24>n00p00r00<3>y00<25>B00900700<3>000<2>455 } spinewphoesec { ; Albrecht Niekamp July, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_7 function=cos/exp/exp/sin passes=t center-mag=-8.88178e-016/-8.88178e-016/1.041667/1/-90/3.8857805861880478\ 9e-016 params=-0.02237006744590594/-0.07473982970671712/40986.3259501001/5000.0\ 608020602/2048.04094/384.0000045/384.00024/256.00768/768.0076800000001/1\ 024.00768 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200677<21>hiijkkkll<3>rss<21>HIIFGGEFF<3>677455344122000<25>0bo0d\ q0es<3>0kz<25>09C08A068<2>022000111<24>niQpjRrlS<3>ysX<25>BB7996775<3>00\ 0<24>n00p00r00<3>y00<25>B00900700<3>000<2>455 } Secantflyer { ; Albrecht Niekamp July, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_7 function=cos/exp/exp/sin passes=t center-mag=0.312805/0/0.6666667 params=-0.02237006744590594/-0.07473982970671712/31997.32595010605/5000.\ 0608020602/2048.04094/384.0000045/384.00024/256.00768/768.0076800000001/\ 1024.00768 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=2000gt<22>09C08A068<2>022000111<24>niQpjRrlS<3>ysX<25>BB7996775<3\ >000<24>n00p00r00<3>y00<25>B00900700<3>000<2>455677899ABBBCC<18>hiijkkkl\ l<3>rss<21>HIIFGGEFF<3>677455344122000<25>0bo0dq0es<3>0kz0jx0hv } Double_image { ; Time 0.19.43.53 ; Albrecht Niekamp July, 03 ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_7 function=sin/cosxx/cos/sin passes=t center-mag=0.426332/6.66134e-016/1.344086/1/-90/-1.23373533611470521e-01\ 4 params=-0.02237006744590594/-0.07473982970671712/10482.64595310601/5040.\ 0608020602/82048.02048000001/384.0000045/384.00024/128.00768/184.00768/5\ 12.0076800000001 float=y maxiter=3072 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=2000bo<19>09C08A068<2>022000211<13>UQFWSGYTH<3>e`LgbMidN<3>qjRslS\ unT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<23\ >eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<4>\ 0dq } Layers { ; of the onion ; Albrecht Niekamp July, 03 ; Time 1.33.03.85 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_7 function=sin/cosxx/cos/sin passes=t center-mag=0.972387/-0.248155/26.88172/1/-90/-1.23373533611470521e-014 params=-0.02237006744590594/-0.07473982970671712/10482.64595110606/5040.\ 0608020602/82048.02048000001/384.0000045/384.00024/128.00768/184.00768/5\ 12.0076800000001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=yes periodicity=0 rseed=-2436 colors=2000bo<19>09C08A068<2>022000211<13>UQFWSGYTH<3>e`LgbMidN<3>qjRslS\ unT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<23\ >eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<4>\ 0dq } Hanging_gardens { ; of Semiramis ; Albrecht Niekamp July, 03 ; Time 0.48.12.55 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_7 function=sin/cosxx/cos/sin passes=t center-mag=+0.36133792768156270/-0.64229253619003070/116197.8/1/-90/3.88\ 578058618804789e-016 params=-0.02237006744590594/-0.07473982970671712/10482.64595110606/5040.\ 0608020602/82048.02048000001/384.0000045/384.00024/128.00768/184.00768/5\ 12.0076800000001 float=y maxiter=3072 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=2000JQ<12>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<13>UQFWSGYTH<3\ >e`LgbMidN<3>qjRslSunT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25\ >C00A00800<3>000<23>eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012<10\ >0IO } mm_meets_spider { ; Time 0.36.26.15 ; Albrecht Niekamp July, 03 ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_7 function=sin/cosxx/cos/sin passes=t center-mag=+0.36139649738980650/-0.64231765276418100/11619.78/1/-90/-1.2\ 3373533611470521e-014 params=-0.02237006744590594/-0.07473982970671712/10482.64595110656/5040.\ 0608020602/82048.02048000001/384.0000045/384.00024/128.00768/184.00768/5\ 12.0076800000001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200555<20>eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012<24>0b\ o0cq0es<3>0kz<25>09C08A068<2>022000211<13>UQFWSGYTH<3>e`LgbMidN<3>qjRslS\ unT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000222\ 444 } Ying&Yang { ; Time 0.19.14.27 ; Albrecht Niekamp July, 03 ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_7 function=sin/cosxx/cos/sin passes=t center-mag=+0.38684901922323730/-0.63969404719008790/37.1833/1/-90/-1.23\ 373533611470521e-014 params=-0.02237006744590594/-0.07473982970671712/10437.32595910656/5000.\ 0608020602/82048.02048000001/384.0000045/384.00024/128.00768/190.0076800\ 000001/384.0076800000001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200pppqqqsss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08\ A068<2>022000211<13>UQFWSGYTH<3>e`LgbMidN<3>qjRslSunT<2>zsX<25>CB7A96875\ <3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<23>eeegggiiijjjlllnnn } The_Brain { ; Time 0.02.53.45 ; Albrecht Niekamp July, 03 ; Shape Phoenix ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_7 function=sin/sin/exp/sin passes=t center-mag=0/0/0.6666667 params=-0.02237006744590594/-0.07473982970671712/32946.32595710155/5000.\ 0608020602/2048.04094/384.0001645/384.00048/128.00768/384.0076800000001/\ 512.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200033021000<4>984BA5DC6FE7HF8JH9<13>jeNlgOniPpjQrlRtnS<2>ysW<25>\ BB6995774553442220000<24>n00p00r00<3>y00<25>B00900700<3>000221<4>9A9BCBD\ EDFGFGHG<15>hihjkjklk<3>rsr<21>HIHFGFEFE<3>676454343121000<25>0bn0dp0er<\ 3>0ky<28>055 } ---------------------------------------------------------------------------- ----end-----------------------

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FOTD 25-07-03 (Blazing Rectangle [6])
by Jim Muth 25 Jul '03

25 Jul '03

FOTD -- July 25, 2003 (Rating 6) Fractal visionaries and enthusiasts: After discovering that the fourth spatial dimension was in my back pocket, I went searching. Maybe I searched in the wrong pair of pants, but I suspect that the extra dimension slipped off into hyperspace while I was not looking, and has escaped for good. What a disappointment -- having a visualization of the fourth dimension so close and then losing it. I guess I'll never see a hypersphere in the condition of double rotation, or a pseudosphere in its infinite entirety. Today's image appears to be rotating. It is a slightly enlarged and distorted view of a small part of yesterday's image, on which I have used a more flexible Fractint generating formula so that I would have more angles to examine. The angle of today's slice is once again very close to, but not exactly, the Julia direction. That slight rotation explains the "Blazing Rectangle" name. The feature in the center of today's image has a roughly rectangular shape, but it is not rectangular enough to justify the word 'rectangle'. Where then is the rectangle? The rectangle is actually very close, but it is hiding. To see the near-perfect rectangle, change both parts of the p1 and the p2 parameters to exactly 0.5 and re-render the image. It takes only a minute or two. Now the rectangle is visible, revealed in all its near-perfect glory at the center of the frame. Actually, I easily might have used the pure Julia version of today's scene as the FOTD of the day, but the distorted version has more action, and the pure Julia version doesn't appear to be blazing. I rated the image at a 6, which equals a bit above average. After searching carefully, I could find little that has not been seen before. (Originality in doing old things rates high with me.) The render time of 2 minutes is unusually short, due mostly to the low magnitude of only 44. Those who download their FOTD images will find today's posted as usual to Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> A perfect day on Thursday, with a temperature of 81F 27C, produced perfect cats. Tippy was a bit too perfect when he viciously attacked my ankle like he used to do long ago when he was still a kitten and wanted to be played with. To see if he was feeling playful, I took the feather on a string from its shelf, where it had rested untouched for several years, and to my surprise, Tippy actually leaped around chasing it. Thomas watched the activity with interest, but weighing over 17 pounds, declined to participate. At the end of the day, both Tippy and Thomas were exhausted, and needed no additional treat before settling down for the night. Today looks like it will be a repeat. I'll make a full report in tomorrow's FOTD, which will appear in 24 or so hours. Until then, take care, and what do you call someone who wastes his time talking about stuff he does not believe in? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Blazing_Rectangle { ; time=0:02:19.51--SF5 on a P200 reset=2002 type=formula formulafile=julibrot.frm formulaname=SliceJB-new center-mag=-0.0021281/-0.1\ 47743/44.02148/1/140/5.12714870559705105e-014 params=0.5013/0.5007/0.5016/0.5012/2.003/0/-1.7435\ /0/0.00019/0.07388 float=y maxiter=2000 passes=1 inside=bof61 logmap=34 periodicity=10 colors=000zFzzFzzFzyFzxFzvFzuFzsFzrFzpFzoFzmFzlFzj\ FziFzgFzdFzaFz_FyXFxTFvQFuOFsLFrIFpFFoCFm9Fl6Fi3Ff\ 0Fc0F`0FY0FV0FS0DP0CM4AJC9IJDCQJMXOGcSCjY6ra1yf0zj\ 0zl0zm0zm0zo0zp0yp0xr0xs0vs0vu0uv0uv0sx0ry0ry0pz0p\ z1oz1mz3mz3lz3lz4jz4jz4gz9dxDasG_oLXjOTfSQaVOY_MTa\ JOfGJjDFmAAr76u41y10z00z00z10z40z70zA0xD0uG0rJ0oM0\ lP0iS1fV3cY3``4Yc6Vf7Si9PlAMoALpGPrMSsSVuY_vcaxidy\ ogzulzzozzrzzuuzrjzoazlSziIzf9xc0v`0u_0xa9ycJzdSzf\ `zgjziszjzzlyzjvziuygrvgosfmpdjmdgjcfgacd````_Y_XV\ YTSYSPXPMVMJTLGTIDSFAQD7QTJLgVGxfCzp7zsCzuFyvJuxMp\ yQmzTizXdz``zcXzgSzjPzmOzoMzpLzrJxsIuuGsvFpxDmyCjz\ Agz9dz7cz6`z4Yz3Vz1Sz0Qz3Oz4Mz6Jz9IvAGsCDpDClG9iI7\ fJ6aL3_O1XP0SQ0PS0MQ0OP0OM0PGSOCPJ9MG6JD1G90D60A30\ 7004001003334CA6MJ7VS9d_AmgCxoCzmAzl9uj7oi6ig4cf4_\ d3Tc1Oa0I`0C`07_1F_3M_4S_7_xoMzmPzjQziTzgXzf_zd`za\ _z_YxXXuTXpQVmPTiMTfJScGQ } frm:SliceJB-new {; by John R. H. Goering, July 1999 pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1), b=pi*imag(p1), g=pi*real(p2), d=pi*imag(p2), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+(p4), z=r+flip(s)+(p5): z=z^(p3)+c |z|<=9 } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] FOTD 24-07-03 (Four-Dimensional Scene [?])
by Russell Walsmith 24 Jul '03

24 Jul '03

The "4-D" fractal definitely transcends any rating schema, as it is much more than the sum of its pixels; it provokes the mind into all sorts of haunting imagery. A 'metaphysical' definition of art that I am fond of is "That which uses those things in the realm of illusion to point beyond the illusion" and that's a quality I discern here... good one... Russell -- --------- Original Message --------- DATE: Thu, 24 Jul 2003 09:47:00 From: Jim Muth <jamth(a)mindspring.com> To: fractint(a)mailman.xmission.com Cc: philofractal(a)lists.fractalus.com > >FOTD -- July 24, 2003 (Rating ?) > >Fractal visionaries and enthusiasts: > >How does one answer the question, "Where is the fourth spatial >dimension?" This, in my opinion, is one of the most puzzling >questions that has ever been asked. We know where it would be >if it existed, but it cannot exist. There is no room for it. >Three-dimensional space is all there is. Yet it does exist. >Using numbers, we can take apart and examine 4-D hyperspace as >rigorously as we examine three-dimensional space. I suspect >that the inability to perceive 4-D space is a limitation of our >awareness, and that the fourth dimension is there all around us, >if only we had eyes to see. How to open our eyes and adjust our >numbers is anyone's guess. > >Today's image is a scene in the Z^2.003+C Julibrot. Julibrots >are four-dimensional things that, sliced in one direction give >Julia sets and, sliced in another direction, give perturbed >Mandelbrot sets. Of course, being hypersolid, the 4-D Julibrot >can also be sliced in oblique directions between the Julia and >Mandelbrot directions. > >Today's scene is sliced in a direction only one degree from the >Julia direction, but that single degree makes a world of differ- >ence. (To see the pure Julia set, change imag(p1) from 89 to >90.) The Z^2.003+C Mandeloid is shaped almost exactly like the >classic Mandelbrot set, whose formula is Z^2+C, the major change >being along the negative stem, which has split into an infinity >of curving, infinitely-divided filaments. The large midget at >-1.75 has also started to split, and today's scene is located in >the East Valley of this midget, which has broadened into a much- >divided wedge-shaped thing. > >I have given the image the name "Four-Dimensional Scene", which >is a fair description. But I am undecided on the worth of the >picture, which comprises all there is of the fractal. Sometimes >I think it is worth an 8, then I view it again and see an image >worth only a 4. The image will likely go unrated. > >The modest render time of X minutes can be avoided by download- >ing the finished GIF image from: > > <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> > >or from: > > <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> > >Though it was quite humid, the temperature rose no higher than >84F 29C and no rain fell here at Fractal Central on Wednesday, >giving the dynamic fractal cats a most pleasurable day. The >good weather also helped conserve the stressed tuna population, >since no treat was necessary. > >Today is promising to be a slightly less humid repeat. I expect >a repeat from the fractal cats. More good news is that the work >shelf is filling up. And the best news of all is that I shall >return in 24 hours with another glorious fractal. Until then, >take care, and when I started the FOTD on the Fractal-Art list >in April of 1997, I expected to keep it going maybe a week or >two. > > >Jim Muth >jamth(a)mindspring.com >jimmuth(a)aol.com > > >START 20.0 PAR-FORMULA FILE================================ > >4-DimensionalScene { ; time-0:06:55.34--SF5 on a p200 > reset=2002 type=formula formulafile=allinone.frm > formulaname=multirot-XY-ZW-new function=ident/flip > center-mag=-0.0156752/-0.0738926/7.021696/1/-90/3.\ > 88578058618804789e-016 params=90/89/2.003/0/0.0001\ > 9/0.07388/-1.7435/0 float=y maxiter=8000 inside=0 > passes=1 logmap=yes periodicity=10 > colors=0000000000000000200400600830A60C90EC0GF0II4\ > KL6MOAOREQUGSXJU_LWbPYeT_hVakZcnbeqdgtgiwhjzikzjmz\ > kmzlmzmmznmzomzpmzqozrqzssztuvuvnvogugTkbEbV0XR0VP\ > 0VN0TN0TL0RJ0RJ0PH0PG0PG0RL2RP8RVERZJRbPRgVRk`RqdU\ > uicxomzurzzzzzvzzrzzmzzhzzfzoosbxiPz`CzT0ob4Rk82uC\ > 0zE0zG0xH0vJ0sL0qN0oP0mR4iR6gTAeVEdXG`ZJZ`NXbbGRPV\ > bCim0xv0zz0zz0zz0zz0oz0dz0Ru0Eq00m00i40g`6ez0mzEeq\ > R`ddVPqNCzH0z00zC8zLJzXTzebzoezigxeigbkRZk2NmAVoH`\ > qPesXkudqvkvxszzzzzzzxuzvqzukzsezqbzoXxoRvmNukHuiC\ > sg8qe2od0md0md0qd8udGxdNzdVzdbz``zXZzTXxPXuLVqJToG\ > RkCRg8Pe4Nb0Na2N`H40RE0`N6iXCseJzoPzxXdbzdbzdbzdbz\ > dbzdbzdbzdczcczcczcczcczcczcczcczcczcczcczcczcczcc\ > zcczcczhc0mc0rc0vc0zV0zT2zP8zLEzJHzGNcczz8Zz6dz2iz\ > 0oz0s20z40z60z60z86zAAzAEzCJzENvERuGZsGdqHioHomJuk\ > JziLzgLzeNzdNzbPz`Pz`NzdNzeNzgNziNzkNzoNzqNzsNzuNz\ > vGsqAmm4gi0be0X`0RX0LT0GP } > >frm:multirot-XY-ZW-new {; draws 6 planes and rotations >;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J >;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J >a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, >z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, >c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: >z=z^(p2)+c, >|z| <= 36 } > >END 20.0 PAR-FORMULA FILE================================== > > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

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Re: [Fractint] FOTD 24-07-03 (Four-Dimensional Scene [?])
by Fr. Jim Lacasse 24 Jul '03

24 Jul '03

Jim I would rate today as a 6 or 6.5. I see the openings as the entrance to something, not sure what. Jim LaCasse >>> jamth(a)mindspring.com 07/24/03 06:47AM >>> FOTD -- July 24, 2003 (Rating ?) Fractal visionaries and enthusiasts: How does one answer the question, "Where is the fourth spatial dimension?" This, in my opinion, is one of the most puzzling questions that has ever been asked. We know where it would be if it existed, but it cannot exist. There is no room for it. Three-dimensional space is all there is. Yet it does exist. Using numbers, we can take apart and examine 4-D hyperspace as rigorously as we examine three-dimensional space. I suspect that the inability to perceive 4-D space is a limitation of our awareness, and that the fourth dimension is there all around us, if only we had eyes to see. How to open our eyes and adjust our numbers is anyone's guess. Today's image is a scene in the Z^2.003+C Julibrot. Julibrots are four-dimensional things that, sliced in one direction give Julia sets and, sliced in another direction, give perturbed Mandelbrot sets. Of course, being hypersolid, the 4-D Julibrot can also be sliced in oblique directions between the Julia and Mandelbrot directions. Today's scene is sliced in a direction only one degree from the Julia direction, but that single degree makes a world of differ- ence. (To see the pure Julia set, change imag(p1) from 89 to 90.) The Z^2.003+C Mandeloid is shaped almost exactly like the classic Mandelbrot set, whose formula is Z^2+C, the major change being along the negative stem, which has split into an infinity of curving, infinitely-divided filaments. The large midget at -1.75 has also started to split, and today's scene is located in the East Valley of this midget, which has broadened into a much- divided wedge-shaped thing. I have given the image the name "Four-Dimensional Scene", which is a fair description. But I am undecided on the worth of the picture, which comprises all there is of the fractal. Sometimes I think it is worth an 8, then I view it again and see an image worth only a 4. The image will likely go unrated. The modest render time of X minutes can be avoided by download- ing the finished GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Though it was quite humid, the temperature rose no higher than 84F 29C and no rain fell here at Fractal Central on Wednesday, giving the dynamic fractal cats a most pleasurable day. The good weather also helped conserve the stressed tuna population, since no treat was necessary. Today is promising to be a slightly less humid repeat. I expect a repeat from the fractal cats. More good news is that the work shelf is filling up. And the best news of all is that I shall return in 24 hours with another glorious fractal. Until then, take care, and when I started the FOTD on the Fractal-Art list in April of 1997, I expected to keep it going maybe a week or two. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ 4-DimensionalScene { ; time-0:06:55.34--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip center-mag=-0.0156752/-0.0738926/7.021696/1/-90/3.\ 88578058618804789e-016 params=90/89/2.003/0/0.0001\ 9/0.07388/-1.7435/0 float=y maxiter=8000 inside=0 passes=1 logmap=yes periodicity=10 colors=0000000000000000200400600830A60C90EC0GF0II4\ KL6MOAOREQUGSXJU_LWbPYeT_hVakZcnbeqdgtgiwhjzikzjmz\ kmzlmzmmznmzomzpmzqozrqzssztuvuvnvogugTkbEbV0XR0VP\ 0VN0TN0TL0RJ0RJ0PH0PG0PG0RL2RP8RVERZJRbPRgVRk`RqdU\ uicxomzurzzzzzvzzrzzmzzhzzfzoosbxiPz`CzT0ob4Rk82uC\ 0zE0zG0xH0vJ0sL0qN0oP0mR4iR6gTAeVEdXG`ZJZ`NXbbGRPV\ bCim0xv0zz0zz0zz0zz0oz0dz0Ru0Eq00m00i40g`6ez0mzEeq\ R`ddVPqNCzH0z00zC8zLJzXTzebzoezigxeigbkRZk2NmAVoH`\ qPesXkudqvkvxszzzzzzzxuzvqzukzsezqbzoXxoRvmNukHuiC\ sg8qe2od0md0md0qd8udGxdNzdVzdbz``zXZzTXxPXuLVqJToG\ RkCRg8Pe4Nb0Na2N`H40RE0`N6iXCseJzoPzxXdbzdbzdbzdbz\ dbzdbzdbzdczcczcczcczcczcczcczcczcczcczcczcczcczcc\ zcczcczhc0mc0rc0vc0zV0zT2zP8zLEzJHzGNcczz8Zz6dz2iz\ 0oz0s20z40z60z60z86zAAzAEzCJzENvERuGZsGdqHioHomJuk\ JziLzgLzeNzdNzbPz`Pz`NzdNzeNzgNziNzkNzoNzqNzsNzuNz\ vGsqAmm4gi0be0X`0RX0LT0GP } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE================================== _______________________________________________ Fractint mailing list Fractint(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint

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FOTD 24-07-03 (Four-Dimensional Scene [?])
by Jim Muth 24 Jul '03

24 Jul '03

FOTD -- July 24, 2003 (Rating ?) Fractal visionaries and enthusiasts: How does one answer the question, "Where is the fourth spatial dimension?" This, in my opinion, is one of the most puzzling questions that has ever been asked. We know where it would be if it existed, but it cannot exist. There is no room for it. Three-dimensional space is all there is. Yet it does exist. Using numbers, we can take apart and examine 4-D hyperspace as rigorously as we examine three-dimensional space. I suspect that the inability to perceive 4-D space is a limitation of our awareness, and that the fourth dimension is there all around us, if only we had eyes to see. How to open our eyes and adjust our numbers is anyone's guess. Today's image is a scene in the Z^2.003+C Julibrot. Julibrots are four-dimensional things that, sliced in one direction give Julia sets and, sliced in another direction, give perturbed Mandelbrot sets. Of course, being hypersolid, the 4-D Julibrot can also be sliced in oblique directions between the Julia and Mandelbrot directions. Today's scene is sliced in a direction only one degree from the Julia direction, but that single degree makes a world of differ- ence. (To see the pure Julia set, change imag(p1) from 89 to 90.) The Z^2.003+C Mandeloid is shaped almost exactly like the classic Mandelbrot set, whose formula is Z^2+C, the major change being along the negative stem, which has split into an infinity of curving, infinitely-divided filaments. The large midget at -1.75 has also started to split, and today's scene is located in the East Valley of this midget, which has broadened into a much- divided wedge-shaped thing. I have given the image the name "Four-Dimensional Scene", which is a fair description. But I am undecided on the worth of the picture, which comprises all there is of the fractal. Sometimes I think it is worth an 8, then I view it again and see an image worth only a 4. The image will likely go unrated. The modest render time of X minutes can be avoided by download- ing the finished GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Though it was quite humid, the temperature rose no higher than 84F 29C and no rain fell here at Fractal Central on Wednesday, giving the dynamic fractal cats a most pleasurable day. The good weather also helped conserve the stressed tuna population, since no treat was necessary. Today is promising to be a slightly less humid repeat. I expect a repeat from the fractal cats. More good news is that the work shelf is filling up. And the best news of all is that I shall return in 24 hours with another glorious fractal. Until then, take care, and when I started the FOTD on the Fractal-Art list in April of 1997, I expected to keep it going maybe a week or two. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ 4-DimensionalScene { ; time-0:06:55.34--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip center-mag=-0.0156752/-0.0738926/7.021696/1/-90/3.\ 88578058618804789e-016 params=90/89/2.003/0/0.0001\ 9/0.07388/-1.7435/0 float=y maxiter=8000 inside=0 passes=1 logmap=yes periodicity=10 colors=0000000000000000200400600830A60C90EC0GF0II4\ KL6MOAOREQUGSXJU_LWbPYeT_hVakZcnbeqdgtgiwhjzikzjmz\ kmzlmzmmznmzomzpmzqozrqzssztuvuvnvogugTkbEbV0XR0VP\ 0VN0TN0TL0RJ0RJ0PH0PG0PG0RL2RP8RVERZJRbPRgVRk`RqdU\ uicxomzurzzzzzvzzrzzmzzhzzfzoosbxiPz`CzT0ob4Rk82uC\ 0zE0zG0xH0vJ0sL0qN0oP0mR4iR6gTAeVEdXG`ZJZ`NXbbGRPV\ bCim0xv0zz0zz0zz0zz0oz0dz0Ru0Eq00m00i40g`6ez0mzEeq\ R`ddVPqNCzH0z00zC8zLJzXTzebzoezigxeigbkRZk2NmAVoH`\ qPesXkudqvkvxszzzzzzzxuzvqzukzsezqbzoXxoRvmNukHuiC\ sg8qe2od0md0md0qd8udGxdNzdVzdbz``zXZzTXxPXuLVqJToG\ RkCRg8Pe4Nb0Na2N`H40RE0`N6iXCseJzoPzxXdbzdbzdbzdbz\ dbzdbzdbzdczcczcczcczcczcczcczcczcczcczcczcczcczcc\ zcczcczhc0mc0rc0vc0zV0zT2zP8zLEzJHzGNcczz8Zz6dz2iz\ 0oz0s20z40z60z60z86zAAzAEzCJzENvERuGZsGdqHioHomJuk\ JziLzgLzeNzdNzbPz`Pz`NzdNzeNzgNziNzkNzoNzqNzsNzuNz\ vGsqAmm4gi0be0X`0RX0LT0GP } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 23-07-03 (Activity-2 [7])
by Jim Muth 23 Jul '03

23 Jul '03

FOTD -- July 23, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today's FOTD takes us to a world very similar to the world of yesterday's image. This explains the name "Activity-2". The parent fractal is another distorted Mandel-thing with a single large bay and a multitude of tiny budlets. Today's scene is located in the filament of a star connected to a high-order budlet on the northeastern shore of the large bay. The generating formula subtracts 1.2 parts of (1/Z) from Z^(1.2) and adds (1/C). Once again I rendered the image with the outside set to the 'atan' option. In fractals as in movies, the sequel is rarely as good as the original, so today's image rates only a 7, which is still a fine rating, but not quite up to yesterday's rating of 8. The render time I wrote for today's image is a rough average. For some reason, the image never seems to render at the same speed twice. The time has been as short as 6:50 and as long as 8:30. But the exact time required for rendering is unimportant, for the completed image may be downloaded from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> A light shower fell just after noon on Tuesday here at Fractal Central. It left the grass just wet enough to spoil the fractal cats' outing in the yard. When the rain was not falling, the sky was partly cloudy. The temperature of 88F 31C felt more like 98 (37) due to the high humidity. A heavy thunder-shower moved in after dark, but by then it made no difference. The cats' day had already been spoiled. Today is forecast to be a repeat. No problem however. The cupboard is filled with tuna. But my work shelf is still quite empty. In the unlikely event that this empty-shelf syndrome continues, it could develop into a problem that tuna cannot solve. In any case, I'll return in 24 hours with the next fractal. Until then, take care, but don't forget to have fun. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Activity-2 { ; time=0:07:30.00--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.70588265541529430/+0.874913710082279\ 70/7.816022e+010/1/72.5/-0.000115336616405538328 params=1/1.2/-1.2/-1/0/0 float=y maxiter=1200 inside=0 outside=atan periodicity=10 colors=000zmnzmmzmkzmjzmhzmgzmezkdyibygaye_ycZxaXx\ _WxYUxWTySRyOQyKOyHNyFLyDKyCIyAHy8Fy7Ex8Fw8Fv8Fv8G\ u8Gt8Gt9Hs9Hr9Hq9Iq9Ip9IoAJoAJnAJmAKmAKlAKkBLjBLjB\ LiBMhBMhBMgCNfCNfCNeCOdCOcCOcDPbDPaDPaDQ`DQ_DQZERZ\ ERYERXESXESWESVFTVFTUFTTFUSFUSFURGVQGVQGVPGWOGWPFV\ OGWOHXOIXOIYOJYOKZOL_OL_NM`NN`NNaNOaNPbNQcNQcNRdNS\ eMSgMTiMUkMVmMVoMWqMXrMYsLYtL_uLavLcwLexLgyLizLjzL\ kzKlzKmzKnzKozKpzKqyKrxKswNtvMuuLwtKusJsrIqqHopGmo\ FknEimDglDekCcjBaiA_h9Yg8Wf7Ue6Sd5Qc4Ob3Ma1K`3Ia4G\ a6Eb7Cb9CcADcCEdDFdFG0000IH0000LJ0000NL0PM0000SO0T\ PiVQiWQjYRjZSk`TkaUkcVldWleXmgYmhZnwZzw_zm`onaopbp\ qcpsdqteqvfrwgrxgrwhqwhqwhpvhpvhovhoviouinuinuimui\ mtimtjltjltjksjksjksjjskjrkirkirkhrkhqkhqlgqlgplfp\ lfplfpleomeomdomdomdnmcnmcnnbnnbmnamnamnamn`lo`lo_\ lo_lo_koZkoZkpYjpYjpYjpXjpXipWiqWiqViqVhqVhqUhqUhr\ TgrTgrTgrSgrSfrRfsRfsRfsQ } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 22-07-03 (Lots of Activity [8])
by Jim Muth 22 Jul '03

22 Jul '03

FOTD -- July 22, 2003 (Rating 8) Fractal visionaries and enthusiasts: A day that starts with only 37 spam e-mails and a nearly empty work-shelf can't be all bad. Unfortunately, the 37 spams are a fluke, and fortunately, the nearly empty work shelf is a fluke also. I could eliminate the spam, at least for a while, by changing my e-mail address, but all those 'hi ya!', 'remember me!' and 'mdqwk zutpdxloj' subject lines have become almost like old friends waiting to greet me and then be deleted when I open my e-mail box every morning. Today's bustling image is also filled with activity. In fact, it is so active that it appears almost hectic. Because of its activity, I have given it the not very poetic name "Lots of Activity". The parent fractal was created by subtracting 0.8 parts of Z^(-1.2) from one part of Z^(1.1) before adding (1/C). It is a twisted Mandeloid consisting of a single large main bay edged with unusually small buds, which are so similar in size that the main period-2 bud is nearly impossible to find without checking. Avoiding the impossible, I checked. Today's scene is located very near the tip of the filament extending from the 'main' bud. The hectic effect has been achieved by rendering the scene with the 'outside' coloring option set to 'atan'. The normal 'iter' outside setting also creates an interesting scene, as do several other options, but the 'atan' option gives the best results, at least with today's image. I have had a run of below-average images lately, so maybe I have over-rated today's. But when I saw the result of the 'atan' option, I was so surprised that I gave the image a rating of a much-above-average 8. The recent render times seem to be in inverse co-relation to the quality of the finished images. Today's image, which renders in only 5 minutes, continues that trend. And if rendering fractals is not your 'cup of tea', the completed GIF image may be down- loaded from the FOTD web sites, which are located at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather was better than had been expected here at Fractal central on Monday. True, it was oppressively muggy and the temperature reached 91F 33C, but the forecasted rain failed to arrive, permitting the fractal cats an extended romp in the grass. By the time their fun ended, the duo were so tired that they settled to sleep without their customary evening treats. Rain is once again forecast for today, and once again I see great patches of blue sky overhead. A forecast of rain and actual rain are two entirely unrelated things, so I'll believe the forecast of rain when I see actual water falling from the sky. If my cynicism is correct, and it usually is, the cats will have another fun day. And with another slow work day coming, today is sure to be a fun day for me. Until next FOTD, take care and be alert for the rain. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Lots_of_Activity { ; time=0:05:11.15--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.05422309850998541/+0.601340703105692\ 80/3.458086e+010/1/-165/0.0022281871845546905 params=1/1.1/-0.8/-1.2/0/0 float=y maxiter=1200 inside=0 outside=atan periodicity=10 colors=000IUFIUHIUJIULJUNJUPJUQJUSJUUJUWKVYKV_KVaK\ VbKVdLVfLVhLVjLVlLVnLVoNYlO_iPafRdcSfaThZVkWWmTXoR\ ZrO_tLcvIhw5myCrxGwwJzvMzuQztTwsWrrZmqbjpekohlnlmm\ onlrrswpovolumhuletjbtiZsgWsfTrePqcMqbIp`Fp_CoY8oX\ 5nX0oW2nV4mV6lU8kT9jTBiSDhSFgRGfQIeQKdPMcPObOPaNR`\ NT_MVZNY`MWZMVYLUWLTVKSTKRSJQQJPPIONINMHMKHLJGJIGI\ GFHFFGDEFCEEADD9DC7CB6CA4B93A60B82BA4BC5BE7BG9CIAC\ KCCMDCOFCQHCSIDUKDWLDYND_PDaQDcSEeTEgVEiXEkYEm_3pf\ 9ocEo`KnYPnVVmT_mQemNjrKkwJmzHorIqjJw_Iz`Ju`Jw`Jr`\ Jo`Jn`Jm`Jl`Jk`Jj`Ji`Jh`Jg`Jf`Je`JdaJcaJbaJaaJ`aJ_\ aJZaJYaJXaJWbJVcJUfJTiJSlJSqHRlJQdKPXLPUMOPNNKOMUQ\ MTRLSSKQTJPUJOVIMXHLYGKZGI_FH`EGaDEcDDdCCeBAfA9g34\ lA8hGBdME`SHYZKUdNQjQMqRGpSIpTJpUKpVMpWNpWOpXPoYRo\ ZSo_To_Uo`WoaXobYocZnc`ndanebnfcngengfnhgnihmjjmkk\ mklmlmmmomnpmoqmnuCUWCUVCUUDUTDUSEUREUPEUOFUNFUMGU\ LGUKGUIHUHHUGIUFIUEHTBIUD } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 21-07-03 (A Stand-in Fractal [3])
by Jim Muth 21 Jul '03

21 Jul '03

FOTD -- July 21, 2003 (Rating 3) Fractal visionaries and enthusiasts: We arrived home much later than expected last evening, putting me far behind in the work. With undone work piled left of me, right of me, before me, and even behind me, I had almost no time to find a proper fractal. I did find an improper (previously discarded) fractal to act as a stand-in however. I named it "A Stand-in Fractal" accordingly. The parent fractal was produced by calculating a different critical point of the formula used for the 'Antlers' image of July 17. (Yes, a single formula can have more than one critical point.) Since I put basically no effort into the image, I could not honestly rate it higher than the lowly 3 it is stuck with. But all is not lost. With so little competition from today's image, tomorrow's is sure to be better. Adding insult to injury is the render time of 36 minutes. Luckily, the image, for what it's worth, is available on Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Sunday was a fine day at Fractal Central, with lots of sun and a temperature of 84F 29C. Unfortunately for the dynamic duo, no one was here to let them out to enjoy the weather, and when we finally did arrive after dark, they were sulky enough to need an extra treat. The extra treat worked, and they ended their day sleeping peacefully. Today is starting well enough, but rain is possible later this afternoon, and there is still a lot of work to finish. The fractal cats will likely be left to their own entertainment devices. The fractal human however will need nothing extra to keep boredom away. Until next FOTD, take care, and be well. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Stand-in_Fractal { ; time=0:36.28.45--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3a function=ident passes=1 center-mag=-1.01537877234625200/+0.522592098338092\ 50/1.083935e+008/1/157.5/-1.99426932897192599e-005 params=1/2/0.5/3/0.333/4/0.25/5/0/0 float=y maxiter=1200 inside=0 periodicity=10 colors=000_k6_j6_i6`h7`g7`f7`e7`d7ac8ab8aa8a`8a_8b\ Z9bY9bX9bW9bV9cUAcTAcSAcRAcQAdPBdOBdNBdMBdLBeKCeJC\ eICeHCeGCfFDfEDfDDfCDeBEfCDgDDgEDhFDhFDiGDiHDjICkJ\ CkJClKClLCmMCmNCnNBoOBoPBpQBpRBqRBqSBrTAsUAsVAtVAt\ WAuXAuYAvZ9wZ9w_9x`9xa9yb9yb9xaAw`Bv_CuZDtYEtYFsXG\ rWHqVIpUJpUKoTLnSLmRMlQNlQOkPPjOQiNRhMShMTgLUfKVeJ\ WdIXdIXeHWfHVfHUgHThGShGRiGQjGPjGOkFNlFMlFMmFLnFKn\ EJoEIpEHpEGqEFrDErDDsDCtDBtDBsECrEDqEEpFFoFGnFHmGI\ mGJlGKkGLjHLiHMhHNgIOgIPfIQeJRdJScJTbJUaKVaKV`KW_L\ XZLYYLZXL_WM`VMaVMbUNcTNdSNdROeQOfPOgPOhOPiNPjMPkL\ QlKQmJQnJQnIRmIRmIRjIQgHOdHMaHKZHKWHLWGNYGP_GMcGCf\ GIhFPhFRhFTgFVgFVgEWfEWfEWeEXeDXeDXdDXdDYdDYcCYcCY\ bCZbCZeCZhBZkB`nBcqBftBiwFlzGoxGpvGptGqrGqpGroGrmG\ skGsiHtgHueHudHvbHv`HwZHwXHxVGzTHxUHvUHtUHrUHpUInU\ IlVIkVIiVIgVJeVJcVJaWJ_WJYWKXWKVWKTWKRXKPXLNXcg8bh\ 8bi7aj7`k7`l6_m6Zn5_m6_l6 } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 20-07-03 (Somewhere-But Where [6])
by Jim Muth 20 Jul '03

20 Jul '03

FOTD -- July 20, 2003 (Rating 6) Fractal visionaries and enthusiasts: Today's image has been named "Somewhere-But Where". This name was chosen because the image is an evaporated one, made visible by the bof61 inside fill. The imag(p3) parameter of one-googol is the give-away sign. The original image still exists some- where, but certainly not on the screen. The parent fractal, before evaporation, is a fairly normal M-set rotated about -30 degrees. Today's image lies in a small spiral in a larger spiral in the evaporated East Valley area of the parent. The unevaporated version of today's image is almost equal to the evaporated version, and in fact might appear as its own FOTD in a day or so. As is always the case, the approximately 20-minute wait for the image to render from the parameter file can be avoided by down- loading the finished GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Both weather and cats were near perfect here at Fractal Central on Saturday. The skies turned sunny by afternoon and the temperature held at 84F 29C, making for contented cats. A secondary advantage was the money I saved when no treat of tuna was needed. Today is starting just as fine. I assume that, unless an unwelcome stray cat wanders by, Thomas and Tippy will be in fine moods also. Well, the human schedule for today includes a trip to one of the apparently countless junque emporiums nearby, where we'll spend several hours looking at the stuff other people discarded. I could think of better ways to spend a Sunday, but it's good enough. When we return, I'll start work on tomorrow's FOTD. Until then, take care, and things are not always as they appear. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Somewhere-ButWhere { ; time=0:19:57.10--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.00716689806988486/+0.155262099939572\ 20/1.008623e+011/1/67.5/-0.00336101615660141378 params=1/-0.8/-1/0.8/1.8/1e+100 float=y maxiter=1000 inside=bof61 periodicity=10 colors=000`EM_ELZEKZEJYFIYGHXHHXIGXIFWJFWKEWLDVLDV\ MCUNBUOBUPATP9TQ9TR8SS7SS7RT6RU5RV5QW4QW3QX3PY2PZ1\ PZ1OX6NVAMTELSILQMKORJNVILZHJbHIfJLfLNfMQfOSfPUfRX\ fSZfU`fWcfXefZhf_jfalfbofdqfesf`mhXgjTakOWmKRnGLpB\ Fq79s34t78qACoEGmHJkKNiORfRUdVYbYa``dZ_eYZeXYeXXeW\ WeVVeVUeUTeTTeTSeSReRQeRPeQOePNePMeOLeNLeNaaKqYHoZ\ Jm_Kk`Lj`MhaOfbPdcQccRadS_eUYfVXfWVgXThZRi_Qi`OjaM\ kbKldJleHmfFngEnhFicGe_H`WIXSJSOKOJLJFMFBNA7O63P85\ Q97RB9SCBTEDUFEVHHWIKXKMYLOZNQ_OS`QUaRmbTmbUmcWmdX\ meZmf_mgZmh_miamjbmkemlfmmionjqomspnupovnlrmjolhlj\ ehicehabgZZeXWdVTcSPbQM`OJ_LFZJCYH9SR6M`3Gi1Jf4Ld6\ Na9P_BSXEUVGWSJYQL_ONbLQdJSfGVhEXkB_m9ao6dq4fs2hp4\ fm6dj8bgAadC_aEYZGWWHVTJTQLRNNPKPOHRMETKBUJDTKFSLG\ RMIQNJPOLOPMNQOMQPLRRKSSJTUIUVHVXGWYFWVGVSGUQHUNHT\ KHSIISFIRDJRAJQ7JP5KP2KO0KO3ML6NJ8OHBQEERCGSAKQEOP\ ISOLWNP_MScLWbFQbFPaFO`FN } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Wild Ride (Sound par for SB Compatibles)
by Bill Jemison 19 Jul '03

19 Jul '03

in case the previous par didn't come through formatted correctly... wowwhoa2 { ; Music par Copyright (c) Bill Jemison2003 ; Works with most SB compat. cards (OPL-3 chip) ; Fractint ver. 20.0 ; y parameter reset=2000 type=chip passes=1 center-mag=0/0/0.001754386 params=-15/-19/1 float=y viewwindows=12/0.75/yes/0/0 cyclerange=1/1 hertz=312 sound=y/fm polyphony=7 attack=8 decay=8 sustain=14 srelease=10 orbitdelay=150 showorbit=yes colors=000<3>000000000000eee<4>eeeeeeeee000<4>000000000zzz<4>zzzzzzzzz00\ 000e0e00eee00e0eeL0eee00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzzzLzzzLL\ LLLzLzLLzzzLLzLzzzLzzzzVV<3>zzV<3>VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3\ >hzh<3>hzz<2>hlz00S<3>S0S<3>S00<3>SS0<3>0S0<3>0SS<2>07SEES<3>SES<3>SEE<3\ >SSE<3>ESE<3>ESS<2>EHSKKS<2>QKSSKSSKQSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KS\ QKSSKQSKOSKMS00G<3>G0G<3>G00<3>GG0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8\ AG88<2>GE8GG8EG8CG8AG88G8<2>8GE8GG8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GF\ BGGBFGBDGBCGBBGB<2>BGFBGGBFGBDGBCG000<6>000 }

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Wild Ride (Sound par for SB Compatibles)
by Bill Jemison 19 Jul '03

19 Jul '03

Hi All, Here is a fun little sound par that I think sounds like a wild ride down a sewer pipe. Be sure to turn on your sounds, and don't expect much of an image. The whole thing lasts about 7 1/2 minutes. Bill wowwhoa2 { ; Music par Copyright (c) Bill Jemison2003 ; Compatible with most SB compatible cards (OPL-3 chip) ; Fractint ver. 20.0 ; y parameter reset=2000 type=chip passes=1 center-mag=0/0/0.001754386 params=-15/-19/1 float=y viewwindows=12/0.75/yes/0/0 cyclerange=1/1 hertz=312 sound=y/fm polyphony=7 attack=8 decay=8 sustain=14 srelease=10 orbitdelay=150 showorbit=yes colors=000<3>000000000000eee<4>eeeeeeeee000<4>000000000zzz<4>zzzzzzzzz00\ 000e0e00eee00e0eeL0eee00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzzzLzzzLL\ LLLzLzLLzzzLLzLzzzLzzzzVV<3>zzV<3>VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3\ >hzh<3>hzz<2>hlz00S<3>S0S<3>S00<3>SS0<3>0S0<3>0SS<2>07SEES<3>SES<3>SEE<3\ >SSE<3>ESE<3>ESS<2>EHSKKS<2>QKSSKSSKQSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KS\ QKSSKQSKOSKMS00G<3>G0G<3>G00<3>GG0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8\ AG88<2>GE8GG8EG8CG8AG88G8<2>8GE8GG8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GF\ BGGBFGBDGBCGBBGB<2>BGFBGGBFGBDGBCG000<6>000 }

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FOTD 19-07-03 (A Rusted Minibrot [6])
by Jim Muth 19 Jul '03

19 Jul '03

FOTD -- July 19, 2003 (Rating 6) Fractal visionaries and enthusiasts: Today's image, which is found in the fractal created when 2 negative parts of Z^(0.75) are combined with 2 negative parts of Z^(-0.75), appears a bit rusty to me. I named it "A Rusted Minibrot" because of the eight rust-colored lobes surrounding the central midget. The parent fractal is a three-bayed thing with X-axis symmetry. Like most fractals whose formulae contain negative powers of Z, today's image is very sensitive to changes in the bailout radius. As the bailout is raised, the scene soon 'evaporates', leaving a blank black screen consisting of 'inside' areas. Several of the inside fills create an image on this blank screen, but none equals the level of today's image, which was rendered and colored in the old-fashioned 'normal' way. If I had given the coloring a bit more effort, today's image might have rated a 7. As it is, a 6 is the best rating I could give. The image is worth a look, though it's nothing that hasn't been seen before. The 8-minute render time is a bit slow, but the wait can be avoided by downloading the finished image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Light rain that began early in the afternoon spoiled the fractal cats' day and left them in bad moods. They sat on the porch for an hour or so, watching the rain and wishing the grass were dry. Then they came indoors to demand their consolation treats. Tuna did the trick. Today is starting cloudy and cooler, but dry. If things go as they should, the duo will have a much better day. For me it will be a pleasant enough day -- if I can avoid any serious work that is. Until next FOTD, take care, and see you in 24 hours. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Rusted_Minibrot { ; time=0:08:21.97--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.17148324655015210/+0.052765428789762\ 48/7.24257e+008/1/-17.5/4.85213927717970117e-006 params=-2/0.75/-2/-0.75/0/0 float=y maxiter=1000 inside=0 logmap=164 periodicity=10 colors=000UDlVCmWCnWCpXBqYBrZBs_Au`AvaAwaAx_9vY9uW\ 8sU8rS7pQ7oP6mN6lL5jJ5iH4hF4fD3eC3cA2b82`61_41Y20X\ 10W53U85SC7QA9OJBMADLQFJAHHXJFhLDcNBgPAgQCgQEhRGhR\ IiSKiSMiSOjTPjTRkUTkUVkUXlVZlV`mWbmWcnXenXgnXioYko\ YmpZopZqpZplXokWtdVk`UpYSgUReQQcMP`IOZFMXBLV7KT3JR\ 0IP3KN6MM9OLCPJFRIITHLVFOWERYDU_BXaA_b9bm7ez6hz5kz\ 3nw2qw1sw0rw3rw6qu8quBpsDpsGopIopLnnNnnQnlSmkVmkYl\ k_lkbkkdkjgjjijjlijnijqijshithhthgthgthftgetgetgdt\ gctgcti_ojWkkTgmPcnL_oIVpERrANs7Jt3Fu0Bs2Dr3Fq4Gp6\ In7Km8LlANkBPjCQiDSiEUiFViGXiGYiH_iI`iJbiJciKeiLfi\ MhiMifOfdPcbQ``RYZSVXTSVUPTVNQXKOYHMZEK_BI`8Ga5Eb2\ Cc0GZ4JV7MQAPMDTHGWDJZ8Ma4Pd0Se3Rf5Rg7Qg9QhCPiEPiG\ OjIOkLNkNNlPMmRMmULnWLoYKo_KqVMrPOsOPtQRvSTwUUxWWy\ YXz_VzaUzcSzeRzgPziOzjNzkLzlKzmIzmHzmFzmEzmDzmBzmA\ zm8zm7zm6zm7zm8zm9zmAzmBzmCzmCzmDzmEzmFzmGzmHzmHzm\ FzmEzmDzmCzmBzm9zm8zm7zm6 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 18-07-03 (Imperfect Minibrot [5])
by JimMuth＠aol.com 18 Jul '03

18 Jul '03

FOTD -- July 18, 2003 (Rating 5) Fractal visionaries and enthusiasts: Another average day brings another average fractal, this one from 3.1415926535898 turns up the complex logarithmic spiral of the formula Z^1.75+C. Yes, I realize that the number of turns is almost equal to pi, but it is not exactly equal. Pi equals 3.14159265358979, and the 0.00000000000001 difference makes a world of difference in the appearance of the finished fractal. The difference must be seen to be fully appreciated. The parent fractal is a Mandeloid with X-axis symmetry, rotated 180 degrees from the normal position. Curiously, the Z^1.75 Mandeloid is the only one that has such symmetry at this point on the log spiral. Today's scene is located on the bud side of the west branch of the valley of a large distorted bud on the northern shore of the main bay of the parent. I named the image "Imperfect Minibrot" because the exponent of Z, which is 1.75, is a fractional value and therefore produces imperfect broken images. The imperfections abound in today's image, perhaps the most notable being the 7 elements that surround the imperfect midget at the center. Not only are these elements broken, but 7 is a strange number that doesn't belong in polite fractals. The next ring inward holds about 12 elements, but not exactly 12 elements, which is not surprising, since 1.75 times 7 equals 12.25. So much imperfection can only make a fractal that is average or below, thus the rating of an average 5. The render time of 19 minutes is admittedly slow, but can be avoided by downloading the finished GIF image file from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Thursday's weather was the best of the summer here at Fractal Central. (Have I said that before?) Deep blue skies flecked with angel-hair cirrus clouds, low humidity, and a temperature of 86F 30C brought out the best in the dynamic cats, who spent most of the afternoon in the holly thicket, wishing they were kittens again. Today is starting fair enough, but rain is possible later this afternoon. It remains to be seen how the duo will adjust. I'll adjust quite well -- once the work is finished, that is. Until next FOTD in 24 hours, take care, and have you tried the fractal miracle diet? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Imperfect_Minibrot { ; time=0:19:01.63--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-0.146140556417671/+0.6352473582880382/\ 7857607 params=1.75/0/3.1415926535898/0 float=y maxiter=12000 inside=0 periodicity=10 colors=000K6lMAjODiPHhRKfTOeURdWVbYYaZa``dZbhYckXd\ l_emafmcgnehnhiojjplkpnlqqmqsnruorwpsrqsmrsissdts_\ tsWusRvsMwsIxsDys8ys4xq6wp7vn8um9tkAtjBshCrgDqeEpd\ FobGoaHdfKVjNLoQBsT1wVBkTL_RVOPdCNn1LkTIisFkoHllJm\ hKoeMpaNqZPrVQxQSwOTvLVuIWsLVpOUlQUiTTeWSbYSZ`RWbS\ ZcTadUdeVgfWjgXmhYpiZsj_uk`ulaum_umXunVunSunPuoNuo\ KupIupFuqDuqAuq8qpDmpIipMeoRaoVYo_UocQnhMnlInqEnuP\ fj__`jSQuLGKZHL`CLb8JUX7tIBsHFrGJpGNoFRnEVmDZkDbjC\ fiBjhBjgAjfAjeAjdAjdAjcAjbAjaAj`Aj`AiaFiaKiaPiaUhb\ ZhbchbhhblXjgZkf`lfblfdmffmfhnfjnflofnofmmemlelkel\ iekhdkgdkfdjddjcdibci`ch_chZchYcfU`dQYbNV`JTZGQXCN\ W9LXBKYDJYFJZHI_JI_LH`NGaPGaRFbTFcVEcWEdVFeUFeTFfS\ FgRFgQGhPGiOGiNGjMGjMGhNIgNKfNMeOOcOQbOSaPU`PWZPYY\ Q_XQaWQcVQeUMbTJ_SFYRCVR9ThkXbcRYWLSPFNH9IA4FK9CTE\ 9aJ6jO4sSCjMJbGRVBYN5dF0WRKNacElvHitKfsNcqP`pMXfJU\ YGRPDOGBL7AMDANJa6FW6QQ6a } END 20.0 PAR-FORMULA FILE==================================

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Re: FOTD 17-07-03 (Antlers in the Treetops [5])
by Jim Muth 17 Jul '03

17 Jul '03

At 02:01 PM 7/17/03 -0400, you wrote: >"Antlers in the Treetops" is actually the name of >an old book - written by Who Goosed the Moose. Yeah! I found it on the shelf right beside "The Yellow River" -- written by I.P.Daily. Jim M.

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FOTD 17-07-03 (Antlers in the Treetops [5])
by Bill Jemison 17 Jul '03

17 Jul '03

"Antlers in the Treetops" is actually the name of an old book - written by Who Goosed the Moose.

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FOTD 17-07-03 (Antlers in the Treetops [5])
by Jim Muth 17 Jul '03

17 Jul '03

FOTD -- July 17, 2003 (Rating 5) Fractal visionaries and enthusiasts: I saw four green antlers when I studied today's image in search of a name. In a fit of whimsy, I named the image "Antlers in the Treetops". I have no idea how antlers might get in the treetops, since deer do not climb trees, but the name has a nice sound to it, so it will remain. The parent fractal was created by combining decreasing portions of Z^2, Z^3, Z^4 and Z^5, calculating a critical point and entering that critical value as initial Z in the MandelbrotMix3a formula. Actually, there are two critical points visible in today's formula when it is calculated in the parabolic direction. I chose the secondary critical point because lesser critical points often produce the most interesting fractals. Though I have not yet checked the main critical point, I suspect it produces a fairly normal Mandelbrot set. The parent fractal is a vaguely triangular thing with X-axis symmetry. Its eastern part degenerates into non-critical chaos, but an 'East Valley' type feature decorates the west part, while prominent buds with three valleys lie on the north and south edges. Today's scene lies in one of the three valleys of the north bud. The four antlers in the image are spectacular to only an average degree. They therefore rate an average rating of a 5. The render time of 13 minutes is also about average for a F.O.T.D. image. The average download time of the completed GIF file is around one minute. And that download may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Wednesday was a hot but dry 90F 32C day here at Fractal Central. The cats were cool as they passed the afternoon resting in the shade of the holly trees. Of course, now that the duo are in their 13th year, resting is just about all they do. Only their location changes. Today is progressing in a similar manner. My tasks for the day begin with the professional work, then shift to fun with fractals. To see the results of that fun, check back in 24 hours. Until then, take care, and be open to new fractal ideas. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ AntlrsInTheTreetps { ; time=0:13:20.15--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3a function=ident passes=1 center-mag=-1.004490349172/+0.54556575218534/18962\ 6.6/1/-15/2.341400962e-010 params=1/2/0.5/3/0.333/\ 4/0.25/5/-1.18856877723752/0 float=y maxiter=1200 inside=0 logmap=76 periodicity=10 colors=000msflrelqekqekpdjodjodincinchmchlcglbgkbf\ jbfjaeiaeiadhadg`cg`cf`be_be_ad_ad_ccZdcZecZfcZgcZ\ hbYibYjbYkbYlbYmbYnaXoaXpaXqaXnaXjbXcc2Uh7KmCArH6w\ M7vL7tL7sL8qL8oL8nL8lL9jK9iK9gK9fKAdKAbKAaKB_JBYJB\ XJBVJCTJCSJCQJCPJBOIBNIAMIAMH9LH9KH8KH8JG7IG7IG6HG\ 6GF5FF5FF4EF4DEADEFCEKBEPBDUADcRDmZDtfdtdbqcanb`ka\ _h`Ze_XbZW_YVXWUUVTRUROTQLSPIROFQNCPMEQOFRQGRRISTJ\ SVKTWMUYNU_OV`QVbRWcSWeUXgVYhWYjYZlZZm__o`_pa`ma`j\ b`gb`ec`bc`_d`Xd`Ve`SeaPfaMfaKgaHgaEhaBha9ia6ia3ia\ 1hbFgcTfdfdadc_bbYaaW_`UY_SXZQVYOUWOTVORTPPSPOQQMP\ QLNQJMRIKRGJSFHSDGSCIUDKWDLXDNZDO_EQaERbETdEUeETdF\ SdFSdGRcGRcHQcHQcIPbIObJObJNaKNaKMaLMaLL`MK`MK`NJ_\ NJ_OI_OI_OJ_NK_ML_MM_LN_KN_KO_JP_IQ_IR_HS_GS_GTbFU\ eEVhEWkDXnCXqCYtBZwA_zA`z9az8az8_zEZzKXzQWzWVz`XzZ\ YzXZzW_zU`zTazRbzQczOdzNezLfzJgzIhzGizFjzDkzClzAdz\ WezYfzZgz_hz`izbjzckzdlze } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 16-07-03 (Mandeloid Spectacle [8])
by Jim Muth 16 Jul '03

16 Jul '03

FOTD -- July 16, 2003 (Rating 8) Fractal visionaries and enthusiasts: hi ya remember me mpdkwsjfzxks . . . Could a FOTD possibly be spam? No, but I just set a new record of over 100 spams in one download. One of these days I'll change my e-mail address, but not quite yet. (We'll let it reach 150.) Today's image is one of the more unusual ones in my vast collection of fractal images. Yet it has been created with nothing more exotic than the classic equal-iteration-bands method of rendering and coloring. I named the picture "Mandeloid Spectacle" on a whim, and rated it at an 8. The rating seems justified for such an unusual image, filled as it is with luminous bits and pieces, which are actually basins containing smaller midgets. The generating formula subtracts 1.1 parts of Z^1.1 from 1.1 parts of Z^(-0.9), then adds (1/C). The parent fractal created by this formula consists of a well-defined Mandeloid, with a fragment of a second Mandeloid to the west and south. Today's scene is located in the rudimentary East Valley of the Mandeloid fragment. The 15-minute render time is in the range where it starts to get boresome. But 13 of those 15 minutes can be saved if the completed image is downloaded from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Both the fractal weather and the fractal cats were near perfect Tuesday here at Fractal Central. The weather featured blue skies, cotton-puff clouds, and a temperature of 84F 29C; the cats featured perfect behavior and a restful day in the yard and on the porch. Today is forecast to be warmer with a chance of rain. The cats' future behavior is totally unpredictable. My future behavior, at least for the rest of the morning, will feature an intensive effort to clear away the few remnants of the work backlog. The next FOTD will appear in 24 or so hours. Until then, take care, and fractal images often speak louder than fractal words. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ MandeloidSpectacle { ; time=0:15:05.22--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.21128088887154150/+0.116698332335055\ 00/1.029713e+011/1/-80/0.00201398738065277499 params=1.1/-0.9/-1.1/1.1/0/0 float=y maxiter=1600 inside=0 logmap=317 periodicity=10 colors=000600800A00C04E04G04H06J06L06N06P06R06T4CV\ AGXGLZLP`RVdXZebdgggkmkmsqqxuszzuzzxzzzzzzzzzzzzvx\ ziozVev08zHXzVxzXuzZsz`qzbozdmzekzgizigzkezmdzobzq\ `zsZzuXzvVzuLzvTzxZzxdzziuzomzvgzz`zzVzzRzzPzzNzzN\ zzLzzLzzJzzJzzHzzGzzGzzEzzEzzCzzCzzAzz0zgAzzEZzG6v\ C0qH0kL0eP0`T0VX0Pb0Je0Ei08m02u00q00o00m00k00g00e0\ 0d00b00Z02X02V02T02P04N04L04E00J04N06R0AX0C`0Ed0Hi\ 0Jm0Nq0Pq0Nu0Rv4VxEZzNbzTezzizzmzzqzzuzzzzzxzzuzzq\ zzmzzizzezzbxzZvzVuzRqxNovJmuGksCiq8bz0gq4kbGoNRs8\ bv0mz0xz0vx0uv0uu0ss0sq0qo0qm0ok0oi0mg0me0qd0sb6v`\ Cx`HzZNzXTzVZzTdzTizZbzdVziPzoHuuCqz4kz0ez0gz0gz0i\ z0iz0kz0kz0mz2mz2oz2oz2zz4zz4zzczt4cu6ct8czAzzCzuE\ zoGziHzdJzbLzZLz`LzbLzdNzgNmiN`kP`mP`qLZoP`oR`oVbo\ Xbo`dmbdmeemgemigmmgkoiksikukkzkkzmkzmdzkXzkRzkkzz\ izzgzzezzdzxbzu`zqZzmXziVzeTzbRzZPzTNzPLzLJzHHzEGz\ AEz6Cz2Az08z06z00z06z0Gz0 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 15-07-03 (Time to Sine Off [7])
by JimMuth＠aol.com 15 Jul '03

15 Jul '03

FOTD -- July 15, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today's discussion will be short. I have to finish the work that backed up while the telephone was not working and customers who tried to call were getting busy signals. To create today's image, 1.1 parts of Z^(-1.15) were subtracted from 1.1 parts of Z, then (1/C) was added, and the whole thing was iterated 42,000 times. The 'tdis' coloring option was then applied to the image and the result given the name "Time to Sine Off". I suppose the sinuously curving features inspired the name. The image has such fine detail in the normally flat areas that moire patterns are actually starting to appear. The whole thing has a deep wine-colored effect that rates a 7. The high maxiter slows the image to 26 minutes, but this wait can be bypassed by downloading the finished image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The forecasted rain never materialized here at Fractal Central on Monday, and as a result, the fractal duo had another pleasant day in the yard. Had Thomas not gotten cranky when Tippy gave him too energetic a face washing, their day would have been perfect. The blue sky, cottonpuff clouds, and temperature of 82F 28C as measured on the Fractal Central digital thermometer were certainly perfect. Today is promising to be another beauty. This is good, for I like happy cats. But within the next few hours I must finish the backed-up work, so my enjoyment must wait. Until the next FOTD appears in 24 hours, take care, and avoid fractal mistakes. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Time_to_Sine-Off { ; time=0:26:55.46--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.1358088165403816/+1.702865705423715/\ 1.432292e+008/1/-25/1.0182567826005906e-006 params=-1/-1.15/1/1/0.1/0 float=y maxiter=42000 inside=0 outside=tdis periodicity=10 colors=000NRaONdPJgPFiJPaEZU8hM3rFDkJNeNX_RfUVpOZy\ IbvJcsKdpLemLfjMggNhdOiaOjZPkWQlTRmQRnNSoKTpHUqFUq\ JSoMQmPPkSNiVMgYKe`JdbKecLeeMffMfhNgiOgjPhlPhmQioR\ ipSjuSqjQddOXXMQRKJJICCG5GFAJFBNEEQEHUDJXDM`CPcCSg\ BViBXeDVaFUZHSUJRQLPRIOOMNKQLHTKEWIA`H7iF4oE1wD4mH\ 6fL8VPBPTDLXFH`HEdIEeKEfLFfMFgNFhPGwQGwRGwSHwUHkVH\ lWIlXImYImaQhdYdhe`zlXzkXzkXzjWwiWriVmhVhhVggUgfUf\ fTfeTfeTefUefUegUegUdhVdhVdiVdiVcjWcjWckWckWblXblX\ blXbmXamYanYanYaoY`oZ`pZ`pZ`qZ_q__r__r__r_Zs`Zs`Zt\ `Zt`YuaYuaYvaYvaXwbXwbXxbXxbXxbQuWKrPEpI8mB2k56gB9\ cGC`LGXRJUWMQ`QNfTJkWGpXHoXIoXInYJnYKmYKmZLlZMlZMk\ _Nk_Oj_Oj_Pi`Qi`Qh`RhaSgaSgaTgbUfbUfbVecWecWdcXdQe\ ATeEWfIZgMagQdhUghXeiWdiWciWbiWajW_jWZjWYjWXkWWkWU\ kVTkVSlVRlVQlVOlVNmVMmVLmVKmVNkYQj`ThcVgfYei`dlbco\ canc_ndYmdXmeVmeTlfRlfQkfOkgMkgKjhJjhHiiFiiDiiChjA\ hj8gk6gk5gl3fO_VLbTMZWNVZ } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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cost
by NEDROG＠aol.com 15 Jul '03

15 Jul '03

What is the cost of this software & do they have a DEMO copy that can be downloaded somewhere? Tnx, Howard W3CQH

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Re: [Fractint] Russ, More ideas for running Fractint under WinXP
by Russell Walsmith 15 Jul '03

15 Jul '03

Hal, First off, in my experience, Fractint has been running amazingly well in XP. If I've encountered problems, they are so intermittent and/or trivial as to have escaped memory... that is until I began experimenting with text screens in small windows. Simply put, to move between Fractint and the desktop is only ever a problem when I try the alt<enter>/text-screen combo. If a rendered fractal exists in the application at this point, then this procedure inevitably corrupts it. That is, regardless of any combination of options I've tried so far. (BTW, alt<enter> shrinks a fractal image to the taskbar, then restores it perfectly.) At any rate, I gather from Jay Hill's comments that this is an ongoing issue that is common to all Windows platforms. Clearly it's time that someone climbs to the rooftop, pulls the covers off of the searchlight and projects the SSG signal to a darkened sky... Ciao, Russ -- --------- Original Message --------- DATE: Mon, 14 Jul 2003 08:24:03 From: Harold Lane <hallane(a)compuserve.com> To: Fractint <fractint(a)mailman.xmission.com> Cc: >================================== >Russ, > Thanks again for trying my suggestions >and reporting their results. > >I had forgotten that Fractint.doc has some >info in it for running Fractint under 'Windows'. >WinXP was released after the Fractint >Version 20.0 Documentation so their >info (in the form of tips from users) >may or may not apply. Note that some >of the tips contradict each other - >such as the usage of 'Always Suspend' >and the versions of windows that the >tips are intended for are not specified. > >Here is what I just found in the Fractint >Version 20.0 Documentation that looks >promising: > >". . . textsafe=save . . . only works if >Always suspend is turned ON." > >textsafe=save works on my >Win98 machine without my having >to turn ON 'Always Suspend' - however, >I recommend that you give it a try. > >How to check the 'Always Suspend' >box is in the docs (which I quote below). > >Also I recommend that you read the >entire section on textsafe= in the docs. > >Here's an excerpt: >". . .'=save' tells Fractint to save/restore >the entire image. Expanded or >extended memory is used for the >save if you have enough available; >otherwise a temporary disk file is used." > >textsafe=BIOS or one of the other settings >may possibly work. You'll never >know if they fix your image corruption >problem until you try them, though... > >Just to be clear on this: am I correct >in thinking that switching between a >fractal *image* in Fractint and the WinXP >desktop and back again also corrupts >the image? <==<< > >Also, if you remain in Fractint (without >switching to the WinXP desktop) can >you switch between a fractal image >and a text screen and back without >corruption? <==<< > >Does checking the box for 'Always >Suspend' in conjunction with >textsafe=save stop your image >corruption? <==<< > >Also, I didn't specifically mention it, >but in sstools.ini you need a line >with [fractint] on it prior to the >textsafe=save line. Without the >[fractint] line Fractint will not recognize >the textsafe=save command. > >I receive the Fractint mailing list in the >digest form. Sometimes it is several >days between times that I receive >digests so my comments to you are >not always as timely as they might be... > >==================================== > >From the Fractint Version 20.0 Documentation: > >Damien M. Jones Windows tips: >Damien M. Jones dmj(a)fractalus.com > "This is what works for me. Your mileage >may vary. > >Create a shortcut to FRACTINT.EXE, >right-click it, choose Properties. >On the Memory tab: set all five >drop-downs to "Auto". On the Screen >tab: choose Full-screen and Fast >ROM emulation, leave Dynamic memory >allocation OFF. Under the Misc tab: >turn OFF Allow screen saver. Turn >ON Always suspend. Set the Idle >sensitivity to about 1/4, closest to >Low. > >In the SSTOOLS.INI file, put >textsafe=save on a line by itself in the >[fractint] section. (This helps >preserve your screen when you switch >away from FractInt, but only works if >Always suspend is turned ON.)" > >------------------------------------ > > Jay Hill's Windows tips: >Jay Hill ehill1(a)san.rr.com > "For starters, make sure the DOS >window properties are set to 'Misc | >Always suspend' = off." Unless you >want the task to stop when it does >not have focus. Also, you can put >the Idle Sensitivity to high. Make >settings on any other DOS windows >you have open according to what they >should be (or what you prefer). > >If your DOS window is full screen, >press Alt-Enter to make it a Window >window. Then click on the MSDOS >icon in the upper left. WARNING, >don't do this in a high res graphics >mode or in text mode (sometimes). >The safest is F3 320x200 graphics >mode. Windows likes that mode. If >you have a high res image, hit 'X' >to get the text screen and then >Alt-ENTER to get the DOS Windows >window... POW...your task will >likely die. So ... don't do that: > >Some DOS programs eat up to 50% >or 80% CPU time just sitting watching >for key strokes. Clearly, these should >be suspended when they don't >have the focus. A simple DOS >prompt, I have found, eats little time. > >Some web pages eat lots of time >(watching prompt boxes) while others >eat little (plain text or graphics with no links). > >It has been noted here before, you >can make a shortcut to Fractint.exe >and tailor its properties. I use in the >program tab: command line: > >FRACTINT.EXE textsafe=save sound=off > >Under the screen tab: Usage: Full >screen. Under Misc: Allow screen >saver=off. > >You should coordinate your DOS >windows according to what you are >doing. I often change the settings >for a short time, just to do some >other task." > >===================================== >> Let me clarify my last statement: In XP, both >> alt<tab> and alt<enter> shrink an image to >> the taskbar, and a doubleclick restores it >> to its original state. If I shrink a text page by >> either method though, the existing image is >> corrupted in the usual way. The H key is >> one way to restore the image. > > - Hal Lane hallane @ compuserve.com >================================== > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

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FOTD 14-07-03 (The Odd Way Out [4])
by Jim Muth 14 Jul '03

14 Jul '03

FOTD -- July 14, 2003 (Rating 4) Fractal visionaries and enthusiasts: The telephone problem here at Fractal Central has finally been fixed. The repairman got here this morning while the problem was evident, found the problem in the line and cured it. Murphy's law has been defeated -- at least for one time. Murphy's law is strange indeed. It never plagues other people. It does not work unless one is paying attention to it. It never works when the intent is to scientifically prove that it exists. Yet we all know that it does indeed exist, and is most likely to appear when it can wreak the most damage. It's a mystery. Today's fractal is no mystery. It's a picture of a hole deep in a valley of the Z^5+C Julibrot. Julibrots are four-dimensional things that contain holes. These holes are neither Mandeloid midgets nor Julia sets unless they are sliced in the Mandelbrot or Julia directions. Since today's scene is sliced in an oblique direction, it is nothing but a hole, perhaps more accurately described as a slit. But the spiral pattern around the hole, most of which has been cropped off, is almost intact, and is the same pattern we would see if the hole were sliced in the Mandel or Julia directions. When I named the image, I gave it the name "The Odd Way Out". I must have had a reason for choosing such an irrelevant name, but if so, the reason totally eludes me. I guess the meaning will have to take its place beside songs such as "Stairway to Heaven", which appear to have a hidden meaning, but most likely do not. Since I was several hours working with the phone man, I had little time to properly color the image, and as a result, it rates no higher than a 4. The render time of 16 minutes is slow, but can be avoided by downloading the already-rendered GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Sunday proved to be the most pleasant day of the summer here at Fractal Central, with deep blue skies, puffy white clouds, low humidity, and a temperature of 83F 28C. The dynamic fractal cats took full advantage of the pleasant conditions by spending several hours in the yard. When evening came, they settled into their resting places without complaint. But this morning, rain is once again in the area and more is forecast. The quality of the cats' day is yet to be determined. As for me, I've got work to do. Until next time, take care, and stay connected. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Odd_Way_Out { ; time=0:16:49.14--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=+0.00000000002679182/+0.000000000001065\ 41/1.118642e+011/0.01766/-2.2772331070925298/88.98\ 76619515795966 params=45/-120/5/0/0.29004780321703\ 86/0.7787549589942936/0.2900478032170386/0.7787549\ 589942936 float=y maxiter=2200 inside=0 logmap=570 periodicity=10 colors=000XU2XU1VV3UW4TX5SY6QY7PZ8O\ _AN`BMaCKaDJbEIcFHdHGeIEeJDfKCgLBhMAhN9iO9iP9iP9iQ\ 9iR9iR9iS9jS9jT8jU8jU8jV8jW8jW8kX8kX8kY8kZ7kZ7k_7k\ `7k`7la7la7lb7lc7lc6ld6le6me6mf6mf6mg6mh6mh6mi6mi9\ jfBhdEfaGd_JaXL_VNYTQWQSTOVRLXPJZNHaKEcICfG9hE7jC5\ iE6iG6iI6iK6iM7hO7hQ7hS7hU8hW8gY8g_8ga9gc9ge9fg9fi\ AfkAfmAfoAeoCeoEeoGenIdnKdnMdmOdmQcmScmTcmVcmXbmZb\ l`blbbldalfalhaljalk_igZgdYeaXcZV`WUZTTXPSVMQSJPQG\ OODNMAMK7OL6PL6QL6RL6SL6TL6UL6VL6XL5YL5ZL5_L5`L5aL\ 5bL5cL5bN6bO7bP7bQ8bR9bS9bTAbUBbVBbWCbXCaZDa_Ea`Ea\ aFabGacGadHaeHafIagJchUbiUbjUakUalT`mT`mT`mT_mS_lS\ ZlSZkRYkRYkRXjRXjQXiQWiQWhQVhPVhPUgPUgPUfOTfOTfOSe\ OSeNRcNRcNRbNT`OUYPVWQWTRYQSZPT_NU`LVbJWcIXdIYeHZf\ F_hF`iDbjBekAhm7kn4no3qp4tq6wp8zoAzoCznEznGzmIzmKz\ lMzlOzkQzkSzjUzjWziYzh_zhazgczgezfgzfizekzemzdmzdm\ zcmzcmzbmzamzamz`mz`mz_mz_mzZmzZmzYmzYmz } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

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Russ, More ideas for running Fractint under WinXP
by Harold Lane 14 Jul '03

14 Jul '03

================================== Russ, Thanks again for trying my suggestions and reporting their results. I had forgotten that Fractint.doc has some info in it for running Fractint under 'Windows'. WinXP was released after the Fractint Version 20.0 Documentation so their info (in the form of tips from users) may or may not apply. Note that some of the tips contradict each other - such as the usage of 'Always Suspend' and the versions of windows that the tips are intended for are not specified. Here is what I just found in the Fractint Version 20.0 Documentation that looks promising: ". . . textsafe=save . . . only works if Always suspend is turned ON." textsafe=save works on my Win98 machine without my having to turn ON 'Always Suspend' - however, I recommend that you give it a try. How to check the 'Always Suspend' box is in the docs (which I quote below). Also I recommend that you read the entire section on textsafe= in the docs. Here's an excerpt: ". . .'=save' tells Fractint to save/restore the entire image. Expanded or extended memory is used for the save if you have enough available; otherwise a temporary disk file is used." textsafe=BIOS or one of the other settings may possibly work. You'll never know if they fix your image corruption problem until you try them, though... Just to be clear on this: am I correct in thinking that switching between a fractal *image* in Fractint and the WinXP desktop and back again also corrupts the image? <==<< Also, if you remain in Fractint (without switching to the WinXP desktop) can you switch between a fractal image and a text screen and back without corruption? <==<< Does checking the box for 'Always Suspend' in conjunction with textsafe=save stop your image corruption? <==<< Also, I didn't specifically mention it, but in sstools.ini you need a line with [fractint] on it prior to the textsafe=save line. Without the [fractint] line Fractint will not recognize the textsafe=save command. I receive the Fractint mailing list in the digest form. Sometimes it is several days between times that I receive digests so my comments to you are not always as timely as they might be... ==================================== From the Fractint Version 20.0 Documentation: Damien M. Jones Windows tips: Damien M. Jones dmj(a)fractalus.com "This is what works for me. Your mileage may vary. Create a shortcut to FRACTINT.EXE, right-click it, choose Properties. On the Memory tab: set all five drop-downs to "Auto". On the Screen tab: choose Full-screen and Fast ROM emulation, leave Dynamic memory allocation OFF. Under the Misc tab: turn OFF Allow screen saver. Turn ON Always suspend. Set the Idle sensitivity to about 1/4, closest to Low. In the SSTOOLS.INI file, put textsafe=save on a line by itself in the [fractint] section. (This helps preserve your screen when you switch away from FractInt, but only works if Always suspend is turned ON.)" ------------------------------------ Jay Hill's Windows tips: Jay Hill ehill1(a)san.rr.com "For starters, make sure the DOS window properties are set to 'Misc | Always suspend' = off." Unless you want the task to stop when it does not have focus. Also, you can put the Idle Sensitivity to high. Make settings on any other DOS windows you have open according to what they should be (or what you prefer). If your DOS window is full screen, press Alt-Enter to make it a Window window. Then click on the MSDOS icon in the upper left. WARNING, don't do this in a high res graphics mode or in text mode (sometimes). The safest is F3 320x200 graphics mode. Windows likes that mode. If you have a high res image, hit 'X' to get the text screen and then Alt-ENTER to get the DOS Windows window... POW...your task will likely die. So ... don't do that: Some DOS programs eat up to 50% or 80% CPU time just sitting watching for key strokes. Clearly, these should be suspended when they don't have the focus. A simple DOS prompt, I have found, eats little time. Some web pages eat lots of time (watching prompt boxes) while others eat little (plain text or graphics with no links). It has been noted here before, you can make a shortcut to Fractint.exe and tailor its properties. I use in the program tab: command line: FRACTINT.EXE textsafe=save sound=off Under the screen tab: Usage: Full screen. Under Misc: Allow screen saver=off. You should coordinate your DOS windows according to what you are doing. I often change the settings for a short time, just to do some other task." ===================================== > Let me clarify my last statement: In XP, both > alt<tab> and alt<enter> shrink an image to > the taskbar, and a doubleclick restores it > to its original state. If I shrink a text page by > either method though, the existing image is > corrupted in the usual way. The H key is > one way to restore the image. - Hal Lane hallane @ compuserve.com ==================================

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FOTD 13-07-03 (They All Look The Same [4])
by Jim Muth 13 Jul '03

13 Jul '03

FOTD -- July 13, 2003 (Rating 4) Fractal visionaries and enthusiasts: The telephone repairman is due again in a few hours; the phone is working perfectly today. The repairman was not here yesterday; the phone was not working yesterday. I'm sure it's all random chance, but then . . . Today's not-so-great image exists in the Z^(sqrt(2))+C Mandeloid, as it appears 30 levels down the logarithmic spiral. This parent fractal is one of the more complex ones to come from this formula, consisting of multiple bays, buds and lengthy filaments. Today's scene lies on the longest filament just beyond the point where it is attached to its bud. While studying the image in search of a name, I thought of how many similar images I have seen, and gave the image the somewhat politically incorrect name "They All Look the Same". The rating of 4 is as good as I could do with the image that resulted from the day's less-than-fully-productive effort. And the 48 minutes it takes to render the image helps not a bit. Luckily for those with other things to do, the completed GIF image is available for download at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather was quite pleasant here at Fractal central on Saturday, with lots of sun and a temperature of 86F 30C. By the time the thunder-storm arrived at 7pm, with its wind and heavy rain, the cats had long since ended their day's romp in the yard, and had finished their evening treats. Today is starting the same as yesterday, so we'll have to wait to see how things work out for the dynamic duo. For me, I plan on a day of rest, but if I happen to get an unexpected burst of energy, I might think about trimming the fractal grass. Regardless of what happens, I'll return in 24 hours with fractal action and maybe more. Until then, take some care, but not too much care. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ TheyAllLookTheSame { ; time=0:48:17.76--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-1.53405979312308/+0.6071585299935/7290\ 88.4/1/-27.5/1.54267118523954139e-009 params=1.414\ 213562373/0/-30/0 float=y maxiter=4200 inside=0 logmap=1330 periodicity=10 colors=0008Uc8dc9ec9ec9fc9fc9gcAhcAhcAicAicAjcBkcB\ kcBlcBlcBmc9neBmcDlbEk`Gj_HiZJiXLhWMgVOfTPeSReRSdP\ UcOWbNXaLZaK_`Ia_HcZGdYEfYDgXCiWAjV9lU8nU6oT5qS4rR\ 2tQ1uQ0tP2tP3tP4sP6sO7sO8sOArOBrNCrNErNFqNGqMIqMJq\ MKpMLpLNpLOpLPoLRoLSoKTnKVnKWnKXnJZmJ_mJ`mJamIclId\ lIelIglHhkHikHkkHlkGmjGojGpjGqjGriFqhFqgFqfFqeFpdF\ pcFpbFpbFpaFo`Eo_EoZEoYEoXEnWEnWEnVEnUEmTEmSEmRDmQ\ DmPDlODlODlNDlMDlLDkKDkJDkICkHCjHCjGCjFCjECjDCiCCi\ BCiACiACiBBhCBgDBgDBfEBfFBeFBeGBdHAdHAcIAcJAbKAbKA\ aLAaMA`M9_N9_O9ZO9ZP9YQ9YQ9XR9XS8WT8WT8VU8VV8UV8UW\ 8TX8TX7SY7RY7RW7QR7QR7PT7PU7OW6OY6NZ6N`6Mb6Mc6Le6L\ g6Ke1Lf4Kg6Kh9KhBJiDJjGJjIJkLIlNImPImSHnUHoWHoZHp`\ GqcGreGrgFsjFtlFupDtoEtnFsnGsmHslHrlIrkJrjKqjLqiMq\ hNphOpgPpgQofRoeSneTndUncVmcWmbXmaYlaZl`_l_`k_akZb\ kZcjYdjXeiXfiWgiVhhVihUjhTkgTlgSmgRnfRofQpfQqePseO\ udOwdNycNzcNzcNzcNzcNzcNz } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END 20.0 PAR-FORMULA FILE==================================

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FOTD 12-07-03 (Crazy Cubical [5])
by Jim Muth 12 Jul '03

12 Jul '03

FOTD -- July 12, 2003 (Rating 5) Fractal visionaries and enthusiasts: The on-again, off-again fractal telephone is still on and off. It's working when the repairman is here and out of order when he's away. Since it works 90-percent of the time, the thing to do seems to be wait until it works zero-percent of the time, whenever that may be, so that the repairman will have something to repair. While I'm waiting for the phone to break completely so that it can be repaired completely, I'll amuse myself by wandering through the world of fractals. Today's image takes us to the Julibrot of the formula (-Z^3)+C, where we enter the fourth dimension to examine one of the cubical midgets from an unimaginable angle. I named the scene that I found there "Crazy Cubical", because, though it is a perfectly normal cubical Mandeloid midget when viewed in the Mandel orientation, it is little more than a narrow slit when viewed in the direction of today's image. It's an average image with an average rating of 5. It's also a fast image with a render time of under 4 minutes. And best of all, the completed GIF file is available for downloading on the internet at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The Friday weather was good enough here at Fractal Central, with lots of sun and a temperature of 86F 30C. A brief heavy shower passed over in the middle of the afternoon, but the fractal cats took it in stride, retreating indoors until the sun reappeared. When the day ended, the duo was happy. I'll be happy when I know that today has gone well, but even if it does, there is always tomorrow. So until then, take care, and be fractally correct. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Crazy_Cubical { ; time=0:03:48.11--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=multimin-XZ-YW-new passes=1 center-mag=-0.0/+0.0/6.12554e+007/0.01488/-5.33864\ 982303061897/-72.6208733939061801 params=-106.2/42\ .5/3/0/-0.939409509662/0.233374120602/-0.939409509\ 622/0.233374120602 float=y maxiter=1600 inside=0 logmap=126 periodicity=10 colors=000PekPbhP_ePXbPUZKRWFOTALQAINLLRVOVdRYjTao\ WdtZhz`kz_jz_jzZjwZjtYjmYjdXiaXiZWiWWiTViQViOViNTb\ NSWNRPNQINPBNO5SQGXSQaU`fWjkYtgZpd_la`iZ`eWaaTbZQb\ VNcSKdOHdKEeHBfD8fA7eB7dB7cB7bB7aB7`C7_C7ZC7YC7XC7\ WD7VD7UU7TX7S_7RbDTbJUePVjJLZECK935JEESOM`YVigbeaS\ aXIZS8WRBUQERPHPOKMOMKNPHMSFLVCKYAK_7Jb5Ie2Hh0Hj1L\ e1Oa1SY1VU1ZQ1aM1eI1hE1kA5fC8aDCYEFTFJPGMKHQFITBJX\ 6K_2LZ7MYCNXHOWMOVRPUWQT`RSeRRjSQoTPsTOmSOhSOcSOZS\ OUSNOSNJSNESN9SN4SR9PVDNYHLaLIdPGhTEkXBo`9rd7oeBle\ FieJfeNceR`eVZfYWfaTfeQfiNfmKfqIftKeqLenMdkNdhPdeQ\ cbRc_ScXU`WVYVW_UYaTZcS_eRagQbiPckOdmNfoagqogsoEub\ QwaUxgZz`czVhzYmz_rzbwzdzzfzzizzkzzmzzjzzhzzezzczz\ azzczzdzzezzgzzhzzizzjzzlzzmzznzzpzzqzzrzzszznzziz\ zdzz_zzVzzQzzLzzGzzKzzOzzSzzWzz_zzczzgzzfzzezzdzzd\ zzczzbzzbzzdzzfzzhzzizzkzzmzznzzpzzrzzszzmzzgzzazz\ XzzRzzLzzFzzAzzIzzPzzOzzO } frm:multimin-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=(-z)^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 11-07-03 (Madhouse-2 [4])
by Jim Muth 11 Jul '03

11 Jul '03

FOTD -- July 11, 2003 (Rating 4) Fractal visionaries and enthusiasts: With the fractal phones still off and on, Thursday was another day of hectic scrambling. The problem on the line is an intermittent short, and as any repair person knows, this gives Murphy's law a perfect chance to work. When the repairman is here, the phone works perfectly and he has nothing to repair. If he hangs around an hour, waiting for the problem to re- appear, the phone continues working. But when he leaves . . . Oh well, eventually it will be fixed . . . I hope . . . Today's fractal is a very short trip to one of the first fractals of all -- the Mandelbrot set. The location is the East Valley area of the large midget on the main stem. Yes, I realize that Julia sets had been known to exist long before Mr. Mandelbrot did his work, but the M-set is the first fractal I knew of, and it will always be the number-one fractal -- the simplest yet most complex fractal of all. I named today's image "Madhouse-2", though it is far less disorganized than yesterday's chaotic image. From the way things are going around here, I expect a few more 'madhouse' images before we move on to better things. The rating of 4 is a run-of-the-mill rating for a run-of-the-mill fractal. Luckily, the render time is almost instantaneous. The finished GIF image is available for download on the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> It stayed cloudy all day Thursday here at Fractal Central. The clouds held the temperature to a very damp 79F 26C. The cats had a few pleasant minutes in the yard. The rest of the time they were sulky. With the fractal phones still marginal, I'll have another hectic day. But if nature permits, I'll return in 24 hours with the next in the unending series of Fractals of the Day. Until next time, take care, and fractals will work for food. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Madhouse-2 { ; time=0:00:05.88--SF5 on a P200 reset=2002 type=mandel center-mag=-1.74333620875472300/+0.00/3.137409e+012 params=0/0 float=y maxiter=1200 inside=0 symmetry=xaxis periodicity=10 mathtolerance=/1 colors=0000c00c00c00c00c00A00AA3AK2AL2AM2AN2AP2AQ2\ AR29T29U28V27X26Y26Z25d24a24j2Lz2az2qz7kMBeKF_IJUH\ LMMNEQPFORGNSGMUHLVHKXIJZII_JHaJGbKFdKEfLDgLCiMBjM\ AkOBkPBkQCkSCkTDkUDkVDjTCjSBiQAiP9hN8hM7gK6gJ5fH4f\ G3fF2gJ3gM4gQ4gT5gW5g_6gb6he7hi8hl8ho9hs9hvAhyAcwB\ ZvBVuBQtCLsCHrCGmBFiAFe9Ea8EX7DT6DP5CL4CH3JM8QQDXV\ IcZMjcRqgWxk_whZwfZwdZwbZw`ZvYYvWYvUYvSYvQYvOYpWZk\ c_fk`asaXzbVy`UyZTyXRyWQyUPySNyRMyPLyNJyMIyKHyIGyH\ LqLPjPUbTYWXaP`fHdjAhn3khthesfbsd_rbXraVr_SqYPqXMq\ VJpTHpREpQBoO8oM6oL7mM7lM7jN7iN7hO7fO7eP7cP7bQ7aQ4\ `SBhKIoCPv4Oq5Nm5Mh5Md5L_5KW5KS5HV6FY6C`6Ac68f65i6\ 3l61n6fVFkPVpJiuExvHqvJjwLcwNXxPQxRKtQNqPQnOTjOVgN\ YdM`aMbYLeVKhSJkOJmLIpIHsFHuIEpLCkOAfR7aU5XX3SY5UY\ 6VZ7WZ9XZAY_BZ_D_`E``Fa`GbUCSN8IG58K49N49R4AU4AY4B\ `4Bd3Cg3Ck3Dn3Dr3Eu3Ec1ZM0rJ4lH8fFBaDFWBJQ9ML7QF5U\ 93X46Z49`4Bb4Ed4Gf4NkfOie } END PARAMETER FILE=========================================

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Re: [Fractint] Russ, Would you please try the following? Thanks...
by Russell Walsmith 11 Jul '03

11 Jul '03

Let me clarify my last statement: In XP, both alt<tab> and alt<enter> shrink an image to the taskbar, and a doubleclick restores it to its original state. If I shrink a text page by either method though, the existing image is corrupted in the usual way. The H key is one way to restore the image. -- --------- Original Message --------- DATE: Thu, 10 Jul 2003 08:56:56 From: Harold Lane <hallane(a)compuserve.com> To: Fractint <fractint(a)mailman.xmission.com> Cc: >=============================================== >Russ, > Thanks for letting me know what happens >when you use <Alt>Enter to cycle DOS >window maximization in Win XP when going >back and forth between Fractint and the >Win XP desktop. > > Would you please try the following to see >if it will avoid corrupting your Fractint >image and Win XP desktop when switching >between Fractint and WinXP? >Thanks in advance... > > - IMPORTANT! Put textsafe=save into > sstools.ini > - Run Fractint your usual way > - Begin to calculate an image (use SF7) > - View a text screen in Fractint (hit Tab > while calculating or viewing the image) > - Type the key combination <Alt>Enter to > change the full screen text to windowed > text. > >Use Windows XP normally. > > - Click on the Fractint window to select it > - Type the key combination <Alt>Enter to > change the windowed text to full screen. > - Hit Tab again and you will be back to > calculating your image. > >The key idea here is that the switching between >DOS and Win XP will be done from a DOS >*text* screen, which should be easier for XP >to get right. Also, if I understand >textsafe=save correctly, your image will be >written to a temporary file when you switch >to the text screen so the video mode >associated with the image will not be >involved in the window context switching >at all. > >Are the image and your desktop still >corrupted when you use this >procedure? <==<< > >If this procedure no longer corrupts the >image and desktop, does it work in both >Home and Pro versions of Win XP? <==<< > > - Hal Lane hallane @ compuserve.com > >=============================================== >> > <======<< <======<< <======<< >> >Will an XP user please let me know if the >> ><Alt>Enter key combination is still bound >> >to the action of switching between a >> >windowed and full screen **DOS** text >> >window? >> > <======<< <======<< <======<< > >> Yes, but a return to full screen eventually takes both >> my XP Home desktop and XP Pro laptop to a partially >> rendered and sometimes slightly garbled fractal image >> (in SF7 video mode). > >> Ciao, Russ >=============================================== > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

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Re: [Fractint] Russ, Would you please try the following? Thanks...
by Russell Walsmith 11 Jul '03

11 Jul '03

Hal, I've tried your suggestion on my desktop (where the only difference from my earlier procedure was the insertion of textsafe=save into sstools.ini), but there is no discernable change. I.e., when I return to the fractal image, the lower 2/3 of the screen is black and the upper 1/2 is corrupted by closely spaced vertical lines. But alt<tab> shrinks Fractint to the taskbar, where a double click then restores a perfect image. Ciao, Russ -- --------- Original Message --------- DATE: Thu, 10 Jul 2003 08:56:56 From: Harold Lane <hallane(a)compuserve.com> To: Fractint <fractint(a)mailman.xmission.com> Cc: >=============================================== >Russ, > Thanks for letting me know what happens >when you use <Alt>Enter to cycle DOS >window maximization in Win XP when going >back and forth between Fractint and the >Win XP desktop. > > Would you please try the following to see >if it will avoid corrupting your Fractint >image and Win XP desktop when switching >between Fractint and WinXP? >Thanks in advance... > > - IMPORTANT! Put textsafe=save into > sstools.ini > - Run Fractint your usual way > - Begin to calculate an image (use SF7) > - View a text screen in Fractint (hit Tab > while calculating or viewing the image) > - Type the key combination <Alt>Enter to > change the full screen text to windowed > text. > >Use Windows XP normally. > > - Click on the Fractint window to select it > - Type the key combination <Alt>Enter to > change the windowed text to full screen. > - Hit Tab again and you will be back to > calculating your image. > >The key idea here is that the switching between >DOS and Win XP will be done from a DOS >*text* screen, which should be easier for XP >to get right. Also, if I understand >textsafe=save correctly, your image will be >written to a temporary file when you switch >to the text screen so the video mode >associated with the image will not be >involved in the window context switching >at all. > >Are the image and your desktop still >corrupted when you use this >procedure? <==<< > >If this procedure no longer corrupts the >image and desktop, does it work in both >Home and Pro versions of Win XP? <==<< > > - Hal Lane hallane @ compuserve.com > >=============================================== >> > <======<< <======<< <======<< >> >Will an XP user please let me know if the >> ><Alt>Enter key combination is still bound >> >to the action of switching between a >> >windowed and full screen **DOS** text >> >window? >> > <======<< <======<< <======<< > >> Yes, but a return to full screen eventually takes both >> my XP Home desktop and XP Pro laptop to a partially >> rendered and sometimes slightly garbled fractal image >> (in SF7 video mode). > >> Ciao, Russ >=============================================== > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

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FOTD 10-07-03 (Madhouse [4])
by JimMuth＠aol.com 10 Jul '03

10 Jul '03

FOTD -- July 10, 2003 (Rating 4) Fractal visionaries and enthusiasts: Well, the fractal phone is still not working and the place is still a madhouse. It's an intermittent problem that appears only when the repairman is not here. Today's fractal has accordingly been named "Madhouse". It features a pathetic remnant of a midget and no order at all. I rated it a 4 because it's not very good. Luckily, it's a quick one. And downloading the image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> is even faster. The cats were cranky on Wednesday and so was the fractalist. The next FOTD will hopefully appear in 24 hours. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Madhouse { ; time=0:02:49.88--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=39.8495/-25.2642/0.1510465/1/-137.5/-5.\ 05012698326368081e-014 params=0.905/1.5/-1/-1.5/-0\ .15/0/0/0 float=y maxiter=3000 inside=255 logmap=28 periodicity=10 colors=000d6Wb5Va5U`5TZ5SY5RX5QW5QUBUTGYRLaQRdOWhN\ `lLfoKksIpwHtzIrwJotKlqLinMfkNchO`ePYcQV`RSYSPVTMS\ UJPVGMWEKZOLaYMdfNgpOjyPhuQgrRfoSdlTciUbfVabW__XZX\ YYUZWR_VO`UKaTHbREcQBdP8eO5eP8gPAhPDiPFjQHkQKlQMmQ\ OoRRpRTqRVrRYsR_tSbuSdwSfxSiyTkzTmzTpzTrzTtzVopWjb\ XePY`CkebkchjIomKjoLfqMbtNZvOVxPRzQNzRJzSFzTBtUHhV\ MWWSKWXNT_QQaTNcWKeZIgXJfWJfVKfUKfTLfRLeQMePMeONeN\ NeMOeKOdJPdIPdHQdGQdFQdESbETaEV`EW_EXZEZYE_XD`VDbU\ DcTDdSDfRDgQDhPIdXN`cSXkXTraQjyXjwYjvZjuZjs_lr_nq`\ pp`rnatmavlbxkbziazhazfazeazcazbaz`az_azYazXazVazU\ `zS`zR`zP`zO`zM`zL`zJ`zI`zG`zF`zE`zF_zFZzFZzFYzFYz\ FXzFWzFWzFVzFVzFUzFTzFTzFSzFSzFRzFQzFQzFPzFPzFOzFO\ zLPzRQzWQzaRzgSzlSzrTzxUzzUzzWzwYzt_zq`znbzkdziezf\ gzciz`jzYlzVnzSpzQqzNszKuzHvzExzBzz9zzCxzEvzGtzIqz\ KozMmzOkzQhzSfzUdzXazZ_z`YzbWzdTzfRzhPzjMzlKznIzpG\ zmIzjJzgKzdLzaNz_OzXPzzzp } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Russ, Would you please try the following? Thanks...
by Harold Lane 10 Jul '03

10 Jul '03

=============================================== Russ, Thanks for letting me know what happens when you use <Alt>Enter to cycle DOS window maximization in Win XP when going back and forth between Fractint and the Win XP desktop. Would you please try the following to see if it will avoid corrupting your Fractint image and Win XP desktop when switching between Fractint and WinXP? Thanks in advance... - IMPORTANT! Put textsafe=save into sstools.ini - Run Fractint your usual way - Begin to calculate an image (use SF7) - View a text screen in Fractint (hit Tab while calculating or viewing the image) - Type the key combination <Alt>Enter to change the full screen text to windowed text. Use Windows XP normally. - Click on the Fractint window to select it - Type the key combination <Alt>Enter to change the windowed text to full screen. - Hit Tab again and you will be back to calculating your image. The key idea here is that the switching between DOS and Win XP will be done from a DOS *text* screen, which should be easier for XP to get right. Also, if I understand textsafe=save correctly, your image will be written to a temporary file when you switch to the text screen so the video mode associated with the image will not be involved in the window context switching at all. Are the image and your desktop still corrupted when you use this procedure? <==<< If this procedure no longer corrupts the image and desktop, does it work in both Home and Pro versions of Win XP? <==<< - Hal Lane hallane @ compuserve.com =============================================== > > <======<< <======<< <======<< > >Will an XP user please let me know if the > ><Alt>Enter key combination is still bound > >to the action of switching between a > >windowed and full screen **DOS** text > >window? > > <======<< <======<< <======<< > Yes, but a return to full screen eventually takes both > my XP Home desktop and XP Pro laptop to a partially > rendered and sometimes slightly garbled fractal image > (in SF7 video mode). > Ciao, Russ ===============================================

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Versions of DOS to run Fractint under
by Harold Lane 10 Jul '03

10 Jul '03

========================================= Kevin, Fractint doesn't need to be on the same floppy that boots DOS. Put Fractint 20.0 and its fractint.cfg on a separate 1.4MB floppy. One would want to boot DOS from a floppy and read Fractint from a 2nd floppy only for the purpose of establishing whether you are having problems with you video hardware or just with the XP video drivers. I also recommend putting textsafe=save into a SSTOOLS.INI file on the same floppy as Fractint since it is the most conservative and thus most likely to work method of insuring nondestructive text and video image swapping. If you do not need the version of DOS that you boot to be able to read your hard drive (as in the scenario above) any relatively recent version of DOS should do. (Say, 4.0 on thru the DOSes that come with Win 9X.) If you want DOS to be able to read a FAT32 partition on your hard drive (as in the scenario that Tim Wegner described and I copied below) you need the DOS from Win98 or a DOS specially written to have this capability. I am not certain, but I assume that Win ME has a DOS that can read FAT32. The DOS from Win95 and earlier DOSes cannot read FAT32. And Windows NT and 2000 have no DOS. An afterthought - laptops often have non-standard video hardware so one can expect to find a few more problems and fewer working compatible video modes than found in the video hardware in desktops. For a good overview of Fractint and video hardware see Noel Giffin's: http://spanky.triumf.ca/www/fractint/hardware_modes.html You will probably want to run Makefcfg (that comes with fractint) from DOS (put it on the floppy with Fractint or on a separate floppy) to have it create a fractint.cfg file compatible with your video hardware. "Makefcfg 1.0 -- A Fractint video utility by The Stone Soup Group" "Makefcfg reads your VESA Video BIOS and writes a Fractint fractint.cfg file with VESA video modes set up." Re Tim's recommendation to "Make a FAT32 partition for fractint"... I recommend that you use Partition Commander or Partition Magic to do this. DOS's FDISK will delete Win XP if you attempt to create a FAT32 partition on your existing hard drive. You also wrote: > ...in the standard video setting, I get an image, then > garbage when I try to leave it. If I set textsave=safe, I > cannot leave it. I can use the windows key to switch out, > and when I go back to fractint, the image is still there. On my Gateway desktop machine running Win98 to safely go between a running copy of Fractint and back to the Windows desktop I: - Put textsafe=save into sstools.ini - View any text screen in Fractint (say, hit Tab while calculating an image) - Type the key combination <Alt>Enter to change the fullscreen text to a window. I can then use my Windows normally. - Click on the window title bar to select the window (rather than in its interior) when you want to go back to Fractint. - Type the key combination <Alt>Enter to change the windowed text to full screen. - Hit Tab again and you are back to calculating your image. Note that Fractint does not contine calculating your image while you are viewing the Tab or X screens. I do not know if this method will work under Win XP I but offer it as something that works consistantly in Win98 for me and might possibly be of help in Win XP. If I don't adhere strictly to the above, the video in Fractint is corrupted or the Fractint task is terminated by Win98. <======<< <======<< <======<< Will an XP user please let me know if the <Alt>Enter key combination is still bound to the action of switching between a windowed and full screen **DOS** text window? <======<< <======<< <======<< The only way I have been able to figure out how to have Fractint continue calculating an image while I am using my machine for other windowed tasks is to use a Disk Video mode. After starting a fractal calculation in Disk Video mode I then use <Alt>Enter to make the text mode Disk Video window of Fractint a window on my desktop. I move the window to where I can see the status message: "Image has been completed" when is done. I have had a dozen copies of Fractint calculating Disk Video images at the same time successfully with no problems other than a decrease in Windows' responsiveness. =============================================== >Kevin asked: >> Ok what dos either can read NTFS or fit with fractint on a floppy? Tim Wegner replied: >Make a FAT32 partition for fractint and keep Fractint there. This >will be accessible under XP but also under DOS. You could then dual >boot or boot from a floppy, and run Fractint off the hard drive in >the FAT32 partition. - Hal Lane hallane @ compuserve.com ===============================================

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No FOTD for July 09, 2003
by Jim Muth 10 Jul '03

10 Jul '03

With unexpected work, telephone repairmen climbing all over the place, cranky cats and severe storms forecast, there is just no time to find a fractal for July 09. The FOTD for July 10 will most likely appear on schedule. Sorry, fractal fans. Jim M.

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Re: [Fractint] Versions of DOS to run Fractint under
by Russell Walsmith 09 Jul '03

09 Jul '03

--------- Original Message --------- DATE: Wed, 9 Jul 2003 12:29:40 From: Harold Lane <hallane(a)compuserve.com> To: Fractint <fractint(a)mailman.xmission.com> Cc: > <======<< <======<< <======<< >Will an XP user please let me know if the ><Alt>Enter key combination is still bound >to the action of switching between a >windowed and full screen **DOS** text >window? > <======<< <======<< <======<< Yes, but a return to full screen eventually takes both my XP Home desktop and XP Pro laptop to a partially rendered and sometimes slightly garbled fractal image (in SF7 video mode). Ciao, Russ

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Source Editors
by Programmer Dude 08 Jul '03

08 Jul '03

Tim Wegner wrote: >> And, sorry, it's not for me. I'm a vi guy. > > So am I, but I'll have you know that many tens of thousands of lines > of Fractint's code were typed in using Wordstar under DOS :-) Ah, an old, old friend! WordStar was my first serious editor, too! My folks made me take a typing course, so the "hands-in-home-position" paradigm of WordStar was a joy for me. I used WordPerfect a lot, too (my cousin was really into it, and it was used in my company as well), but that was all Function keys. I later found the "best" MS-DOS editor: QEdit. Multiple split screens, macros, user-configurable....it was my primary editor for many, many years (didn't have to remember to "Save As Text"). > I even had to write a little utility to strip out the ^Z at the > bottom oif each file I edited ... You know, I think I wrote one of those, too! > I'm not sure about Jonathan, but if memory serves Bert Tyler used > Wordstar also. I have never found another editor that does column > block operations as well as Wordstar. QEdit did. And QEdit was freeware! ;-) -- |_ CJSonnack <Chris(a)Sonnack.com> _____________| How's my programming? | |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | |_____________________________________________|_______________________|

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re: FOTD 08-07-03 (Cellular Fractal [6])
by Programmer Dude 08 Jul '03

08 Jul '03

Jim Muth wrote: > My day will be better if they can get the fractal phone fixed > sometime today and keep it fixed this time. Until then, I have > the use of another phone and ample other work to distract me > from the bumbling attempts at phone repair. Isn't that a little unkind? Do you *know* they are "bumbling" attempts? Or could they be skilled attempts faced with difficult conditions? -- |_ CJSonnack <Chris(a)Sonnack.com> _____________| How's my programming? | |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | |_____________________________________________|_______________________|

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FOTD 08-07-03 (Cellular Fractal [6])
by Jim Muth 08 Jul '03

08 Jul '03

FOTD -- July 08, 2003 (Rating 6) Fractal visionaries and enthusiasts: The fractal phone, which had just been repaired, went out again Monday afternoon. When I last checked, it was still not working. As a result, I had to use an alternate connection and today's FOTD is once again late. The parent fractal is an impossible-to-describe, oversized nest of bays and pieces with X-axis symmetry, produced when 9 parts of Z^(-2.1) are subtracted from 9 parts of Z^(-1.9). A long, looping, zig-zagging filament extends east of the main action. Today's scene is located very close to the point where this filament crosses the X-axis. When rendered in the traditional manner, with the outside colored according to the iteration count, today's image is . . . well, all right. When rendered with the outside colored by the 'tdis' option, today's image reaches FOTD status, and rates a 6, which equals a bit above average. When studying the image in search of a name, I was still annoyed by the out-of-service telephone. In my state of mind, I saw in the image the cells of a cellular phone system, which do not always switch as smoothly as they were originally supposed to do. I named the image "Cellular Fractal". Luckily, the attached parameter file runs smoother than a cellular phone switches cells, and it runs in 3-1/2 minutes. With a good cellular connection, or a working wire connection, the finished GIF file can be downloaded in even less time from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The hot sun and temperature of 91F 28C here at Fractal Central on Monday was good enough to give the dynamic fractal cats a generous outing in the yard and an exciting adventure in the surrounding brush. For a brief period, a storm threatened, but passed by harmlessly to the south, permitting the duo to finish their afternoon of fun. Today looks like a repeat. Could the duo possibly have three good days in a row? My day will be better if they can get the fractal phone fixed sometime today and keep it fixed this time. Until then, I have the use of another phone and ample other work to distract me from the bumbling attempts at phone repair. Regardless, I'll return in 24 or so hours with another FOTD. Until then, take care, and maybe this second outage is not the phone company's fault. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Cellular_Fractal { ; time=0:03:37.67--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+3.81765632548784200/+0.000422484324479\ 60/2.134992e+010/1/-140/-0.0521980194412531157 params=9/-1.9/-9/-2.1/0/0 float=y maxiter=600 inside=0 outside=tdis periodicity=10 colors=000Xo8Xo4Xq2Xs0Xs0Xu0Vu0Vv0Vv0Vx0Vx0Vz0Vz0`\ z0dz0iz0mz0qz0vz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0\ zo0ze2zVEvLPiA`Z0kN0vC0zH0zN0zT0zX0zb2zg6zkCzqGzvJ\ zzPzzTzzXzzbzzezzizzozzszzvzzzzzuzzqzzmzzizzezzbzz\ ZzzVzzRzzNzzJzzGzvCzs8zq4zs6zu6zv6zx8zz8zz8xzCvzHs\ zLqzPozTmzXiz`gzdezibzm`zqZzuXzxTzzRzzPzzNzzRzzTzz\ XzxZzvbzudzqgzoizmmzkozgszeuzdvz`zzZzzXzzVzzRzzPzz\ NzzJzzHzzGzzEzzAzz8zz6zx2zu0zs0zo0zm0zi0zg0zd0zb0z\ Z0xX0vT0uR0sP0oP0mN0kN0gL0eL0dL0`J0ZJ0XH0TH2RG4PG6\ LG8JECHEEECGCCJAAL6AN4AP28R48R46T66T66V64V84X82XA2\ ZA2ZA0`C0`C0bE0bE0bE6dCEeALg8Ti6Zk6em4mm2uo0zq0zs0\ zu0zv0zx0zx0zz0zz0zz0zz0zz0zz2zz4zz4zz6xz8uzAqzAmz\ CizEezGbzGizNozTvz`zzezvkzsszoxzmzzeuzZkzRbzJTzCJz\ 4Az00zZezzzzzzzzzzzvzzozzezzZuzRozJizCqzHvzLzoPzdT\ zRXzG`z2dz0gz0kz0bz0Vg0LP0E60640A40C`ei`ee`eb`e``e\ X`eVZgRZiPZiLZkJZkGZmEXmA } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Port to java
by Thaddaeus Parker 07 Jul '03

07 Jul '03

To all: I have a question concerning the different ports that Spanky has ongoing. Are there any efforts to port the awesomeness of Fractint over to Java? I see NT, Linux, and a few others, but I am curious about utilizing the cross platform capability of Java to enhance the Fractint feel. Has the Stone Soup Group thought about it? Or would a port to Java be too inhibitive? Your thoughts? T. Parker

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FOTD 07-07-03 (Rings [4])
by JimMuth＠aol.com 07 Jul '03

07 Jul '03

FOTD -- July 07, 2003 (Rating 4) Fractal visionaries and enthusiasts: Due to heavy weather at Fractal Central last evening, today's FOTD is both late and brief. What do you get if you subtract Z^2.1 from Z^1.9? You get a Mandelbrot set that is splitting up, but does not know which way to split. In addition to being rotated 180 degrees, the figure has two main stems, and East Valley, now on the west side, has split into two separate valleys, with a broad area between them containing a whole new world. Today's scene is located in a basin rather deep in the northern half of East Valley. With little thought, I named today's image "Rings". Then I rated it at a 4. The rating of 4 is honest. There is little in the image that has not been seen many times before, and I gave little effort to the coloring. The slow render time of 46 minutes is mostly due to the high maxiter of most of the elements of the image. But this 3/4 hour wait can be avoided by downloading the finished GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Sunday was sunny and hot here at Fractal Central, with a temperature of 93F 34C, giving the dynamic cats a lazy afternoon in the yard. But at sunset a severe thunder-storm moved in, cutting both power and phone service. The power was back on within three hours, but the phone was out until 3pm today. I've still got a bit of work to get caught up on, so until next FOTD, take care, and enjoy fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Rings { ; time=0:46:10.66--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.10603072257787430/+0.687760382223484\ 00/3122560/1/107.5/3.88578058618804789e-016 params=1/1.9/-1/2.1/0/0 float=y maxiter=12000 inside=0 logmap=817 periodicity=10 colors=000VOdXPh_QlaRpeRucSsaSq`TpZTnYTlWUkVUiTVhR\ VfQVdOWcNWaLX`KXZIXXGYWFYUDZTCZRAZP9_O7_M6_L7ZN8ZO\ 8YP9YQAXRAXSBXTCWUCWVDVXDVYEUZFU_FU`GTaHTbHScISdJR\ dISeISeHTfHTfGUgGUgFVhFVhFWiEWiEXjDXjDYkCYkCZlCZlB\ _mB_mA`nA`n9ao9ao9ao8bi7bd7c_6cV7eR6cQ6bP6aO6`N6_N\ 6ZM6YL6XK6WK6UJ6TI6SH6RG6QG6PF6OE6ND4LC6MD8ME9NEBN\ FCOFEOGFPGHPHJQIKQIMRJNRJPSKQSKSTLUTMVUMXUNYVN_VO`\ WObWPcWP__SXbVUeYQh`NlcKofGriDul9ypAxnBwmCvkDujEth\ FsgGreHqdIpbJoaKn`LmZMlYNkWOjVPiTQhSRgQSfPTeNUdMUd\ MVdLciFln9zz1ww3rr5sm7qc9pZBo`DmOFlJHkEJk0Oj9LZIIM\ mF8hDAgCCcCEZCGUBIPBKKBM_AO_AQ_AS_9h_9m_9m_8r_8m_A\ haKccUYecXfmWgmVchT_hSYhRUhQPhPKhO9hP8hQ8hQ7hR7hS6\ hS6hT5hA56A45A44A34A33A22A22A11A11AB6AOBAUFAUKCUTE\ UOGUJKUFURIcULcXOc_RcbTceWchZckacnccqfctiGwlGzrEzn\ DzjczfczbczZczVczRczRczNczKCzHFzDIzAJz5Kz7Lz9LzBMz\ DMzFNzHOzJOzLPzNOzUQzYTza } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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fractint and a newer laptop
by Kevin Sexton 07 Jul '03

07 Jul '03

Anybody been able to get fractint to work on a newer xp laptop? I could try disk video, but haven't worked that out. Trying some of the basic modes the fractal is drawn, but then when I go back to the text screen I get scrambling, when I force fractint to close, explorer is scrambled. I was going to keep trying modes until something worked, but on one, the fractal never went away, and forced a power reset to get out. I'm trying manpwin, and this computer is pretty fast to the limits of the program, but I'd like to get to locations others have found with fractint, and fractal types in fractint.

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Re: fractint and a newer laptop
by Bill Jemison 07 Jul '03

07 Jul '03

<< If I set textsave=safe, ...>> It should be textsafe=save

3 2

Multifractal_6
by Albrecht.Niekamp＠t-online.de 06 Jul '03

06 Jul '03

Hi, a lot of changes and new options this time. 1. All channels now have an own input, which is referred to by name, no shared inputs anymore. This means all formulas can be tested without doing any changes except imag(p2) as explained. Use the second input to alternately use an (almost) basic mandel (channel1) or julia (channel2) instead of the default frms. If you want to test a formula exclusively, just type the number followed by four zeros as first input. 2. Just add 5 to the secondary inputs after the 2digits many_mods input to activate the warp-effect separetely for each channel. This is useful in many instances f.e. to change the looks of the inside/outside images and to preserve the julia settings. Add 5 to the primary inputs to do a reset for each channel. This causes that the in/outside image is adjusted to the screen instead of the surroundings. This also works if the warp-effect is shut off, test it. 3. For simplicity reasons "ismand" is not used anymore, so one more line of the text is displayed and the inputs are not ambivalent anymore. 4. A new mixing formula "Secant" is available as default channel one. Check the first par to see what it looks like. In order to go on with this I need some feedback, so I know what Iïm doing this for. So please post your images and your comments. I regard this as a "living" process on the way to perfection, I still have some ideas and critics should help to improve it. Dont hesitate to play around with multifractal, if youïre interested. Youïll see that itïs fun and quite easy once the basics are understood. An easy tweak is to use other functions, fn1 if bees or many_mods is used, the other ones to affect the warp effects. Cosxx will create weird effects in many cases. Fractal greetings, Al. ----------------------------start-par------------------------------------- Mandelbug { ; Albrecht Niekamp July, 03 ; Outside secant inside newton\bees\julia ; Time 0.18.47.56 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult244.frm formulaname=multifractal_6 function=cos/exp/exp/cos passes=t center-mag=0.420263/4.44089e-016/1.718213/1/-90/3.88578058618804789e-016 params=0.8202154606769005/-0.06207464827417833/11972.3215501/5040.060802\ 1613/4084.02048/384.000004/768.00024/128.00768/384.00768/768.00768000000\ 01 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200000<3>764985BA6DC7FE8<17>niQpjRrlS<3>ysX<25>BB7996775<3>000<24\ >n00p00r00<3>y00<25>B00900700<3>000<2>455677899ABBBCC<18>hiijkkkll<3>rss\ <21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<30>022 } ---------------------------------end--------------------------------------- Gran_canyon { ; inside mandel,mandel,julia ; Albrecht Niekamp July, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult244.frm formulaname=multifractal_6 function=cos/exp/exp/cosxx passes=t center-mag=1.10912/0.314452/26.9208/1/-90/3.88578058618804789e-016 params=0.8202154606769005/-0.06207464827417833/10667.3210111/2543.060802\ 1613/4084.02048/384.0000076/768.00024/128.0076800000001/384.007680000000\ 1/512.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=old periodicity=0 rseed=-2436 colors=200200000<2>455677899ABBBCC<18>hiijkkkll<3>rss<21>HIIFGGEFF<3>677\ 455344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000111<24>niQpjRrlS<3>\ ysX<25>BB7996775<3>000<24>n00p00r00<3>y00<29>400 } Gran_canyon_zoom { ; Albrecht Niekamp July, 03 ; Time 0.20.10.67 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult244.frm formulaname=multifractal_6 function=cos/exp/exp/cosxx passes=t center-mag=+1.14003818818291000/+0.35936443447906610/197.9471/1/-90/3.88\ 578058618804789e-016 params=0.8202154606769005/-0.06207464827417833/10667.3210111/2543.060802\ 1613/4084.02048/384.0000076/768.00024/128.0076800000001/384.007680000000\ 1/512.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=old periodicity=0 rseed=-2436 colors=200N00<6>900<3>200000122<5>BCCDEEFGGGHHIJJKLL<13>hiijkkkll<3>rss<\ 21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>0220001\ 11<22>jeOlgPniQpjRrlStnT<2>ysX<25>BB7996775<3>000<24>n00p00r00<3>y00<18>\ P00 } Bishops_hat { ; Albrecht Niekamp July, 03 ; Time 0.33.58.01 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult244.frm formulaname=multifractal_6 function=exp/sin/exp/sin passes=t center-mag=0.431817/2.22045e-016/1.34604/1/-90/3.88578058618804789e-016 params=0.8202154606769005/-0.06207464827417833/10112.3210611/2543.060802\ 1613/4084.02048/384.0000076/768.00024/128.0076800000001/512.007680000000\ 1/768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=6 periodicity=0 rseed=-2436 colors=200700<3>000<5>9AABCCDEEFGGGHH<15>hiijkkkll<3>rss<21>HIIFGGEFF<3>\ 677455344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000111<22>jeOlgPniQ\ pjRrlStnT<2>ysX<25>BB7996775<3>000<24>n00p00r00<3>y00<26>900 } Magic_circle_2 { ; Albrecht Niekamp July, 03 ; Time 0.10.55.37 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult244.frm formulaname=multifractal_6 function=cos/exp/exp/exp passes=t center-mag=2.22045e-016/-2.22045e-016/0.8392416/1/90/3.88578058618804789\ e-016 params=0.8202154606769005/-0.06207464827417833/40673.3255005/25040.06080\ 21613/2048.02048/768.0000045/768.00024/128.0076800000001/512.00768000000\ 01/768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=old periodicity=0 rseed=-2436 colors=200JHA<13>jeOlgPniQpjRrlStnT<2>ysX<25>BB7996775<3>000<24>n00p00r0\ 0<3>y00<25>B00900700<3>000<2>455677899ABBBCC<18>hiijkkkll<3>rss<21>HIIFG\ GEFF<3>677455344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000111<7>HF9 } Universal_robot { ; Time 0.34.13.72 ; Albrecht Niekamp July,03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult244.frm formulaname=multifractal_6 function=cos/exp/exp/sin passes=t center-mag=-0.0124931/3.747e-016/11.03753/1/-90/3.88578058618804789e-016 params=0.8202154606769005/-0.06207464827417833/14178.321055/2540.0608021\ 613/4084.02048/384.0000045/768.00024/128.0076800000001/256.0076800000001\ /512.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200554<2>000<24>n00p00r00<3>y00<25>B00900700<3>000<2>455677899ABB\ BCC<18>hiijkkkll<3>rss<21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz\ <25>09C08A068<2>022000111<22>jeOlgPniQpjRrlStnT<2>ysX<27>775 } Mandelmania_zoom { ; makes the 4th generation mandel visible ; Albrecht Niekamp July,03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult244.frm formulaname=multifractal_6 function=cos/exp/exp/sqr passes=t center-mag=+0.84947498866192170/+0.00000000000000022/895.0965/1/180 params=0.8202154606769005/-0.06207464827417833/10111.3210116/2543.060802\ 1613/4084.03072/384.0000055/768.00024/128.0076800000001/384.007680000000\ 1/512.00746 float=y maxiter=10000 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=200b00<6>p00<3>w00y00w00<24>C00A00800<3>000<2>455677899ABBBCC<18>\ hiijkkkll<3>rss<21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<25>09C\ 08A068<2>022000111<24>niQpjRrlS<3>ysX<25>BB7996775<3>000<17>`00 } Mandeline { ; most unsual musical instrument ; Albrecht Niekamp July,03 ; Mandelmania deepzoom, takes a while reset=2002 type=formula formulafile=mult244.frm formulaname=multifractal_6 function=cos/exp/exp/sqr passes=t center-mag=+0.84820315604180700/+0.00000000000000022/29638.96/1/-90/3.88\ 578058618804789e-016 params=0.8202154606769005/-0.06207464827417833/10111.3210116/2543.060802\ 1613/4084.03072/384.0000055/768.00024/128.0076800000001/384.007680000000\ 1/512.00746 float=y maxiter=10000 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=200C00<4>200000<2>455677899ABBBCC<18>hiijkkkll<3>rss<21>HIIFGGEFF\ <3>677455344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000111<24>niQpjR\ rlS<3>ysX<25>BB7996775<3>000<24>n00p00r00<3>y00<24>E00 } The_big_bed { ; Time 0.29.40.30 ; Albrecht Niekamp July,03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult244.frm formulaname=multifractal_6 function=cos/exp/exp/sin passes=t center-mag=-0.0108791/3.46945e-016/16.7049/1/90/3.88578058618804789e-016 params=0.8202154606769005/-0.06207464827417833/14182.3215551/5040.060802\ 1613/4084.02048/384.0000045/768.00024/128.0076800000001/384.00768/768.00\ 76800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=2000Wd<14>09C08A068<2>022000111<22>jeOlgPniQpjRrlStnT<2>ysX<25>BB\ 7996775<3>000<24>n00p00r00<3>y00<25>B00900700<3>000<2>455677899ABBBCC<18\ >hiijkkkll<3>rss<21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<9>0Xf } Mandelmania_2 { ; Time 0.16.49.48 ; Albrecht Niekamp July,03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult244.frm formulaname=multifractal_6 function=cos/exp/exp/sqr passes=t center-mag=0.47425/2.22045e-016/1.249125/1/-90/3.88578058618804789e-016 params=0.8202154606769005/-0.06207464827417833/10111.3210116/2543.060802\ 1613/4084.03072/384.0000055/768.00024/128.0076800000001/384.007680000000\ 1/512.00746 float=y maxiter=4084 inside=maxiter outside=tdis logmap=yes periodicity=0 rseed=-2436 colors=200VVV<7>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq0es<2>\ 0jy0kz0jy<24>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB7A96875<3>000\ 400<23>o00q00s00<3>z00<25>C00A00800<3>000<16>UUU } ------------------------------------------start-frm----------------------- FRM:Multifractal_6 { ; Albrecht Niekamp 020703 ;only integers as first input, second input 5 digits to the right ;real(p2) 5digits: shape, outside, in1, in2, in3 ; 0_off 1_secant/mand 2_bees/jul 3_m_mods 4_newt +5_reset (not shape) ; input2 : 2digits_m_mods 5digits_mand/jul use : 0_no 1_yes +5_warp ;imag(p2)(-) 2-4digits : quasinewton input (max 2000) ; 1digit : no m_mods multipl. : 1_out 2_in1 3_in2 4_all ; 1digit : iter-reset 1_out 2_in1 3_in2 4_all ; input2 : 4digits(-)_mand 2digits_secant 4digits_bees ;real(p3) many_mods bailout, bailout ;imag(p3) shape : factor (fn1), outside : border-in ;real(p4) outside : factor (fn2), border-out ;imag(p4) inside1 : maxiter1, factor1 (fn2) ;real(p5) inside2 : maxiter2, factor2 (fn3) ;imag(p5) inside3 : maxiter3, factor3 (fn4) ;fn(1) is shared by bees and many_mods ; da=real(p2) dd=trunc(da) da=round((da-dd)*10000000)+11111 d=trunc(dd/10000) t=d>5 dd=dd-d*10000 d=d-5*t d3=(d==2)+(d==4) d4=(d3==0) vb=(d==3)+(d==4) d=trunc(dd/1000) ex1=d>0 dd=dd-d*1000 rs1=d>5 d=d-5*rs1 v1m=(d==3) v1j=(d==4) dd1=(d==2)+(d==4) d=trunc(dd/100) ex2=d>0 dd=dd-d*100 rs2=d>5 d=d-5*rs2 v2m=(d==3) v2j=(d==4) dd2=(d==2)+(d==4) d=trunc(dd/10) ex3=d>0 dd=dd-d*10 rs3=d>5 d=d-5*rs3 v3m=(d==3) v3j=(d==4) dd3=(d==2)+(d==4) ex4=dd>0 rs4=dd>5 dd=dd-rs4*5 v4m=(dd==3) v4j=(dd==4) dd4=(dd==2)+(dd==4) ; mm=trunc(da/100000) da=da-mm*100000 d=trunc(da/10000) ex0=d>5 ab=(d==2)+(d==7) da=da-d*10000 d=trunc(da/1000) w1=d>5 ab1=(d==2)+(d==7) da=da-d*1000 d=trunc(da/100) w2=d>5 ab2=(d==2)+(d==7) da=da-d*100 d=trunc(da/10) w3=d>5 ab3=(d==2)+(d==7) da=da-d*10 w4=da>5 ab4=(da==2)+(da==7) tt=ex0+ex1+ex2+ex3+ex4 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) d=round((d-dd)*10000000000) pp=trunc(dd/100)/10 dd=dd-1000*pp da=trunc(dd/10) so1=((da==1)+(da==4)==0) so2=((da==2)+(da==4)==0) so3=((da==3)+(da==4)==0) dd=dd-10*da ir1=(dd==1)+(dd==4) ir2=(dd==2)+(dd==4) ir3=(dd==3)+(dd==4) ; p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=real(p3) mb=trunc(d) ba=(d-mb)*100000 ; d=imag(p3) sfac=trunc(d) b1=(d-sfac)*100000 b0=b1/2 ; d=real(p4) ofac=trunc(d) b2=(d-ofac)*100000 ; d=imag(p4) mi1=trunc(d) fac1=(d-mi1)*100000 ; d=real(p5) mi2=trunc(d) fac2=(d-mi2)*100000 ; d=imag(p5) mi3=trunc(d) fac3=(d-mi3)*100000 ; bg=((ab+vb)==0) bg1=((ab1+v1j)==0) bg2=((ab2+v2j)==0) bg3=((ab3+v3j)==0) bg4=((ab4+v4j)==0) ; if (d4) z=0 if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel z=pixel*(ab==0) endif else if (bg) c=p9 else c=p1 endif z=pixel endif t=0 u=d3 bo=z p=pp z0=p7 : If (tt) t=t+1 if ((ex0) && bo>b0) u=2*(fn1(t/sfac)) if (d4) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) ba=mb else c=pixel endif else z=pixel if (bg) c=p9*u else c=p1*u p=pp*u endif endif ex0=0 tt=tt-1 elseif ((ex1) && bo>b1 && bo<b2) if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif rs=rs1 ab=ab1 if (dd1) if (rs) z=pixel endif vb=v1j d3=1 if (bg1) c=p9*u else c=p1*u p=pp*u endif else d3=0 z=z*u c=z if (rs) z=pixel*(ab==0) endif vb=v1m if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir1) t=0 endif ex1=0 tt=tt-1 elseif ((ex2) && t>mi1) if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif rs=rs2 ab=ab2 if (dd2) if (rs) z=pixel endif vb=v2j if (bg2) c=p9*u else c=p1*u p=pp*u endif d3=1 else d3=0 z=z*u c=z if (rs) z=pixel*(ab==0) endif vb=v2m if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir2) t=0 endif ex2=0 tt=tt-1 elseif ((ex3) && t>mi2) if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif ab=ab3 rs=rs3 if (dd3) if (rs) z=pixel endif vb=v3j if (bg3) c=p9*u else c=p1*u p=pp*u endif d3=1 else d3=0 z=z*u c=z if (rs) z=pixel*(ab==0) endif vb=v3m if (vb) if (so3) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir3) t=0 endif ex3=0 tt=tt-1 elseif ((ex4) && t>mi3) if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif ab=ab4 rs=rs4 if (dd4) if (rs) z=pixel endif vb=v4j if (bg4) c=p9*u else c=p1*u p=pp*u endif d3=1 else d3=0 z=z*u c=z if (rs) z=pixel*(ab==0) endif vb=v4m if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif ex4=0 tt=tt-1 endif endif if (vb) if (d3) ;quasinewton Pusk s Istv n z1=z^p-1 z2=p*z*z z=z-z1/z2 else z2=fn1(z)+c ;many_mods Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z2=z*z ;mandel Pusk s Istv n z=z2*z2+p6*z2+c-p0 elseif (d3) z1=fn1(z)-c ;bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) else z3=z ;secant unknown z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<=ba }

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FOTD 06-07-03 (Chicken Scratches [7])
by JimMuth＠aol.com 06 Jul '03

06 Jul '03

FOTD -- July 06, 2003 (Rating 7) Fractal visionaries and enthusiasts: For today's FOTD we take a trip to the barnyard to see the "Chicken Scratches" in the dirt there. Well, what else could I name such a scratchy image? The expression behind the scratchi- ness combines various portions of Z, (1/Z), Z^2, and Z^2.1. The whole works is iterated by the MandelbrotMix3a formula, which works like the MandelbrotMix4 formula, except that it combines 4 different powers of Z instead of 2, and the critical points must be calculated somehow by the user and entered as real(p5). I use the graphical method of calculation. The parent fractal appears as an oversized M-set rotated 180 degrees, so that east is west. This figure is quite normal appearing in its overall shape, but in its filaments, craziness appears. The filaments start out from their buds in a normal enough manner, but halfway to their ends, they split in two. This splitting is most obvious in the period-2 filament, which starts out pointing directly east along the positive X-axis, but before it reaches the large midget, splits in two. Today's image is located near the point where the splitting takes place. The -0.25*(Z^2.1) part of today's formula is the main driving force behind the image. The main feature of the image is the 'scratches' that surround the midget. Such scratches are a common feature along the 'main stem' area of Mandeloids of orders such as 2.1. When coloring the image, I added the purplish aura around the midget to intentionally give the whole image a kind of coronal discharge effect. The rest of the colors were intensified in a separate program. The intensification is included in the attached parameter file, which runs in 3-1/2 minutes on my tired machine, faster on newer models. Another way to see the chicken scratches is to download the finished image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> though by the time the finished image has downloaded and brought into the Fractint program, around 3-1/2 minutes will have passed. Saturday was sunny and hot here at Fractal Central. Luckily for the cat duo the rain bypassed this area, giving them a lazy afternoon in the yard. The temperature of 93F 34C insured that their afternoon would be lazy. Today is starting in a similar manner. If the rain stays away, the duo will have another pleasant day. As for me, I'm ready to pass the day doing as little real work as possible. Until next fractal, take care, and see you in 24 hours. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Chicken_Scratches { ; time=0:03:30.64--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3a function=ident passes=1 center-mag=+16.3204451061389/-0.011735917608758/44\ 979.7/1/137.5/-3.38639630226289512e-010 params=1/1\ /-1/-1/0.25/2/-0.25/2.1/7.26855686921/3500 float=y maxiter=300 inside=0 logmap=34 periodicity=10 colors=000000000000000000000000000400A0OG0SL4XRAaV\ Jh_NodPtjRzNd0Zq0sz0zv0us4boGRkP2gZ4di8`s8XzHZzNZz\ X`xb`xi`xsbvzbvzduzduzduz`vzXvzTvsPvkLvdHxXExPAxH6\ xA2xC0xE0sG0mH0iJ2dL2ZN2VP2PR4JT4GV4AX46Z80`A0bC0d\ E0eG0g00i00k00m00o20q80sE0uH0vN0xT0zZ0zd0zi0zm0ze2\ zZ4zR6zJ8zCAz4Cz0Ez0Gz0Hz0Hz0Gz0Ez2EzCCzLCzVAzdAzm\ 8zv8zz6zz6zz8zzAzxCzuEzoEziGzdHz`JzVLzPLzJNzGPzARz\ 4Tz0TzARzHPzRPzZNzgNzoLzvLzzGzzAzzCzzCzzEzzEzzEzzC\ zzAzz8zz6zz4zz2zz0zz0zz0zz0zz0zz0zz2zzCzzJzzTzz`zz\ izzqzzszzuzzuzzvzzvzzxzzxzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzxzzvzzuzzszzqzzozzmzzkzzizzgzzezzezzmzzv\ zzzzzzzzzzzzzzvzzszzmzzizzdzz`zzVzzRzzLzzHzzCzz8zz\ AzzAzzCzzCzzCzzEzzEzzGzzGzzGzzCzzAzz8zz4zz2zz0zz0z\ z0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz4zzG\ zzPzz`zzizzuzzzzzzzzzzzzzzszzmzzezz`zzTzzNzzGzzAzz\ EzzGzzJzzLzzPzz8zz6zz4zz2 } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 05-07-03 (Olde-Tyme Minibrot [6])
by Jim Muth 05 Jul '03

05 Jul '03

FOTD -- July 05, 2003 (Rating 6) Fractal visionaries and enthusiasts: Today's FOTD reminds me of the kind of Fractint image that was popular around 10 years ago, when the second edition of "Fractal Creations" was published. I named it "Olde-Tyme Minibrot" accordingly. And yes, I realize that 10 years ago is hardly ancient history, but in this era where books are outdated before they hit the bookstands, and operating systems come and go like day and night, it is far enough in the past to be called "Olde-Tyme". The parent fractal is an oversized thing with X-axis symmetry, created by subtracting 11 parts of Z^(-2.3) from 11 parts of Z^(-1.7) and adding (1/C). Today's scene is located in a valley of a lopsided bud lying quite close to the origin. The olde-tyme look was achieved by coloring the outside parts of the image with the 'atan' option. The standard 'iter' coloring results in an image with flat areas of color that are too large to be interesting. When the time came to rate the image, I decided on a 6, which is the average of the images good enough to make a FOTD. The 7-minute render time is short enough to be practical, and even that short wait can be avoided by downloading the finished GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Friday was sunny and hot here at Fractal Central, with a temperature of 91F 33C. Thunder-storms threatened in the late afternoon, but passed off quickly, permitting the fireworks to go off as scheduled. The dynamic duo had a pleasant afternoon in the yard, though they got a bit skittish when the fireworks noise started. Independence Day has now passed. It's another hot day, and all else is well. Until next FOTD, take care, and the past always seems better than today. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Olde-Tyme_Minibrot { ; time=0:07:16.77--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.07173085565404393/-0.394457304834334\ 30/111092.7/1/132.5/1.62781177426296608e-010 params=-11/-2.3/11/-1.7/0/0 float=y maxiter=1800 inside=0 outside=atan periodicity=10 colors=000UaoVboWboWcpXdpYdpZepZeq_fq`gq`gqahrbhrc\ ircjrdjsekseksflsgmthmthntintjoujpukpulqvmrvmrvnsv\ oswotwpuwquwrvxrvxswxtxxtxyuyyvyywzywzzxzzyzzzzzzz\ zyzzwzzuzzszzqzzozzmyzkyziyzgxzexzcwzawz_wzYvzWvzU\ wzSuzQuzOuzMuzLtzKtyKtyJsyJtxIsxIsxHswHswHrwGrvGrv\ FqvFqvEquEpuDpuDptDotCotCosBnsBnsAnrAmr9mr9mr9lq8l\ q8lq7lp7kp6kp6ko5ko5jo5jo6jn7jn8im9imAilBilChkDgkE\ fjFejGdiGbiHahI`hJ_gKZgLYfMXfNWeOVePUdQTdQRcRQcSPb\ TObUNaVMaWL`XK`YJ_ZI__HZaF``G__GZZHZYHYXHXWIXVIWUI\ VTJVSJURJUQKTPKSOLSNLRMLQLMQKMPJMOINOHNNFMMHNNINOJ\ OOKOPMPPNPQOQQPQRRRRSRSTSTUSTVTUXTUYUVZUV_VWaVWbWX\ cWXdWYeXZgXZhY_iY_jZ`lZ`m_an_ao`bp`cracsadtbdubewc\ excfydfzdgzdgzcfycfxcfwbevbevbeuadtadsadr`cr`cq`cp\ `bo_bn_bm_amZalZakZ`jY`iY`iY_hY_gZ_f_Ze`ZdaNcbNbcN\ bdMaeMafM`gMahI`iK`jM_kN_lPZkRZjSYiUYiWXhXXgZXf`Wf\ aWecVdeVcfUchUbjTakT`mT`n } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 04-07-03 (Lemon-Lime Country [7])
by Jim Muth 04 Jul '03

04 Jul '03

FOTD -- July 04, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today's image takes us back to the number-one fractal, the Mandelbrot set, which still does and always will contain an infinity of undiscovered scenes. Today's scene is one of a midget located in a spiral in a valley of a bud lying quite deep in East Valley, in the area where the features are on the verge of becoming pinched off. This deep in East Valley the iteration count is quite high. The maxiter of today's image is 500,000, and almost every feature has a count above 10,000. With iteration counts such as today's the coloring often works best if the logmap feature is turned off. Doing so results unavoidably in areas of total chaos which I call sand, but it adds definition to those features that would otherwise be flat. Several outside coloring options give nearly identical results with today's scene. I chose the 'summ' option for no reason in particular. The 'fmod' and 'tdis' options were not considered, since they slow the render time to over an hour. The 'mathtolerance' statement is included in the parameter file so that the image will not flip into arbitrary precision math and take several hours to complete when it is rendered at a high resolution. I named the image "Lemon-Lime Country". I thought I saw enough lemon and lime colored areas in the picture to justify the name. I rated it at a 7 because it is always a pleasure to find interesting new scenes below the arbitrary math magnitude in the M-set. The render time in the 11-minute range can be avoided by downloading the finished image from one of the FOTD web sites: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The light showers ended in early afternoon here at Fractal Cen- tral on Thursday. At 5pm the sun appeared, a little late, but better late than never. The temperature at the time was 77F 25C, which is near perfect for cats. Taking full advantage of the opportunity, the once-dynamic duo spent over an hour in the yard, which was not as much time as they would have preferred, but still enough to keep them happy. Today promises to be hot as a firecracker, and since it is Independence Day here in the USA, there will be a lot of firecrackers as well as other assorted fireworks going off. The duo does not like sudden loud noises, so they will probably be skittish. Check here tomorrow to see how they make out. Until then, take care, and are fractals a blast or not? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Lemon-Lime_Country { ; time=0:11:20.81--SF5 on a p200 reset=2002 type=mandel passes=1 center-mag=+0.2531\ 3254012409130/-0.00035259026063394/5.075036e+011/1\ /-27.5/0.001974 mathtolerance=/1 params=0/0 float=y maxiter=500000 outside=summ inside=0 periodicity=10 colors=000tnJsmJslKslKskLrjLriMrhMrhMqgNqfNqeOqdOq\ dOmfXjgdjccj_bjWajS`jO_jKZjIYjHXjHWjIVkJUkKTlLSlLT\ mMVmNXnOZnO`oPboQdpRfqShqSjrTlrUnsVpsVrtWttXvuYxuY\ zrXvpWsmVokUlhThfTecSbaRZZQWXPSUOPSOMPNINMFKLBIK8G\ K5IM8JOAKQCLSEMUGNVIOXKPZMQ`ORbQSdSTeUUgWViYWk_Xmb\ iohrpmzorzorzorwommnhdmcehZgcUiZPjUKkPBjK5iF4fF3bG\ 3_G2WH1TI1PJ0MJ0OM6QPCSRIUUOVWUXZ_Zae`ckbfqchvbfub\ etadsacs`br`aq_`p__pZZoZYnYXmYWmOYhEZc4__ed_ggahkc\ jnekrgmuinxjkvlhumetobsp_rrXqsUpuRovOnwSoxWpx_qxcr\ xgrxksxotxsuxvuxsrwqpvonumltkjsihrgfqedpcboa_n_YmY\ WlWUkTSkRQjPOiNMhLKgJHfHFeFDdDBcB9b97a75`53_31_84`\ C7aHAaLDbQGbUJcYMcZNe_Of`PgaPiaQjbRkcSmdSneToeUqfV\ rgVshWuizzizwgznfzedyXcxPauO_sNZqMXoLWmKUkJTiIRfHQ\ dGObFN`ELZDKXCIVBHSAFQ9EO8CM7BK6AI5FI4KKGPKKSKOUKS\ WKWYK__IcaEecEgeFigGkiHmkIphPmjUilZencaphYrmUtrQvu\ MutIutGusGurHtqHtpItpItoJ } END PARAMETER FILE=========================================

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FOTD 03-07-03 (Shimmering Midget [7])
by Jim Muth 03 Jul '03

03 Jul '03

FOTD -- July 03, 2003 (Rating 7) Fractal visionaries and enthusiasts: Sometimes fractals shimmer. Or they can be made to appear to shimmer. The subtle wavy fringes around the edges of the main pattern in today's image remind me of something shimmering in the distance on a hot afternoon. With only a moment's thought I named the image "Shimmering Midget". The parent fractal was created by subtracting Z^(-1.33) from Z^(1.33) and adding (1/C). It is a distorted Mandeloid rotated 45 degrees from the 'normal' position, with its East Valley on its southeast side. Normally, this would mean that its main period-2 bud was on its northwest side, but as I said, today's parent fractal is distorted. The main bud, or the bud that should be the main bud, is actually located on the south-south- west side of the parent. It is not the largest bud -- that honor goes to the period-4 bud to the right of the main bud, with the period-3 and period-5 buds right behind. This is one of the things distortion does to Mandeloids. Today's scene is located near the tip of a chain of pseudo-buds on the bud side of the left branch of the Seahorse Valley of the parent fractal. Seahorse Valley is always the valley that encloses the period-2 bud, regardless of whether that bud is the largest or is located exactly opposite East Valley. The features that are found there will always have an underlying similarity to those in the classic Mandelbrot set, though the details will change. In today's image, the shimmering effect is one of the changed details. For midgets with really new features, one must find unlikely areas of non-classic-shaped parent fractals, and examine the parts that are critical. It is not always easy, in fact it is often downright hard to tell which areas are critical. As is so often the case in life, the harder the scene is to find, the more it is likely to be worth. Finding these critical areas is a large part of the fun of using the MandelbrotMix4 family of formulas. Because of the unusually brilliant blue coloring of today's image, I have rated it at an above-average 7. The render time of 17 minutes is getting into the area where the download of the already-completed image makes more sense. The download can be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The rain held off until 3pm on Wednesday, giving the fractal duo ample time in the yard before being forced indoors. The tempera- ture of 77F 25C was close to ideal, making their day at least good if not great. But this morning the rain is still falling. It is due to end soon, but who knows for sure what will happen, certainly not the weather experts. And who knows the moods of a cat? One thing certain to happen is several hours of work. I've got another job from a customer who doesn't know what he wants, but does know when he gets something he does not want. And the time to start on it is now. Until 24 hours from now, take care, and adopt a needy fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Shimmering_Midget { ; time=0:17:45.60--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.11844856655981260/+0.742760244255860\ 20/1.782961e+010/1/27.5/-0.000246466487240595833 params=-1/-1.33/1/1.33/0/0 float=y maxiter=2000 inside=0 periodicity=10 colors=000z0zu0yk0oe0gY3ZRDRIKIDVB5c30k09`0HR0PH2Y\ 73e05n07v09z0Bz0Bz0Fv0Ho0Kg0NZ0RT5TKBYFIZ7Rc0Ye0ei\ 0nk0un0oc0kT0gI0cB0Z20V00R02V03Z55`F7ePBiZDkiFouHr\ zDozBnz7az5by2cy0cx0cy3cy9bzDZzIfzPWzT`zZ`zc`ziZzo\ ZzuZzzZzzZzeIuI5`00I002TnzRgzP`zNYzNRrKNiIH`IDVH7N\ F2FD07D00B009009009009209D09P09`07e05k53oB3uF2zK0z\ R0zV0oN0YF0F700000000000000000200520B20F20K20P30V3\ 0Z30e30i50o50u50z50zH0zR0zc0yn0vz0uz0rz0oz2`uPNgn9\ nuFrzIyzNzzTzzYzz`zzezzgvzikzk`znRzoHyz7tu0ov0ky0g\ z0cz0_z0Wy0Uu0So0Pk0Ne3K`9HYHFTNDNVBIo9Fv7Bv57vD9v\ IBvPDcVFZ`FYiHToIRvKNzNKzNVzBez2nz0yz0zz0zz0yv0uoD\ ogRk`eiVreRu`NuYIuTFuPDuK9uH5vD2v90v50v20v00v00v00\ u00r30r50o90nB0nD0kH0iI0iN0gP0eT0eV0cY0cZ0g`0kc2ne\ 7reDvgHyiNzkTzkYzcRzVNzPIvHFu9Bo37k03g00e00`00Y00V\ 00R07P0BN0DK0FI0HI0IH0KF0ND0PD0TB0V90Y70Z70`50c30e\ 20g20i50k70n90oD0rFzRFzi3 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 21-06-03 (Beware the Lava Pit [5])
by Jim Muth 02 Jul '03

02 Jul '03

FOTD -- June 21, 2001 (Rating 5) Fractal visionaries and enthusiasts: What do you get when you mix some Z^(1.1) with some Z^(-1.1)? A pit of boiling hot lava of course. I named the image "Beware the Lava Pit". Actually, I should have named it "Beware the Magma Pit" since the scene is underground, and molten rock is known as magma until it reaches the surface. Only then is it called lava. When the time came to rate the image, I studied it several minutes before realizing that it was merely an average image. The rating of 5 is average. There's nothing wrong with being average, it's just that I like my FOTD images to be above average, and the greater the number of above-average images I post, the higher the standard of average becomes. One thing that does not change however is the average render time of my FOTD's, which currently stands around 12 minutes on my tired, worn-out P200 machine with the exhaust fan that needs to be nudged before it starts turning. When I forget to nudge it, the smell of the over-heated power-supply unit soon reminds me to give it its nudge. Today's image requires 25 minutes to complete on my machine. It will finish faster on faster machines. But the fastest way of all to see the lava pit is to download the completed GIF image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Heavy rain fell during the day Friday here at Fractal Central. The cats, who were confined to the indoors, turned sullen in the afternoon. Several treats of tuna were needed to restore their spirits. Today is starting with a bit of sun, but heavy storms, and perhaps hail, are due this afternoon. I doubt that the cats will have a good day. If the grass dries enough, I'll trim it today. If not, I'll let it grow another couple inches. In any case, I'll visit Fractal Land to track down the next fractal. Until next time, take care, and beware. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Beware_the_LavaPit { ; time=0:25:44.24--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+0.15929781727837890/+0.033662025303030\ 13/7.522503e+007/1/52.5/4.46614381509335967e-006 params=-0.86/1.1/-0.53/-1.1/0.03/525/0/0 float=y maxiter=3400 inside=0 periodicity=10 colors=000pl8niAmeCkbFjZHhWJfSMePOcLQbIT`EV_BXgUZo\ l_dmNVqBWtDXwEYzFZzG_zH`zJazKbzLczMczN_zTWzYSzbOzh\ KzmHzrzkKziKzgKzeKzcKzaKz_KzYJzWIzUHzSGyQGxOGwMFvK\ FuFEtAEs5ErBJoFNnJ_hNWeRhbWcZ_mWclTgpQhtReqRfrRdrR\ aqR_qRYpRVpSToSRoSOnSMnSKmSHmSFlSDlRHmRKnQOnQRoQUp\ PYpP`qPcrOgrOesOksPcmQVhRLbSCYT3TUAXUTlUNdUZrU_kUe\ oUlsUjwUrzMlwFot7kq0gn1fk2ei3dg4cd5cb6b`6aY7`W8`U9\ _RAZPBYNBYLVMAmA0f63_25Z36Y37X38W39V3AV4AU4BT4CS4D\ R4ER4ET7FUAFVCFWFFXHFYKGZMG_PG`RGaUGbWGams_kqZjoXi\ mWhkVgiTfgSeeRddSbbSa`S_ZTZXTXVTWTUURUTQUSOVQMVPKV\ NIWMGWKEWJCWIBZKI`MPbNWePbgRiiSoeVmbXlZZkWaiSchPeg\ Q`aRXXSTRSPMQOKONJNMILLHKKGIJFHIEFHDDGCCFBAEA9D97C\ 86B7AF6DI6GM5JP5MT4PW4V`4_e4ei4jn4ps4uw4WoH6hUHXJR\ M8VJAZGCaDEeAGi7Il5JhJUdXc`jmXwwUrkRm_OhOLcCOVGRMJ\ UDMX5PeeUdbSc`QbYObWMaUK`RI_PG_MFZKDYIBXF9XD7WA5V8\ 3V62ZD3aK3eR4hX4lc5oj5rp5 } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 02-07-03 (A Fractal in Paradise [6])
by Jim Muth 02 Jul '03

02 Jul '03

FOTD -- July 02, 2003 (Rating 6) Fractal visionaries and enthusiasts: Where do good fractals go when they die? I would assume, to fractal paradise. And what do these fractal angels see in paradise? Glorious fractals of course. Today's image might not be glorious, but it's been good enough to earn a place in paradise, so I felt justified in naming it "A Fractal in Paradise". I looked up the roots of the word 'paradise' in my dictionary, and found that the word is derived from 'pairi', which means 'around', and the word 'daeza', which means 'to build a wall'. I suppose this means that the original paradise was seen as a refuge of unlimited happiness surrounded by a wall strong enough to keep out all unhappiness. I might add that anything one could desire must be present in paradise or their happiness would be limited. I have yet to decide how those such as myself, who enjoy things such as stormy weather, are going to have their storms in a place where the weather, if there is any, is always perfect. And how could those who want the peace of perfect weather be happy in a place with storms. I had best leave the theological discussion to the theologians and move on to the fractal discussion. Today's fractal combines Z^(1.25) with Z^(-0.75) and adds (1/C) to make a parent fractal that appears as a Mandeloid rotated 90 degrees, with a large area of chaos to its north and east. Today's scene is located in a broken line of chaos that runs down one side of the interior of the unusually small East (south) Valley of this Mandeloid. I chose the name of the image when I had a fleeting thought about fractals in heaven, a thought that might make for some active philofractal discussion. The image itself departs from my usual perfectly symmetrical style and shows some of the non- symmetrical surroundings of the midget. In fact, there are two midgets in the image, with the second being located near the top center of the frame. I colored the image, which consists entirely of outside material, with the 'tdis' option. When colored in the normal 'iter' manner, the image drops one or two rating points. As it is, the image has nothing in it that would rate it any higher than a 6, regardless of its lofty place in paradise, though the render time of 6 minutes is short enough to be practical. As always, those who would rather download a ready-to-view image can find that image on the internet at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fine weather for cats held through the day Tuesday here at Fractal Central. Lots of sun, light winds, and a temperature of 83F 28C kept the intrepid duo happy from noon until dusk. Their biggest excitement came when the trash was collected and they ducked for cover in the holly thicket. Today is starting cloudy, with rain forecast. Hopefully, the rain will hold off until the cats have had their fun. My fun will start when the work ends, which looks to be in about 4 hours. Until next time and next FOTD, take care, and if paradise is so wonderful, why do so many try so hard to postpone their trip? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ AFractalInParadise { ; time=0:06:06.57--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.71753899920961710/+0.527791195534077\ 30/76865.91/1/87.5/-1.82916205793137721e-009 params=0.9/1.25/-1/-0.75/0/0 float=y maxiter=1200 inside=0 outside=tdis periodicity=10 colors=0000vO0sW0p_0sW0uQ2xK8zFHzBMz4Uz0Zz0ez0kz0g\ z0dz0az0Zv0Xs0Up0Ql0Og0Kd0I_2FX4BS68R84PB2ND000DTO\ IXUM_XQeaWkgZplaspilspeuu_vzUszOpzQiyQdvSbrS_oSXkU\ WiUQgUKfWFcW8cW2nQKxK_zHpzBzz6zHzqMzlQzgUzaXzX_xUd\ uOgqIknDnk6qg2slDspMssWsvdszlszuszzszzszzszzqzzqkz\ qUzqBzq0zu4zxHzzQzz_zzizzszzzzszvdzpOzg6z_4za4za4z\ d4zd4ze2ze2zg2zg2zi2zi2zi6zgDzdHz_WzUZzOdzHguBkl4q\ zUxzpqzglz_ezS_zKazOazSazWazZZzXXzXXWFWzXUzWSzWQzW\ 00e4Bd8MaDX_FgZIqXMzWzsvszldzdzz0gzH0Zz8snF0xIKnMl\ d0D00M20W80dD6lIDuMIzSz0Wz0Wz8WzKWvWWngWeqWXzWSzvQ\ ziU0z0F04_0FsHxUQliS_xUl0xi0seDpaQkZagWnaSzZI0zzQ6\ saFinKZzQWQ0Sg4QvIzevza0Xu4SzIz0BzDHsUKiiOZxSz2i0z\ z0zv0zp8ziHza_00X00WH0UW8SkHQxOk00g00dD4_QBXaHUnMQ\ zSk0De2H_MKXdOSuSiFUZiWzpH00I00K0BM0MO4XQBgSFqUKzW\ zUqviiexaz0zvUqa0zZ4xXKsWZlSlgQz_WzzIQ2KgDMvMizQez\ SdzS_zUZzUSz0Kz0Fz26zB0zH } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

2 1

"Monarch" - Zoom into Mixdown3
by Harold Lane 01 Jul '03

01 Jul '03

Although I called this "Monarch" I later found that the predominantly orange monarch butterfly has white spots on a black background on their wing tips rather than the black on white in this image. Thanks to Albrect Niekamp for a rich base formula (multifractal_5) and fractal (Mixdown3) and to Lee H. Skinner for the color map. The timing may be off as I often calculate more than one fractal at a time to Disk-Video. I once had Win98 calculating a dozen at a the same time. They share the processor relatively evenly while calculating the fractals but then loop, reading the keyboard, (using a similar amount of processor time) when the fractal itself is done. This behavior might possibly be modified by playing with the Idle Sensitivity in the DOS window properties. Info on the web has been contradictory. An exception to the rule of thumb of multiple windowed Fractint processes sharing the processor evenly occurs when you give focus to one of the Fractint windows. This gives the lion's share of the cpu to that process. I use this to quickly finish up a fractal that I see is nearing completion. After the fractal is saved and that instance of Fractint has been exited, the remaining instances of Fractint each get a greater portion of the cpu and can finish up more quickly. If I remember correctly, when I submit a .PAR file my ancient Compuserve mail program converts all instances of "=" to "=3D". When I find this problem with other people's .PAR files I use Robin Bussell's Paste & Go Windows utility which has an "=3D" button which quickly repairs the damage. http://web.ukonline.co.uk/robin.b2/pastengo.htm Any text editor with a "Replace" function can also change all instances of "=3D" back to "=" to get the same repair. Paste & Go V1.3 uses the Microsoft Visual Basic runtime DLL (msvbvm50.dll) which many people already have on their machines. If not, Robin also has a downloadable version of Paste & Go that includes this file also. For those who successfully use Fractint with a version of Windows, Paste & Go is a great way to painlessly get a set of parameters and a formula into Fractint. I've gotten lazy and now paste both the parameter text followed by the formula in the Par window. When you do this just insure that the text: FRM: precedes the formula. This also saves one from having to change the existing formula file's name to: pastengo. A nice feature of Paste & Go is that in addition to the parameter file name and parameter list name it can add custom parameters to the command line that invokes Fractint. I use Paste & Go's Setup feature to add the following parameter to get a quick windowed version of the fractal to see if I want to calculate a full size version: viewwindows=4/0.75/yes/0/0 If I like it I then send the fractal off to Disk-Video and then hit Alt-Enter to change the Fractint window from full screen to a normal window so I can proceed with my usual use of my machine. ################################################### mf5-001{ ; Title - "Monarch" Albrect Niekamp's ; Multifractal_5. Zoom into Mixdown3 ; Approx 1:30:00 on P2 400MHh 1024x768 ; Color Map by Lee H. Skinner ; Fractal by Harold Lane (c)2003 ; Version 20.02.04 reset=2002 type=formula formulafile=pastengo.par formulaname=multifractal_5 ismand=y function=cos/exp/exp/sin passes=1 center-mag=1.26399/1.12753e-005/33.86394/1/2.5000\ 0000000015055/1.56522017569216132e-012 params=-0.1156346324045534/-0.5338602862636189/14\ 237.3200001/53000.1314021613/2048.02048/384.00000\ 49/768.00024/128.0076800000001/768.0076800000001/\ 1024.00768 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 symmetry=none periodicity=0 rseed=-2436 cyclerange=2/255 sound=off colors=000000zzz<2>nsjQdrLdtblU<3>Mb8<3>LQ8KM8KJ8\ <2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAt\ m9vq8xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5zP5zL6zI6zE6wE\ 6tD6<6>vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW4E<2>\ _4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz\ 0gy0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7F\ O4KW0Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>\ civflvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<\ 3>8JP8FL8CI<3>SCCXCAaB9<3>uA2zA0xA0<12>SA1QA1NA1<\ 3>D92<6>UXAW`BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJ\ oSFlWAi_5fc0ce7_jFRoNIzb0<2>zz1zzCzzTzzi } ################################################### - Hal Lane hallane @ compuserve.com

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FOTD 01-07-03 (Fractal of Light [6])
by Jim Muth 01 Jul '03

01 Jul '03

FOTD -- July 01, 2003 (Rating 6) Fractal visionaries and enthusiasts: Today we begin the seventh month, yet the exact mid-point of the year does not arrive until noon tomorrow. In honor of these un-astounding facts, I have created a fractal. I named the fractal "Fractal of Light". When I gave the image this name last evening, I did so for a definite reason. This morning, that reason appears much less persuasive, but the name has already been given, and it will remain. The parent fractal was created with the MandelbrotMix3a formula, which mixes together four different powers of Z, but requires that the critical points be calculated by hand. In today's case, Z^2, 1/Z, Z^3 and Z^4 were combined, and Z was initialized to 3.5059.... The parent fractal, which has X-axis symmetry, is a Mandeloid rotated 180 degrees, with a large triangular area of chaos beyond its East (or in this case, its West) Valley. The East Valley itself is split in half, with a very skeletal line of disconnected elements strung down its open center. Today's scene is located near the edge of one of the smaller elements in this string. Because of the skeletal nature of the entire East Valley area, today's image consists mostly of inside areas that have been made visible and given detail by the 'fmod' inside-fill option. I have rated the image at a 6, which is the most common FOTD rating. Because it must calculate 4 different powers of Z at every iteration, the M-Mix3a formula is rather slow. Today's image takes a full 11 minutes to render on my machine. The wait can be avoided by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> With a temperature of 91F 33C and lots of sun, Monday was another good cat day here at Fractal Central. Showers prowled the area in the evening, but none made it to Fractal Central. The intrepid duo passed the afternoon sleeping on the porch and sitting in the shade under the holly trees. Today promises to be a slightly cooler repeat. This is good, because old cats become quite settled in their ways, and prefer good days. So until next FOTD, take care, and keep a good fractal thing going. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_of_Light { ; time=0:11:04.76--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3a function=ident passes=1 center-mag=+1.224869498561344/-0.000190723153669/1\ 997855/1/-5/-8.58104708817e-009 float=y params=0.2\ /2/-1/-1/0.1/3/-0.03/4/3.50592829665/0 maxiter=1200 inside=fmod proximity=0.5 periodicity=10 colors=000WgbVebVcbVacU`cUZcUXcUWcXUa_S_bQZeOXhMVj\ KUdPSZURUZQOcPIhODmN7rM2wL6uNAsPEqRIoSMmUQkWUiXYgZ\ ae`ecaiacm_eqYfSLm28sBAkJBdRDXZEQfGInHBtT_ydwpdqgd\ l_dgRdaIdXAdS9oL8yECtDFpCIlBLhAOd9R_8UW7XS6_O5bK4e\ G4bH8`ICZIFXJJUJNSKQQLUOLYLM`JMdHNhFNk8di2ug5pd7ja\ 9eZBaXEYUGVRISOKPMNOPPRSSUUUXXX__Zbaaedchgfkihnlko\ omqqprtrsutuvvwwxxxzzyzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzz_Ef_EhZDiZCkZBlYBnYAoY9qY9r_Ep`InaNlbRkcVi\ e_gfcfghdhlbipaeibabbYXbcQbZJcUDcP6cG0cL6eQCgVIi_O\ kdUli_nnepskrxpsvqruqrsqqrrqprporpmsolsojsnitngtmf\ tmdulculauk`ukcqbfmUiiLhhMggNgfOffOeePedQdcRdcRcbT\ caUbaVb`Wb`Ya_Za__aZ``Ya`Yc`Xd_Xe_Wf_WgYXgXXgWYgUY\ gTZgSZgRZgVacYd_`fXciTglQjnMmqJptFsvCqtForHmpJloLj\ mNhkQgiSehUcfWbdY`b`ZabY_dWYfUWhTVjWPeYKa_EXa9TaBS\ aCSaDRaERaGQaHQaIPaJPaKP73R73T73V73X73Z73`73a85`96\ `A7_B8_C9ZDAZXmaWlaWjbWhb } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END 20.0 PAR-FORMULA FILE==================================

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unsubscribe
by Ricardo M. Forno 01 Jul '03

01 Jul '03

Please unsubscribe me from this list. TIA.

1 0

Multifractal_5
by Albrecht.Niekamp＠t-online.de 30 Jun '03

30 Jun '03

Hi, Now a Newton formula is included. This was not easy as all newton types have a different bailout and generally they dont like to be mixed. The one I finally found is again by Pusk s Istv n, the third one I use in the multifractal series. A big Thank you! just in case heïs listening. The images really are unique for me and I guess for all of you. Fractals are fun! Al. ------------------------------start-par------------------------------------- Newtonflowers { ; Time 0.11.02.46 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult243.frm formulaname=multifractal_5 ismand=y function=cos/exp/exp/sin passes=t center-mag=1.17906/-0.00478368/1.573582/1/-90/3.88578058618804789e-016 params=-0.1156346324045534/-0.5338602862636189/12482.00001/130000.321314\ 0212/2048.02048/384.000008/384.00024/128.0076800000001/512.0076800000001\ /768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200F00<4>500400200000<2>455677899ABBBCC<18>hiijkkkll<3>rss<21>HII\ FGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000111<22>\ jeOlgPniQpjRrlStnT<2>ysX<25>BB7996775<3>000<24>n00p00r00<3>y00<22>H00 } Magic_circle { ; Time 0.25.12.59 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult243.frm formulaname=multifractal_5 ismand=y function=cos/exp/exp/sin passes=t center-mag=1.17906/-0.00478368/1.573582/1/-90/3.88578058618804789e-016 params=-0.1156346324045534/-0.5338602862636189/14282.3200001/130040.1314\ 021203/2048.02048/384.000002/384.00024/128.0076800000001/512.00768000000\ 01/768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200332<21>jeOlgPniQpjRrlStnT<2>ysX<25>BB7996775<3>000<24>n00p00r0\ 0<3>y00<25>B00900700<3>000<2>455677899ABBBCC<18>hiijkkkll<3>rss<21>HIIFG\ GEFF<3>677455344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000111 } Newtmand { ; Time 0.32.45.46 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult243.frm formulaname=multifractal_5 ismand=y function=cos/exp/exp/sin passes=t center-mag=1.1197/-0.00478368/1.573582/1/-90/-1.23373533611470521e-014 params=-0.1156346324045534/-0.5338602862636189/14282.3200001/2540.131402\ 0602/2048.02048/384.0000045/384.00024/128.0076800000001/512.007680000000\ 1/768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=2000Wd<14>09C08A068<2>022000111<22>jeOlgPniQpjRrlStnT<2>ysX<25>BB\ 7996775<3>000<24>n00p00r00<3>y00<25>B00900700<3>000<2>455677899ABBBCC<18\ >hiijkkkll<3>rss<21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<9>0Xf } Mixdown2 { ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult243.frm formulaname=multifractal_5 ismand=y function=exp/exp/exp/sin passes=t center-mag=1.1197/-0.00478368/1.573582/1/-90/-1.23373533611470521e-014 params=-0.1156346324045534/-0.5338602862636189/14237.3200001/72500.13140\ 216052/2048.02048/384.0000049/768.00024/128.0076800000001/768.0076800000\ 001/1024.00768 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200000<2>455677899ABBBCC<18>hiijkkkll<3>rss<21>HIIFGGEFF<3>677455\ 344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000111<22>jeOlgPniQpjRrlS\ tnT<2>ysX<25>BB7996775<3>000<24>n00p00r00<3>y00<30>200 } Mixdown3 { ; Time 0.38.29.40 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult243.frm formulaname=multifractal_5 ismand=y function=cos/exp/exp/sin passes=t center-mag=1.1197/-0.00478368/1.573582/1/-90/-1.23373533611470521e-014 params=-0.1156346324045534/-0.5338602862636189/14237.3200001/53000.13140\ 21613/2048.02048/384.0000049/768.00024/128.0076800000001/768.00768000000\ 01/1024.00768 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=000<3>000000000<9>X0a_0dc0h<3>p0w<4>_0dX0aU0Y<2>K0NH0JG0NE1R<3>7U\ X6`Z4h_2oa0wc<11>2TG2RE3OC<3>4D3<17>kkammcpoe<3>zwm<6>cYO`UKYQG<3>KA0000\ <43>000<4>000330<11>110110110<3>000KA4<7>gcOjgRmjT<3>zzc<9>UOFRKDOGA<3>A\ 00<9>f0Ci0Dl0F<3>z0K<6>Z0EV0DR0C<3>A08004000<25>000 } Newton_frame { ; Time 0.17.06.50 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult243.frm formulaname=multifractal_5 ismand=y function=cos/exp/exp/sin passes=t center-mag=-0.507813/-0.00478368/0.9488575/1.0685/180 params=-0.1156346324045534/-0.5338602862636189/14287.3210001/53000.13140\ 61613/2048.02048/384.0000049/768.00024/128.0076800000001/768.00768000000\ 01/1024.00768 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200000<2>455677899ABBBCC<18>hiijkkkll<3>rss<21>HIIFGGEFF<3>677455\ 344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000111<22>jeOlgPniQpjRrlS\ tnT<2>ysX<25>BB7996775<3>000<24>n00p00r00<3>y00<30>200 } Only_one { ; can be the winner ; Time 0.17.15.61 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult243.frm formulaname=multifractal_5 ismand=y function=cos/exp/exp/sin passes=t center-mag=-0.302531/-0.00478368/0.842554/1.0685/180 params=-0.1156346324045534/-0.5338602862636189/19287.3210001/53000.13140\ 81613/2048.02048/384.0000135/768.00056/128.0076800000001/768.00768000000\ 01/1024.00768 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=000<2>110110000KA4<7>gcOjgRmjT<3>zzc<9>UOFRKDOGA<3>A00<9>f0Ci0Dl0\ F<3>z0K<6>Z0EV0DR0C<3>A08004000<26>000<4>000<9>X0a_0dc0h<3>p0w<4>_0dX0aU\ 0Y<2>K0NH0JG0NE1R<3>7UX6`Z4h_2oa0wc<11>2TG2RE3OC<3>4D3<17>kkammcpoe<3>zw\ m<6>cYO`UKYQG<3>KA0000<43>000<4>000330<12>110 } -------------------------start-frm------------------------------------------ FRM:Multifractal_5 { ; Albrecht Niekamp 230603 ;only integers as first input, second input 5 digits to the right ;real(p2) 5digits: shape, outside, in1, in2, in3 ; 0_off 1_mand 2_jul/bees 3_many_mods 4_newtjul +5_reset digit1: +5_warp ; input2 : 2digits_many_mods 5digits_frm2 use : 0_no 1_yes ;imag(p2)(-) 2-4digits : quasinewton input (max 2000) ; 1digit : many_mods multipl. off 1_out 2_in1 3_in2 4_all ; 1digit : iter-reset 1_out 2_in1 3_in2 4_all ; input2 : 4digits(-)_frm1 2digits_frm2 4digits_bees ;real(p3) many_mods bailout, bailout ;imag(p3) shape : factor (fn1), outside : border-in ;real(p4) outside : factor (fn2), border-out ;imag(p4) inside1 : maxiter1, factor1 (fn2) ;real(p5) inside2 : maxiter2, factor2 (fn3) ;imag(p5) inside3 : maxiter3, factor3 (fn4) ; da=real(p2) dd=trunc(da) da=round((da-dd)*10000000)+11111 d=trunc(dd/10000) ex0=d>5 d=d-5*ex0 vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) ex1=d>0 dd=dd-d*1000 rs1=d>5 d=d-5*rs1 v1m=(d==3) v1j=(d==4) dd1=(d==2)+(d==4) d=trunc(dd/100) ex2=d>0 dd=dd-d*100 rs2=d>5 d=d-5*rs2 v2m=(d==3) v2j=(d==4) dd2=(d==2)+(d==4) d=trunc(dd/10) ex3=d>0 dd=dd-d*10 rs3=d>5 d=d-5*rs3 v3m=(d==3) v3j=(d==4) dd3=(d==2)+(d==4) ex4=dd>0 rs4=dd>5 dd=dd-rs4*5 v4m=(dd==3) v4j=(dd==4) dd4=(dd==2)+(dd==4) tt=ex0+ex1+ex2+ex3+ex4 ; mm=trunc(da/100000) da=da-mm*100000 d=trunc(da/10000) ab=(d==2) da=da-d*10000 d=trunc(da/1000) ab1=(d==2) da=da-d*1000 d=trunc(da/100) ab2=(d==2) da=da-d*100 d=trunc(da/10) ab3=(d==2) da=da-d*10 ab4=(da==2) ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) d=round((d-dd)*10000000000) pp=trunc(dd/100)/10 dd=dd-1000*pp da=trunc(dd/10) so1=((da==1)+(da==4)==0) so2=((da==2)+(da==4)==0) so3=((da==3)+(da==4)==0) dd=dd-10*da ir1=(dd==1)+(dd==4) ir2=(dd==2)+(dd==4) ir3=(dd==3)+(dd==4) ; p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=real(p3) mb=trunc(d) ba=(d-mb)*100000 ; d=imag(p3) sfac=trunc(d) b1=(d-sfac)*100000 b0=b1/2 ; d=real(p4) ofac=trunc(d) b2=(d-ofac)*100000 ; d=imag(p4) mi1=trunc(d) fac1=(d-mi1)*100000 ; d=real(p5) mi2=trunc(d) fac2=(d-mi2)*100000 ; d=imag(p5) mi3=trunc(d) fac3=(d-mi3)*100000 ; bg=((ab+vb)==0) bg1=((ab1+v1j)==0) bg2=((ab2+v2j)==0) bg3=((ab3+v3j)==0) bg4=((ab4+v4j)==0) ; if (ismand) z=0 if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else if (bg) c=p9 else c=p1 endif z=pixel endif t=0 d3=(ismand==0) u=d3 bo=z p=pp : If (tt) t=t+1 if ((ex0) && bo>b0) u=2*(fn1(t/sfac)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) ba=mb else c=pixel endif else z=pixel if (bg) c=p9*u else c=p1*u p=pp+u endif endif ex0=0 tt=tt-1 elseif ((ex1) && bo>b1 && bo<b2) u=2*(fn2(t/ofac)) rs=rs1 ab=ab1 if (dd1) if (rs) z=pixel endif vb=v1j d3=1 if (bg1) c=p9*u else c=p1*u p=pp+u endif else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1m if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir1) t=0 endif ex1=0 tt=tt-1 elseif ((ex2) && t>mi1) u=2*(fn2(t/fac1)) rs=rs2 ab=ab2 if (dd2) if (rs) z=pixel endif vb=v2j if (bg2) c=p9*u else c=p1*u p=pp+u endif d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v2m if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir2) t=0 endif ex2=0 tt=tt-1 elseif ((ex3) && t>mi2) u=2*(fn3(t/fac2)) ab=ab3 rs=rs3 if (dd3) if (rs) z=pixel endif vb=v3j if (bg3) c=p9*u else c=p1*u p=pp+u endif d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3m if (vb) if (so3) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir3) t=0 endif ex3=0 tt=tt-1 elseif ((ex4) && t>mi3) u=2*(fn4(t/fac3)) ab=ab4 rs=rs4 if (dd4) if (rs) z=pixel endif vb=v4j if (bg4) c=p9*u else c=p1*u p=pp+u endif d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v4m if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif ex4=0 tt=tt-1 endif endif if (vb) if (d3) n=z^p-1 d=p*z*z z=z-n/d else z2=fn1(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z1=fn1(z)-c ;Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p0 endif bo=|z| bo<=ba } ----------------------------------end-------------------------------------

2 1

FOTD 30-06-03 (Washboard [6])
by Jim Muth 30 Jun '03

30 Jun '03

FOTD -- June 30, 2003 (Rating 6) Fractal visionaries and enthusiasts: Today's trip into Fractal Land takes us to the parent fractal created by subtracting Z^(1.1) from Z^(-1.1) and adding (1/C). This parent fractal should more properly be called the parent fractals because the entire parent consists of two similar sized Mandeloids sitting side by side. The Mandeloid on the right is fairly intact, with all its bays and valleys, while the one on the left is only half there. Its main bay, along with other accessories, is missing. Today's image is located in the East Valley area of the intact Mandeloid on the right. I named the image "Washboard" when I noticed the square ribbed effect around the central midget. This ribbed effect is due entirely to the unavoidable discontinuities in the image. It is a good example of discontinuities leading to a positive result. And BTW, a washboard is an object that was used to wash clothes before we had washing machines. The image rates a 6, which is just the slightest above the average of all my fractals. If I had compared it to only the FOTD fractals, it would rate around a 4. I really should broaden my rating system, since nearly every FOTD image rates between a 4 and a 7. But doing so would distort the record. Perhaps I'll shift to a 0-to-100 scale and rate my images as though they were a school test. We'll see what I think about the idea. With a render time of 5 minutes, (and a rinse time of 3 minutes) the washboard cycle is a fast one. Downloading the completed image from one of the FOTD web sites: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> is even faster. Except for being a bit too warm for comfort, Sunday was a near perfect day here at Fractal Central, especially for cats. The rain held off, and the warm sun, gentle breezes and temperature of 88F 31C gave them a most enjoyable day in the yard. Of course, at their age, enjoyment for cats means sleeping as much as possible. Today is promising to be a repeat. With a little bit of luck, the duo will have another great day. And with a bit more luck I'll finish the day's work by noon, leaving lots of time to find the next FOTD. Until that next FOTD appears, take care, and the meaning of life could be encoded in a fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Washboard { ; time=0:05:10.88--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.01267188732830007/-0.352921833830621\ 70/3.316742e+009/1/107.5/0.000111833820926623972 params=-1/1.1/1/-1.1/0/0 float=y maxiter=1000 inside=0 logmap=95 periodicity=10 colors=000WhwW_uWQsWFoW6nW0lW0jW0hW0eW0aU0YS0UQ0QP\ 1PN6LL9HJDDHH9FL8DSBD_FBeHBlL9nN9xQ8sU8zW6z_6zaLz_\ Yx_zlYz_YzPYzaoznzwzziwzeszcqzQnzFlz3hz0fz0cz0az0Y\ z0Wz0Sz0Qx0Ns0Ln0NQ0N008D00eH0zN0zS0zW0za0zf1zj6zo\ 9zsDzl9zf6z_1zU0zN0zH0z90z30z00W000z6zw0zcFlJf6NaF\ QYNSUUWQaYNhaHocDwf9zh6zl1zn0zc3zS8zHBo6Fe0JU0H_0F\ c0Dh0Dl0Bq09u09x08z06z03z03z01z00z00z09z0Hz0Pz0Yz0\ ew0lo0uj0zc0zY0zU0zS0zQ0zP0zNDjWfUejeSnoHqz6uz0xz0\ Pz00z00o00c00Q80DF00N00U30SB9SHLSPWSWeSaoShzSozSuz\ SnzLhzDcz6Wx0Qs0Ln0Fj0Hl0Hl0Hn0Jn0Jo0Jo0Lq0Lq0Ls0N\ s0Nu1Nu3Pw6Pw8Px9PxBUzFYzHczJfzNlzPozQszSDqjSFWe0J\ U0DLB8BS30j00z00z00z00z10z90zF0zN0zS0w_0ue0ql0oq0n\ o0lo6njDoeLq_SsU_sPfuJnwDux8zz1zz0zx6zzFzzNzzWzzcz\ zlzzszzzzzzzzzzzzzzzzzzqzzzzzzzczzFzz00zz0zz0zz0zz\ 0zz0zz0zz0zx0zq0zl0zf0za0zW0zQ0zL0zF0z90z30z0Yze_z\ caz_azYDzs0zz0zzzzzzzzzzx } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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RE: [Fractint] FOTD 29-06-03 (Time Lash [5])
by Jim Muth 29 Jun '03

29 Jun '03

At 11:34 AM 6/29/03 -0400, Thaddaeus Parker wrote: >Jim: > >For all the time that I have been on the list I >have not once seen an FOTD below a 4. Is it similar >to our national threat level, where we will never >see a green or a red level? Curiosity is just >killing me at this point. There are so few FOTD's with a rating below a 4 because I discard these images and never use them. In the rather distant past, I have posted a few FOTD's with a rating as low as 2, and a number of images with a rating of 3. When I rate an FOTD image, I compare it to all my fractals, including those that never make FOTD. I would be more correct if I compared my FOTD images with only the other images that actually made FOTD's. BTW, you also have never seen a rating of 10. Jim M.

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FOTD 29-06-03 (Time Lash [5])
by Jim Muth 29 Jun '03

29 Jun '03

FOTD -- June 29, 2003 (Rating 5) Fractal visionaries and enthusiasts: Today's image was created by the MandelbrotMix3 formula. This formula mixes together and iterates four different powers of Z. But it has a down side. It does not automatically initialize Z to a critical point of the formula. That task must be done by hand, and the resulting value entered as real(p5), which is the reason I use the formula so rarely. Formulas such as those calculated by the M-Mix3 formula have several critical points, which are points where the function is stationary and midgets thrive, so several different fractal images can be obtained from the same formula when the critical points are calculated by hand. This is one of the good points. But big disadvantages are that calculating critical points is boring work and the resulting fractals are not that much better than those created by the MandelbrotMix4 formula. Today's parent fractal for example mixes various portions of Z^(10), Z, (1/Z), and Z^(2). The resulting image, which resembles a flying saucer or Marvin the Martian wearing an army helmet, could just as easily been created by the MandelbrotMix4 formula. The unusually precise value of real(p5) is one of the critical points of the formula, which I calculated and entered by hand. The parent fractal has X-axis symmetry, with a tiny East Valley just where it should be, and many other valleys that also probably hold worthwhile images. Today's scene is an unusually shallow one located in this East Valley. Today's image rates an average 5, largely because of its spectacularly brilliant colors, which I tweaked in a graphics program. Those who run the parameter file need not be concerned about missing the enhanced colors. The colors are fully encoded in the parameter file. The name of the image, "Time Lash", was chosen while I was watching a 'Doctor Who' episode of that name on TV late Saturday night. The render time of 1/10 second over 10 minutes on my machine, which is nearing the fossil stage, can be cut at least in half on newer units. And as always, the completed GIF image can be downloaded for convenience from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Though lots of clouds hung around here at Fractal Central on Saturday, they were thin enough to let the temperature reach 82F 28C -- near perfect cat conditions. Enjoying the conditions to the fullest, the dynamic pair had a peaceful day in the yard. The pushy cat from two doors down the hill stayed where he belongs for a change, so their peace was uninterrupted. Today is starting sunny, and the temperature is still near ideal, but showers are possible. It remains to be seen how the cats' day will go. I'm going to spend the day doing as little as possible. If I get ambitious, I might resume work on the FOTD CD, which has been nearly but not quite ready for several months. I'll probably end up releasing the CD in imperfect form, but I'm not quite ready to give up hope of perfection yet. Until next FOTD, take care, and stay in there with the big-time thinkers. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Time_Lash { ; time=0:10:00.10--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3a function=ident passes=1 center-mag=+1.506891153995481/-0.00013746456513907\ /205962.1/1/-172.5/2.01858393888976195e-009 params=0.001/10/1/1/1/-1/0.1/2/-1.403897684563/0 float=y maxiter=4200 inside=0 periodicity=10 colors=000z0zz0zz0zv0zP0z0lz0zz0zz0zz0zz0zz0zz0zz0\ zz2zz6zzBzvGzhKzZPzPUzBZz2cz0hz0vz0zz0zz0zz0zz0zz0\ zz0zz2zz6qzBhzGZzKPzPBqU2cZ0Pc0Bh02l00q00v00z00z6K\ 6zz0zz0zz0zz0zz0zz0zz0zq0lc0cK0P60G0220G00P00c00l0\ Xz0Wx0Vw0Uv0Tu0St0Rs0Qs00s00s00t00t00u00u20w20w60z\ B0zB0zG0zG0zG0zG0zP0qU0Zc0Gh20lB0vK0zU0zc0vZ0lU0cU\ 0ZP0PP0GK0BK02G00G00B00B00600200200000000000000000\ 000000000Z0zzPzzzzzzzzvzzhzvUzZGzG2h00P00600000000\ 00000000000000000000000000000000000000000000000000\ 000000000000000600B00K00P00Z60cG0hK0qU2vc2zl6zvBzz\ BzzGzzKzzKzzPzzUzzUzzZzzczzczzhzzhzzhzzlzzlzzlzzqz\ zqzzqzzvzzvzzvzzzzzzzzzzzzzzzzzzzzzzvUzK0z00z00P00\ 0000zz2zz6zzBzzGqzKlzKczPZzUPvZKqcBhc6ch0Zl0Pq0Kv0\ Gv06z02z00z00z02z2BqUKhqPczZUzhKzlGzP6z62z00z00z00\ z00z00z00z00z00z00z02z06z0Bz0Gz0Kz0Pz0Zz0cz0hz0lv0\ qv0vq0zl0zl0zh0zGUzU2zl0z } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END 20.0 PAR-FORMULA FILE==================================

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EMACS
by Programmer Dude 29 Jun '03

29 Jun '03

David Jones wrote: > Methinks when I replace my current CorelLinux > installation with a more moden Linux, I should try out > Emacs ... Wouldn't surprise me if both EMACS and vi came with linux. I know vi comes with most unices. Learning either is a major time investment. A technique that has worked for me is to try to learn one new thing each time I use it ("it" being vi in my case). The EMACS/vi thing reminds me a little of the old Word/WordPerfect religious war.... ;-) -- |_ CJSonnack <Chris(a)Sonnack.com> _____________| How's my programming? | |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | |_____________________________________________|_______________________|

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[Fractint] Re: Fractals Relate to Expansion-Contraction of the Universe
by JackOTradez 28 Jun '03

28 Jun '03

"All the Universe's a Fractal, and all the men and women merely pixels . . .. ... ..... ........ " "New Scientist" 21 August 1999. Stay Amazed JoTz

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FOTD 28-06-03 (A Merry Land [4])
by Jim Muth 28 Jun '03

28 Jun '03

FOTD -- June 28, 2003 (Rating 4) Fractal visionaries and enthusiasts: Today's image rates only a 4. This sub-standard rating is justified because the image has a flaw known in the world of visual art as muddiness. Muddiness results when colors with too great a difference in brightness are mixed together. Today's image has exactly this flaw, which earns it the 4. Some of the muddiness can be eliminated by changing the inside color from a flat black 00 00 00 to something like a grey 40 40 40. But nothing can save a fractal picture like today's, which is flawed from the start by too much detail. I named the picture "A Merry Land". The name has nothing to do with the fact that Fractal Central happens to be located in the state of Maryland. I gave it the name because, despite the muddiness, there is a kind of merriness in the picture. The generating formula takes the tiniest bit of Z^100 and adds Z^(-2) to it. Even though the portion of Z^100 is only 1/10^32, this tiny bit overwhelms the Z^(-2) and creates an oversized lopsided hole filled with a triangle. Today's scene is located near the tip of the western arm of the triangle. Like yesterday's image, today's is slow. It takes over one hour to render on my machine. The best way to see the image is to wait an hour or so for Paul and Scott to render it, and avoid the hassle of rendering it yourself by downloading the completed GIF image from one of the FOTD web sites: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The sun and temperature of 90F 32C on Friday here at Fractal Central was just what the dynamic fractal cats needed to put them in a good mood. They spent the afternoon romping in the yard and lounging on the porch. At one point the cat from two doors down the hill appeared, lurking behind the holly trees. Luckily, I was there to restrain Tippy, who was ready to start a fight. The day ended peacefully, with a pair of exhausted but hungry cats ready to eat and sleep. Today is starting cloudy and cooler. I've got enough work to keep me busy an hour or so, and there is always the grass to trim. It looks like it will be another normal day here at F.C. The next FOTD will appear in 24 hours. Until then, take care and life could be a never-ending fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Merry_Land { ; time=1:21:18.60--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-1.67128436773857100/-0.029296149029013\ 39/5.503277e+009/1/116.9017790300461/1.20521654432\ 482617 params=1e-032/100/1/-2/0/0 float=y maxiter=7200 bailout=5 inside=0 periodicity=10 colors=000bQ`cP`dOaM1pWChdNamYVwhPvgOvfOueNudNucNt\ cMtbMtaMs`Ls_LrZKrZKrYKqXJqWJqVJpUIpUIpTIoSHoRHnQG\ nPGnPGmOFmNFmMFlLElKElKEkJDkIDjHCjGCjFCiFBiEBiDBhC\ AhBAj86iA8hBAhCCgEEfFGfGIeIKdJMdKOcMQbNSbOUaQWaRY`\ S__Ua_VcZWeYYgYZiX_kWamWboVcqUetVdsWdrWdrXdqXdqYdp\ YdoZdoZdn_cn`cm`claclackbckbcjcciccidbhebhebgfbffb\ fgbegbehbdhbciacjabjabkaaka`la`la_ma_maZn`Yo`Yo`Xp\ `Xp`Wq`Vq`Vr`UvZVr`UoaTlbTidSfeScfR`hRYiQVjQSlPPmP\ MnOJpOGqNCsMDrNDqNDqNDpNEpNEoNEoNEnNFmOFmOFlOFlOGk\ OGkOGjOGiOHiOHhPHhPHgPIgPIfPIfPIePJdPJdQJcQJcQKbQK\ bQKaQK`QL`QL_QL_RLZRMZRMYRMXRMXRNWRNWRNVRNVSOUSOUS\ OTSOSSPSSPRSPRSPQTQQTQPTQOTQOTRNTRNTRMTRMTSLUSKUSK\ USJUTJUTIUTIUTHURHVTHUUHTVHTWHSYHSZHRWRXUUVSXUQ_TO\ bRMeQJhPHkNFnMDqLBtJ9wI7yH8wI9vJAuJBtKCsKDrLEqLFpM\ GoNHnNImOJlOJkPKjPLiQMhRNgROfSPdSQcTRbTSaUT`VU_VUZ\ WVYWWXXXWXYVYZUZ_TZ`S_aR_ } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 27-06-03 (Deep in Scepter Valley [4])
by Jim Muth 27 Jun '03

27 Jun '03

FOTD -- June 27, 2003 (Rating 4) Fractal visionaries and enthusiasts: Due to an unexpected rush job, today's FOTD is late. Since I had almost no time to find a proper FOTD image, I returned to that old warhorse, the Mandelbrot set and found a scene deep in Scepter Valley. During the 3-1/2 hours the scene was rendering, I accomplished other things. When the image was finished, I named it "Deep in Scepter Valley". I gave almost no attention to coloring the image, which limits it to a rating of a 4 -- a little below average. The average fractalist will have little desire to spend 3-1/2 hours waiting for a below-average scene to finish. I recommend visiting one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> and downloading the completed image from there. I sent Paul and Scott the finished image several hours ago, so it should be posted shortly. The temperature reached 97F 36C here at Fractal Central on Thursday. This was too hot for the sensitive duo, who passed the afternoon under the cool air vent. Their moods were surprisingly good for a day that was so hot. No tuna was needed. Today will once again be hot, but not as hot as yesterday. I expect the duo to have another good day. My day will turn good when I wrap up the unexpected pile of work that came in last evening. The next FOTD will appear on schedule in less that 24 hours. Until then, take care, and be practical. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= DeepInScepterVally { ; time=3:24:13.78--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-1.2537\ 967393837293717/0.02363815462420420844/1.061236e+015 params=0/0 float=y maxiter=12000 bailout=5 inside=0 logmap=2534 periodicity=10 colors=000HabC``GabJadNbfQbhUcjXckVZmTVnRRoQNpPMrP\ MuOLwOLyPUnPbdQkVQsLXoNbkOhgPncQt_RrXQpVQnTQV4OmQQ\ kOQiMPgKPfHPdFPbDP`BO_8OY6OW4O3jM5fN7cN9`NBYNDUNFR\ NHONJLOLIONEOPBOR8OT5OMbNNZOOWOPTOPQOQNORKOt9fy4gw\ 8huBitEjrHkqKloOmnRnlUokXpi_qhbqjankaklahmafnacoa`\ q`Yr`Ws`Tt`Qu`Nv`LmeTei`YngQroEyxIvvLttPrsSoqWmpZk\ naim_klZmkYokXqjWsjVuiTylUviVtgWreWpcXn`YlZZiXZgV_\ eS`cQaaO_aJa_MbYPcWSeVVfTYgR`hPcjOfkMilKlmIooHrpFu\ qDxrCzlHxgLwaQvXUtRZsMbrLapKaoJ`nI`lH`kG_jF_hEZgDZ\ fCZdBYcAYb7_d9YaBX_DVYFUWHSUIRSKPQMOOONLQLJRKHTIFV\ HDXFBZE9X76_D7bI7eN7hS7kX7mZ4na7ncAofDohGpkJuoOpmM\ llLhkJdiI`hHWgFSeEOdCKcB8c1GbAObJWbSca`kaisarzazs`\ sl_lf_f_Z_UYUNYNHXHAWA1Z04W46T88RCBOGDLJFJNIGRKDVM\ BYyK`HCHIGQJKYKOeLSmKYwMVuOStPPsRMrTJpUGoWDnYAmZ7l\ YAjYCiYFhYHgYKfYMeYPdXRbXUaXW`XZ_X`ZXcYXeXVdYUdYTd\ ZRcZQc_Pc_Nb`Mb`LbaJaaIab } END PARAMETER FILE=========================================

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[Fractint] re: Fractals Relate to Expansion-Contraction of the Universe
by Programmer Dude 27 Jun '03

27 Jun '03

Osher Doctorow (not Marleen Doctorow) writes: > I have been arguing [...] that fractals relate directly to > expansion-contraction of the universe. "Directly" perhaps remains to be seen. The idea of surfaces is interesting, though. I've read that some fractal "purists" only ever color the Mandlebrot in two colors: inside & outside. > The most unusual thing about expansion-contraction is that it differs > from ordinary curvilinear or linear motion in involving GLOBAL and > CONTROL properties... How does this really differ from ordinary movement, which also would seem to involve GLOBAL and CONTROL properties? For example, doesn't the earth's orbit involve properties "global" to the system (e.g. the earth's mass) as well as "control" properties (e.g. gravity)? It would seem that motion through space of an object where the object does not change form is distinct from motion involving a form change. In my experience, the term "orthogonal" is sometimes used to refer to properties that are not related. I would think that shape-changing movement is orthogonal with respect to non-shape-changing movement. Certainly some objects may do both. Throughout my life, my shape has changed (mostly gotten larger!), but I have also constantly moved through space (and time). > Fractals are BOUNDARY phenomena, and therefore are vitally related > to surfaces which are also boundaries of their insides and outsides > in 3 dimensions, or to projections of surfaces in 2 dimensions > (boundaries of continents, leaves, trees, etc.). There are many BOUNDARY phenomena, however. Is not the most salient aspect their fractal dimensionality? Do the expansion/contraction phenomena under study here demonstrate this? If not, I would question the connection. > It might be agreed by readers that Fractals are related to expansion- > contraction as surfaces,... The relation seems tenuous thus far. The fractal dimension aspect seems missing or not covered. Further, a given fractal seems static; neither expanding nor contracting. > Well, it turns out that there aren't that many types of objects in > the Universe which are expanding or contracting as their > characteristic motions. [grin] Yet your own list names some rather significant ones! After life, thought, energy and the entire universe, what's left? (Incidentally, I would add metals and water to that list.) > There is some prospect that not only can we generate fractals in the > above manner, but that ALL expansion-contraction objects obey similar > algebraic and calculus/analysis/differential equation formulas which > sharply distinguishes them from ordinary objects which only have > curvilinear or linear motion. I'll try to keep readers informed of > major developments as they occur. Okay! ;-) -- |_ CJSonnack <Chris(a)Sonnack.com> _____________| How's my programming? | |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | |_____________________________________________|_______________________|

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Fractals Relate to Expansion-Contraction of the Universe
by MARLENE DOCTOROW 26 Jun '03

26 Jun '03

>From Osher Doctorow (not Marleen Doctorow) I have been arguing on http://www.superstringtheory.com/forum, in the Strings/M Duality subforum of their Forum section, that fractals relate directly to expansion-contraction of the universe. In the cosmology branch of physics and mathematical physics (the latter is technically a branch of mathematics), where I spend much of my time, there is considerable interest in the expansion, contraction, and acceleration of the universe. The most unusual thing about expansion-contraction is that it differs from ordinary curvilinear or linear motion in involving GLOBAL and CONTROL properties - a whole bunch of coordinated parts of an object like a balloon expand or contract simultaneously, and theoretically different parts of an object can be controlled to expand at different rates. Up to this point in my posting, it doesn't look as though fractals and expansion-contraction have anything unusual about them, but now notice that the SURFACE of a balloon is critically involved in its expansion- contraction. The SURFACE, not just the volume, expands in coordination, and the surface reflects different rates of expansion. Fractals are BOUNDARY phenomena, and therefore are vitally related to surfaces which are also boundaries of their insides and outsides in 3 dimensions, or to projections of surfaces in 2 dimensions (boundaries of continents, leaves, trees, etc.). It might be agreed by readers that Fractals are related to expansion- contraction as surfaces, but what does this have to do with the Univese other than the fact that the Universe is supposed to be expanding? Well, it turns out that there aren't that many types of objects in the Universe which are expanding or contracting as their characteristic motions. Most things move curvilinearly (in a curve) or linearly (in a straight line). They don't blow up or contract like balloons. Here's a list of things in the Universe that do expand-contract as their characteristic motions. A. The whole universe itself as for example in the usual spherical model. B. Radiation (light, heat, etc.) from a source (a point or string) C. Biological life (growth, muscular movements, etc.) D. Human consciousness, memory, perception E. Galaxies (evolving with expansion or contraction from spiral to elliptic, etc.) F. Organic materials such as plastics which have viscoelasticity. David J. Wright (Oklahoma State) "Dynamical systems and fractals lecture notes," 8-19-96, www.math.oksate.edu/mathdept/dynamics/lecnotes/lecnotes.html, explains very clearly how fractals are generated by CONTRACTIONS of iterated function systems (IFS), either linear or hyperbolic. There is some prospect that not only can we generate fractals in the above manner, but that ALL expansion-contraction objects obey similar algebraic and calculus/analysis/differential equation formulas which sharply distinguishes them from ordinary objects which only have curvilinear or linear motion. I'll try to keep readers informed of major developments as they occur. Osher Doctorow Ph.D. One or More of California State Universities and Community Colleges

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Re: HTML and web pages
by JackOTradez 26 Jun '03

26 Jun '03

Folks - I too have usually done my web page(s) initially with notepad; basic HTML is quite EZ 2 learn. However, I would enlighten you to a FREEware program I have just recently encountered, called HTML-kit. You can fetch it at http://www.chami.com/html-kit/ and it is fully functional and free. WHY someone gives away a good program like that free is a question for a better philosopher than I. It automatically inserts tags, has a friendly interface, can check coding format, and do a lot other things I can not begin to list here. It is quite sophisticated. Check it out! JoTz

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FOTD 26-06-03 (Hers and His [6])
by Jim Muth 26 Jun '03

26 Jun '03

FOTD -- June 26, 2003 (Rating 6) Fractal visionaries and enthusiasts: Yesterday's FOTD picture was named "His and Hers". But because I inadvertently substituted a space band for an underscore between the words 'and' and 'hers', the word 'hers' did not appear when the parameter file was loaded into Fractint, and a great inequality was done to women. Since yesterday's image was named "His and Hers" for no reason at all, today's image can also be named for no reason at all. And so that justice might prevail, I have named today's image "Hers and His", with the feminine aspect in first place. The image is a scene in the parent fractal that results when 0.7 parts of Z and 0.7 parts of Z^5 are combined and C is added. This parent resembles a distorted M-set with its nose pointed southeast and its butt pointed northwest. Some distance beyond its butt lies a string of Julia-like open circles. Today's scene lies on a filament on the shore of one of the larger circles. To produce the strange effect, the scene was rendered with the outside set to 'fmod' and the inside set to 'bof61'. The inside part of the image consists of the interior of the central midget as well as the egg-shaped areas. I used these non-standard fills because when rendered in the normal manner, the image is downright dull. When the time arrived to rate the scene, I saw a picture that had been rescued from an abysmal rating of 3 or so and raised to an image that was actually a little above average. I rated today's image at a 6. The render time comes in at under 3 minutes on my tired-out fractal machine. It downloads in even less time from the FOTD web sites, which can be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Wednesday brought another typical 93F 34C summer day to Fractal Central. The sun was hot, the humidity was high, the wind was light, and the air was polluted. It was just the kind of day to bring out the laziness in the fractal cats, who spent the entire afternoon sleeping on the lawn chairs in the shade of the holly trees. Today will be a hotter repeat. It will also be a repeat for me. I don't have much work to finish, but the little bit I do have must be finished today. Until next FOTD, take care, and the world is filled with unseen fractal wonders. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Hers_and_His { ; time=0:02:54.61--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.610840504599416/+0.61145130410153/30\ 9223.4 params=0.7/1/0.7/5/0/0 float=y maxiter=800 inside=bof61 proximity=0.5 outside=fmod logmap=yes periodicity=10 colors=000otznszmrylqxkpwjovinuhmtg\ lsfkrejqdipchobgnafm`el_dkZcjYbiXahW`gV_fUZeTYdSXc\ RWbQVaPU`OT_NSZMRYLQXKPWJOVINUHMTGLSFKREJQDIPCHOBG\ NAFMAELBDKBCJEBIGAHHBGHBFJEELEBNGBPGBPGBRHBSHBUJBU\ JBWLBXLBZLB`NA`NAbPAdPAfRAfRAgRAiSAkSAlUAlUAnW7pW7\ rW7rX7sX7uZ7wZ7x`7x`7z`7zb7zb5zd5zd5zf5zf5zf5zg5zg\ 5zi5zi5zi5zg7zgAzgBzfBzfEzfGzdHzdHzdJzdLzbLzbNzbPz\ `Rz`Rx`SwZUwZUuZWuZXsXZsXZrX`pWbpWdnWdnWflUgkUgkUi\ iSkiSlgSlfRnfRpdRpdRrbPs`Pu`PuZNwZNxXNzXNzWLzULzUL\ zSJzSJzRJzPHzPHzNHzNHzLGzJGzJGzHEzHEzGEzAHzEGzGEzH\ BzJAzL7zN5zP4zR1zS0zW0zX0zZ0z`0zb0zd0zf0zg0zi0zi0z\ k0zk0zl0zl0zn0zn0zp0zp0zr0xr0ws0us0su0ru0pw0nw0kw0\ ix0gx0fz1dz4bz4`z5Zz5Wz7Uz7SzARzBPzBNzELzEJzGGzGEz\ HBzJAzJ7zL5zL4zN1zN0zP0zR0zR0zS0zS0zU0zZ0zW0zU0zS0\ zP0zN0zL0zH0zG0xE0uB0r70n51k44g05d07`0AZ0A`0B`0B`0\ B`0B`1B`4B`4Bb5Bb7BbABbABbBBbEBbEBbGBdHB } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] FOTD 21-06-03 (Beware the Lava Pit [5])
by gnome＠hawaii.rr.com 26 Jun '03

26 Jun '03

>Programmer Dude wrote: >> >> I cannot recommend highly enough "gvim", which is "GUI vim", which >> is a window version of vim, which is a charityware version of vi...on >> steroids! 100% compatible with vi (in all important respects), plus >> much, much more. It's been my primary editor for years! (You even >> find a lot of unix platforms that have aliased it for "vi".) >> >> Vim (Vi iMproved): http://www.vim.org/ >> > >Wha about Emacs ( http://www.gnu.org/software/emacs )? > >Ciao, >Danilo Emacs isn't just a text editor. Emacs can do so much more that it has become a religion! ;-) David an old vi user gnome(a)hawaii.rr.com

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Re: FOTD 25-06-03 (His and Hers [7])
by Jim Muth 25 Jun '03

25 Jun '03

At 09:54 AM 6/25/03 -0500, Paul Lee wrote: >For those that save PAR files (and for Jim's FOTD CD), you >may wish to add another underscore to the 'name': >His_and_Hers > >Sincerely, >P.N.L. I caught the mistake as soon as I sent the FOTD. Since the PAR file still renders correctly, and the error is obvious, I did not repost it. Murphy's law says that every FOTD I check before posting will be correct, while those that I do not check will all have errors. :-) Jim M.

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FOTD 25-06-03 (His and Hers [7])
by Jim Muth 25 Jun '03

25 Jun '03

FOTD -- June 25, 2003 (Rating 7) Fractal visionaries and enthusiasts: Adding Z to Z^3 changes the entire shape of the resulting fractal. Adding Z to Z^2 merely shifts the position of the fractal without changing its overall shape. When the exponent is between 2 and 3, the closer to 3 the greater the change. For today's image I varied the exponent between 2 and 3 to observe the gradual change. I settled on Z+Z^2.05+C because I noticed a lot of interesting chaos along the splitting negative X-axis. Today's image is located in this chaos. Most of the artistic effect is created by the 'fmod' option, which was applied to the outside parts of the image. Don't ask me why I chose the name "His and Hers". I can see nothing whatever in the picture to justify such a name. But even though the name makes little sense, the image is still worth a 7. The render time of 5 minutes is reasonable for the above-average result. And the completed GIF image is available on the internet for download at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> A perfect summer day with lots of sun and a temperature of 91F 33C on Tuesday here at Fractal Central made for perfectly happy cats who spent several hours on guard in the yard. When the cat from two doors down appeared in the brush, Tippy was ready to attack. Luckily for someone, the cat backed off and no force was needed. Thomas slept through the danger. The similar forecast for today should bring similar conditions. And if I finish the necessary work early enough, I might find some time to enjoy the day myself. Until next time, take care, and search for that lost fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ His_and Hers { ; time=0:05:02.98--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-1.57498835838500200/+0.013976629359833\ 04/1.084695e+011/1/80/-0.0922994127536091724 params=1/2.05/1/1/0/0 float=y maxiter=650 inside=0 proximity=0.25 outside=fmod logmap=yes symmetry=none periodicity=10 colors=000SGdRGdQHcQHcPIcOIbNJbNJbMKaLKaKL`KL`JM`I\ M_HN_GQYHN_HLaIJcIHeIFgJDhJBjJ9lK7nK5pL0qK2qK3qJ4q\ J5qJ6qI7qI9qIAqHBqHCqHDqGEqGGqGHqFIqFJqFKqELqENqDO\ qDPqDQqCRqCSqCUqBVqBWqBXqAYqAZqA`q9aq9bq9cq8dq8eq8\ er8fq8fp8fo8fn8fn8gm8gl8gk8gj8gj8hi8hh8hg8hf8hf8he\ 8id8ic8ib8ib8ia8j`8j_8j_8jZ8jY8kX8kW8kW8kV8kU8kT8l\ S8lS8lR8lQ8lP8mO8mO8mN8mM8mL8mLAnNCnODnPFoQGoRIoSJ\ pTLpUMpVOqWPqXRqYSrZUr_Vr`XsbYsc_sd`tebtfctgeuhhui\ kujnvkqvltvmwwnzwozwpzxuyxswwquuostmqskoqimpgkoeim\ cglaej_ciYahW_fUYeSWdQUbOSaMQ_KOZIMYGKWEIVCHU9HTAF\ SBDRBBQCAPD8OD6NE4MF2LD3KE3JF3IG3HH3GI3FJ3EK3FK3GL\ 3HM3JN3KO3LP3MQ3NR3OR3PS3QT3RU3SV4UW4VX4WY4XY4YZ4Z\ _4_`4`a4ab5bcAddFedKfePgfUhgZihdjijkjolkumjxmkulkp\ lkjkkejk_jlVilPhlKhlFgl8fl7fm7em7dm7dm8cm8bm8bn8an\ 9`n9`n9_n9ZnAZoAYoAXoAXoBWoBVoBVpBUpCTpCTpCSp6Uw9T\ sCSpFRmHRiWDfVEfUEeTFeTFe } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 24-06-03 (Good Fortune [6])
by Jim Muth 24 Jun '03

24 Jun '03

FOTD -- June 24, 2003 (Rating 6) Fractal visionaries and enthusiasts: The formula that created today's image is one of the simplest -- Z+Z^3+C. Yet it creates a parent with scenes that rate at least a 6, as in today's picture, and likely with scenes that would rate a 9, if only they could be found. Curiously, adding Z to Z^2 makes no change in the appearance of the Mandelbrot image, though it does move it to the west, but adding Z to Z^3 totally changes the appearance of the resulting fractal. The parent fractal of today's scene consists of an obvious Mandelbrot set standing on its nose, with much interesting detail beyond its East (or North) Valley, and an almost completely obscured Mandelbrot set hidden beneath the detail beyond the first Mandeloid's East Valley. This second M-set is visible only with carefully chosen coloring. Today's image is located in a spiral in a valley near the northern extremity of the parent. The unusually-well-defined pattern surrounding the midget is a result of the coloring. With other palettes the pattern vanishes. I named today's image "Good Fortune". When I gave it this name, I had an idea in mind, but whatever it was, it has eluded me. So let's just say the scene in the image is very lucky to have been found. The odds against it ever having seen the light of day are at least one-googol-to-one. The image takes 1/2 hour to render on my machine. This is a bit of a drag for busy fractalists. So I recommend downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Summer weather finally arrived at Fractal Central on Monday, as the temperature reached 89F 32C and the hot sun beamed down on the fractal cats, who were pleased with the turn of events and showed their pleasure by playing like kittens. Tippy actually scampered up a holly tree, while Thomas watched with amusement. No tuna was needed. Since today will be a repeat, I expect a repeat performance from the dynamic duo. I'll do my part by finishing the work early. But to finish the work, I must first start it, so until next FOTD, take care, and wait until the fractals come home. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Good_Fortune { ; time=0:29:42.99--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.00290337839407/+1.12763603161069/6.4\ 25424e+008/1/-177.5/-0.00023613749 params=1/1/1/3/\ 0/0 float=y maxiter=4200 inside=0 periodicity=10 colors=000AVK8TK6TM6RM4PM2PM0OM0MM0MM0KM0IM0GI0IM0\ IO0IP4IR6ITAIVCIXGIYIIbMIdOIeRIgTIiXIkYIlbIndIpgIs\ iIulIwnIxrIzsIzwIzxIzzIzzIzzIzzIzzIzzIzzIzzIzzIzzI\ zzKzzMzzOzwPzpRziTzbVzVXzOYzG_z4XzA_zGdzKgzPkzVnzY\ rzduzixwlzunwwpswrpwslwuiwwewx_wzXwzTwzPwzMwzIwzCw\ z8wz4wz0wz0wz0wz0sz0wz0xz0zs8zkEzbKzTRzKXzCbzI_zMY\ zPXzTVxXTu_RrePniOllMipKesIbwG_zEXzCTzAPz8Oz6Kz4Gz\ 2Cz2Az08z06z06z04z02z02x00u00p00l00i00e00_00X00T00\ P00K00G00C008006006006004004204602A02C02G02K00O00P\ 00T00X00Y00b00e00i00k00n00r00u00w00z00z00z00z00z00\ z00z04z4IsEVgPgXYsKgz6rz0zz0zz0zz0zz0zz0xz0uz0sz0p\ x0nu0kr0in2ek4dg6_d8Y_AXXCTTERPGOMIMIKIEMGAOC6PA2R\ 60T40V00X00Y00_00b00_00Y00X00V00V22T46R6AP8COAGOCK\ MEOKGRIIVGKYGMbEOdCPgARk8Tn8Vr6Xu4Yx2_z0bz0dz0iz0n\ z0sz0xz0zz0zz0zz0zz0zz2zw6zrCzlGzgKzbOzXRzRVzM_zGd\ zAgz4kz0nz0rzG_KEYKCXKCXK } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 23-06-03 (More of the Brush [7])
by Jim Muth 23 Jun '03

23 Jun '03

FOTD -- June 23, 2003 (Rating 7) Fractal visionaries and enthusiasts: To start the day, I downloaded the usual hundred or so junk e-mails. Before deleting them, and being certain I was off- line, I checked the content of one e-mail, which had an unusually clever subject line about an old friend who had just found me. Not surprisingly, the letter was not from an old friend, but from one of those questionable on-line pharmacies with doctors who prescribe prescription drugs without an examina- tion. It would have been just another unwanted piece of junk had it not been for the line that read, "if you act now, your order can be shipped by January". No wonder only one recipient in ten-thousand replies to such letters. Fractals are far more reasonable. Today's image has been created by an entirely different formula than yesterday's, but the same brush-like shape is there. Whereas I decided that yesterday's image rated a 6 and then lowered it to a 5 at the last minute, today's image rates a firm 7. I named the image "More of the Brush" in recognition of the fact that its basic shape closely resemble the brush shape of yesterday's image. The formula behind today's image is Z^10-Z^9+C. This formula produces a parent fractal that is little more than an circle with broken bays around its perimeter. It displays critical characteristics only in the area of its 'East Valley', which is where today's scene is located. The outside parts of today's image were rendered by the 'fmod' option, which in this case does a better job than the standard equal-iteration-bands method. The brilliant turquoise color of the inside of the central midget is a departure from my standard dead black inside color, used today because it works well. The 5-minute render time is within reason, but the 1-minute-or- less download time is even more reasonable. The GIF image can be found, ready for download at either one of the two FOTD web sites: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The clouds hung around most of Sunday at Fractal Central while we were away on the shopping trip. When we returned at 6pm, the sun was trying to break through, the temperature was 79F 26C, and the cats were ready to romp. They enjoyed the yard for over two hours before hunger brought them inside to eat. Today is sunny and warmer -- the kind of weather fractal cats approve of. I've got a bit of work to do before I re-enter the world of fractals, and the sooner I get started, the sooner I'll finish. So until next FOTD, take care, and don't lose the faith. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ More_of_the_Brush { ; time=0:05:24.29--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=ident passes=1 center-mag=+1.00172680834191900/-0.000089662866518\ 10/8255452/1/-147.5/1.85261191e-007 params=1/10/-1\ /9/0/0/0/0 float=y maxiter=850 inside=255 proximity=0.7 outside=fmod logmap=yes periodicity=10 colors=000zzwyztxzqwznuzkszhqzhozhmzhkzhizhgzieyic\ xiawi_viZuiYtiXsiWrjVqiUpiTohSnhRmgQlgPkgOjfNifMhe\ LgeKfeKedKddJccJbcJabJ`bI_bIZaIYaIX`HW`HV`HU_HS_GR\ ZGQZGOYFNYFMYFKXFJXEIWEGWEFWEEVDCVDBUDAUD9UE8VF8WG\ 8WG8XH8YI8YI8ZJ8ZK8_K8`L8`M8aM8aN8bO8cO8cP8dQ8dR8e\ R8fS8fT8gT8hU8hV8iV8iW8jX7kX7kY7lZ7lZ7m_7n`7n`7oa7\ ob7pc7qc7qd7re7se7sf7tg7tg7uh7vi7vi7wj7xk7yk7zl7zm\ 7zm7zl9zlAzlCzkDzkEzkFzjGzjHzjIziJziKziLzhMzhNzhOz\ gPzgQzgRzgSzfTzfUzfVzeWzeXzeYzdZzd_zd`zcazcbzcczbd\ zbezbfzbgzahzaizajz`kz`lz`mz_nz_oz_pzZqzZrzZszYtzY\ uyYvxYwwXxvXxuXwtWvsWurWtqVspVroVqnUpmUolUnkTmjTli\ TkhSjgSifSheSgdRfcRebRdaQc`Qb_QaZP`YP_YPZXOYWOXVOW\ UNVTNUSNTRMSQMRPMQOMPNLOMLNLLMKKLJKKIKJHJJGJIFJHEI\ GDIFCIEBHDAHC9HB8HB8HFBHJDHMFHQHHUJHXLH`NHdQHgSHkU\ HoWHrYHv_Gz`HyaHxaIwaIvbJubJubKtcKscKrcLqcLpdMpdNg\ fNhfNhfNifNigNjgNjgNkg0zz } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 22-06-03 (Haidinger's Brush [5])
by Jim Muth 22 Jun '03

22 Jun '03

FOTD -- June 22, 2001 (Rating 5) Fractal visionaries and enthusiasts: Today's image reminds me of Haidinger's brush, and that is what I named it. Haidinger's brush is not a cleaning device or scrubbing device; it is almost like a fractal. The brush is not a real brush at all; it is a figure seen at the center of the field of vision when gazing at a smooth and polarized source of light, such as the clear blue sky at 90 degrees from the sun. This ability of the unaided human eye to detect polarized light is little known, but most certainly does exist and can be scientifically demonstrated. Though it is not actually a sixth sense, it comes rather close. A far more complete discussion can be found on the internet at: <http://polarization.com/haidinger/haidinger.html> As a fractal, today's image rates a 6. It was created by subtracting 1.2 parts of Z^(-0.93) from 1.2 parts of Z^(0.93) and adding (1/C) instead of plain C. The resulting parent fractal has a large bay with a very extended, drawn-out shore- line dotted with tiny bays. Today's scene is located on one of the arms of a 'star' at the tip of the filament extending from one of these bays. The image is not all that different from what would be found in the classic Mandelbrot set at a similar location. Therefore, I could rate it no higher than an average 5. But this is the *FOTD* average. And the FOTD average is well above the average of all fractals :-) so the image is worth a quick look, if not the 23-minute render time. That quick look may be found at Paul's web site: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or at Scott's site: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Scattered thunder-showers started popping up in the local area around 4pm on Saturday, finally joining together into one monster storm at 7pm, which flooded many sections on the east side of town. Fractal Central, which is on the east side, escaped with only a puddle of water in the basement; others were not so lucky. Before the rain arrived, the temperature reached 73F 23C, and there was enough sun to give the cats a satisfac- tory day in the grass. The forecast for today is for improved conditions. We'll see what happens . . . Today I find myself going on another of those trips to examine the old junque that others have discarded. Departure time is in an hour, so until next FOTD, take care, and the best is yet to come. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Haidingers_Brush { ; time=0:23:23.32--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=-1.97873106110103800/+1.880302311215394\ 00/486402.7/1/-30/1.06422635703928847e-008 params=1/0.93/-1/-0.93/0.2/-30/0/0 float=y maxiter=3200 inside=0 logmap=347 periodicity=10 colors=000UKUXY_TZaP_cLcgIgkFjoBns8rw5uzG_gQFQBHRD\ JQFKQHMQJNQLOQNQQORPQSPSUPUVPWWPYYPZZP`_ObaOdbOfcO\ heOjfOkgNmiNojNqkNsmNuoNwqQvoNukKtfHsaErZBqU8pM5jP\ AdSEZVJTXNN_SHbWBe`6gd8eb9c`BaZC_XDYVFWTGVRHTPJRNK\ PLLNJNLHOJFPIDRGBSE9TC7VA5W83X71Y93YA5YB7YC9YEBYFD\ YGFYHHYJJYKLYLNYMPYORYPTYQVYRWZSV_SU`TTaTTcUSdVReV\ QfWPhWOiXNjXNkYMlZLnZKo_Jp_Iq`Hr`Hq_Iq_Jq_Kq_KqZLp\ ZMpZNpZNpZOpYPpYPoYQoYRoYSoXSoXTnXUnXVnWVnWWnWXnWX\ mWYmVZmV_mV_mV`lValUblUblUclUdmSclUdlWelXelZfk_gka\ gkchkdijfijgjjikjkkillinmiomiqnirngslfskesjdsicsga\ sf`se_sdZscYsaWs`Vs_UsZTtXStWRtVPtUOtTNtRMtQLtPJtO\ ItMHtLGtKFtJCvJEtIFrIHpHInHKlGLjGNhFOfFQdERbETaEU_\ DWYDXWCZUC_SBaQBbOAdMAeK9gI9jE8hH9fJ9dL9bOA`QA_SAY\ VBWXBUZBS`BQcCPeCNgCLjDJlDKmDMnDOoEQpESqFUrFWsGYtG\ _uGavHcwHexIgyIizIkzJmzJozKqzKrzLszLtzLuzMvzMwzNxz\ NyzNzzNzzNzzNzzQzzSzzUzzW } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: Danilo Spada Animations
by JackOTradez 21 Jun '03

21 Jun '03

Fractint does not directly output to animation, however, it is possible to write scripts that run fractint to create a series of images which can then be compiled to AVI, MPEG, WMV etc. See if any posted on http://www.sonic.net/~jot/ufvp.html can be of use to you. Neuropsychology? Way cool! Stay Amazed. JoTz

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FOTD 20-06-03 (Pure Wholeness [6])
by Jim Muth 21 Jun '03

21 Jun '03

FOTD -- June 20, 2003 (Rating 6) Fractal visionaries and enthusiasts: When a discontinuous function is iterated, a discontinuous fractal results. Most of the FOTD fractals that are generated by the MandelbrotMix4 (or 2) formula are discontinuous, and indeed, the discontinuities often create the image. Today's image however is continuous. It combines 0.3 parts of Z^(-2) with 0.3 negative parts of Z^4 before it adds (1/C). The resulting parent fractal is an oversized area of chaos, rotated 45 degrees, which needs two outzooms before it totally fits on the screen. Near the center are two symmetrical and completely outrageous mutant Mandeloids, with no relation at all to the proper Mandel shape. But these Mandeloids have no discontinui- ties, and that alone makes them interesting. Today's scene is located rather deep in one of the less-likely valleys of the eastern Mandeloid. (In this Mandel-figure, all valleys are unlikely.) One of my taken-for-granted midgets is located as usual at the center, though it is too small to occupy more than a few pixels. But the midget is not the center of attention. That honor goes to the elements that fill the image, and delineate a kind of cogwheel. These elements are almost totally disconnected, but they are unbroken. Not a single discontinuity mars the wholeness of the image. This is how the fractals with fractional negative exponents would appear if a way could be found to eliminate the discontinuities, a task that is impossible but still fun to speculate about. I named today's image "Pure Wholeness" because that's what it is. Too bad I could rate it no higher than a 6, but even a 6 is at least slightly above average. Running the parameter file, with its render time of almost 9 minutes, is one way of admiring the wholeness of today's image. A second way is to download the completed GIF image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Clouds were plentiful here at Fractal Central on Thursday, but the temperature reached 81F 27C and the rain held off until nightfall. These pleasant conditions enabled the cats to enjoy several hours in the yard and enabled me to save a can of tuna. Today should be a wetter repeat. If I get the routine work done early enough, and if the rain does hold off, it might turn out to be another good day for both cats and humans. But to finish I must start, so until the next FOTD in 24 hours, take care, and study them as we might, we will never understand all there is to know about fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Pure_Wholeness { ; time=0:08:37.50--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+2.486158315330713/-0.00021229147922154\ /3.847846e+009 params=-0.3/4/0.3/-2/0/525/0/0 float=y maxiter=3600 inside=0 periodicity=10 colors=000cyVbzPbzKVqHNfGGXE8MC0CBEJ9SP9cT8q_8ze6z\ i6zcPz_eyVvx`pveiuicsp_quTpyNpzJupByc4zQ0zE0z10z40\ x80sB0mC0fG0bJ0XM0SN1XK8_HEbEJeBPi8Vm4_p1es0im0kf0\ n`0pV0sP0uGzuSzxcvzpnzzfzxcvsbmn`ci_VeYM`XCXV3ST0J\ _qXfvhnzvvzzzz0QH0VM8_QGbVPf_XiccnhkqkcpfYnbSm_MkV\ EiQ8hN1fJ0fG1cC8`9EY6KX3QT0XQ0bN0hM0s8Mz0p0zz8xzNk\ zbYzqMzkJueGm_CeVB_xmYmqScuMVyGMz9Cz33z00z00z00z0C\ z0Pz0bz0pz0zz0zk8yXExHMx1ScKKM`E3s60z00z93zJCzSMz`\ VzicyskxzfssbnkYicTeXP`PKXHGT9JXCM_EPbGScHVfJYiK`k\ MVQCQ44T18X09_0B`0Cc0Ef0Gh0He0Jc1Kb9M_HNYPPXXPQ0cT\ 4hV6p0Qy4GsB6mH0f`TnVNhPJcJE_C9V84QHG_PPhXYpcfykpz\ syzmnzfczbTzXKzS9zM0zH0zf0`z440pu6qiHq_SsPbsEmu3xu\ 0ui0s_0pQ0nG0m60iE8hKEeQMcXSbc__ieYpmXvsPpkJicCcX4\ YP0SH0M90H30Q40Y60e80m90uB0zC0vE0qG1kH3fJ6bK8XMBSN\ CNPHHYMBeQ4nT0vN0uH1sB3q44p06p9cmG`TKY9PX00J0ihqme\ snbup_vqXvuTxvQyxNzyKzev` } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 15-06-03 (Fractal Peaches [4])
by Jim Muth 21 Jun '03

21 Jun '03

FOTD -- June 15, 2003 (Rating 4) Fractal visionaries and enthusiasts: A day of cleaning up after the big storm, which dropped 6-1/2 inches or 16-1/2 centimeters of rain on Fractal Central in under one hour, left but little time for fractal diversion. But I did find a few spare moments, and in those moments, today's FOTD is what I found. It rates only a 4, and the render time is a dragging 20 minutes, so it is not the best value of all time. But it is worth at least a quick download. I named the image "Fractal Peaches" for reasons I have already forgotten. The formula takes Z^3 and adds 1/100 part of Z^(-99) before adding the final (1/C). The resulting parent fractal is a grossly enlarged Mandeloid rotated 180 degrees and surrounded by extended fields of chaos. Today's scene in located in the East (or in this case, the West) Valley of the parent. The less-than-superb fractal for today can be seen by running the attached parameter file and waiting 20 minutes or by down- loading the finished image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Saturday was a much improved day here at Fractal Central, for which the dynamic fractal cats were thankful. The temperature reached 88F 31C. The only rain was a light shower late in the afternoon, but by then the duo had satisfied their wanderlust. The rain is forecast to be light again today, so the cats should once again be happy. I'll be happy when I finish the clean-up from Friday. Until next FOTD, take care, and see you in 24 hours. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Peaches { ; time=0:20:35.16--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-162.1990694820002/-0.06542605764978/10\ 64827/1/47.5/-2.81791724725255488e-007 params=1/3/\ 0.01/-99/0/0 float=y maxiter=2700 inside=0 logmap=348 symmetry=none periodicity=10 colors=000K0BN2CP3DR4DT5EV7FX8FZ9GaAHcBHeDIgEJiFJk\ GKmHKiLHfPFbTC_XAW`7Tc5R_7PX9OUAMRCKNEJKFHHHFEJEBK\ DCMDDODEQDERDFTDGVDHWDHYDI_DJ`DKbDKdDLeDMgDNiDNjDM\ kDLlDKlDJmDImDHnDHnDGoDFoDEpDDpDCqDCqCMrBWsAet9ou8\ yuEvqKtmPqiVoe_laejYjhVifWidXicYiaZi__iZ`iXahVbhUc\ hSdhQehPfhNghLhhKhiJgjIgkHfkGflFfmEenDenDdoCdpBdqA\ cq9cr8bs7bs7b9U9POOdJasEotHmtKluMkuPjvSivUhwXgw_fw\ aes_dpZdmXdjWdfVccTc`ScYRcfOkoLrkOggQYcSO_UE`XFaZF\ baGccGdeGdhHejHflHgoIhqIhsIcrJ_qJWpJSoJNnKJmKFlKBk\ KIjLPiMWhNbgOifPofPncNmaMlZKkXJjUIiSGhPFgNEfPHfRKf\ TNfVPfWSfYVf_Xfa_fbbfddffgfhjfildimcinbin`io_ipZip\ XiqWirVirTisSitRitPgqOeoNcmMaj001L_hKYfJWdIYaH__Ga\ YFKVEcTCcRBcPAcM9cK8cI7cF6dD5eB4f93g62h41i2VjjTkgS\ leQmcPnaNo_MpYLqWJsTIuRGwPFxNEzLCzJBzH9zE8zC7zA5z8\ 4z62z41z2XzKVzJUzITzISzHRzGQzGPzFOzFNzEMzDLzDKzCJz\ BIzBHzAGzAFz9Ez8Dz8Cz7Bz6 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Multifractal
by Albrecht.Niekamp＠t-online.de 21 Jun '03

21 Jun '03

Hi, here is a deep zoom, which definetly is worth waiting, I think. Fractal greetings, Al. ------------------------------start-par---------------------------------- Julia_dream { ; Time 2.01.04.11 ; Albrecht Niekamp May, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=n function=sin/exp/sin passes=t center-mag=+0.01280533739168685/+0.78163092899207910/8375.587/1/2.499999\ 99998589262/1.41729405989110546e-011 params=-0.1738944669942329/-0.3000579851680044/768.00001/256.1133/3072.0\ 0016/768.0003200000001/768.0076800000001/64.01024/13977.52/5 float=y maxiter=3072 inside=maxiter outside=tdis logmap=7 periodicity=0 rseed=-2436 colors=200888<20>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq0es<2\ >0jy0kz0jy<24>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB7A96875<3>00\ 0400<23>o00q00s00<3>z00<25>C00A00800<3>000<3>777 } -------------------------------start-frm----------------------------------- FRM:Multifractal { ; Albrecht Niekamp 13.3.03 ;only integers as first input, second input 5 digits to the right ;real(p2) factor1,border1 ;imag(p2) (-)maxiter1,input bas.frm1_2digits input bas.frm2_2digits ;real(p3) bailout,hyb.mandel: number of sides (Many_mods L.Allison) ;imag(p3) factor2,border2 ;real(p4) maxiter2,factor3 ;imag(p4) border3,maxiter3 ;real(p5) 1digit_shape only 5digits: shape,out1,out2,in1,in2 ; 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset (not shape) <0_no in/out1 ; optional basic frm2: out-nbr 1digit in-nbr 1digit 3_both +5_shape ;imag(p5) 1digit : 1_iter1reset 2_iter2reset 3_both +5_shape effect ; 2digits : many_mods multipl.shutoff +10_in/out1 +20_in/out2 +30_both ; optional input2: frequency_2digits level_2digits amplitude_2digits ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=d<0 if (da) d=-d endif mi1=trunc(d) d=round((d-mi1)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) ba=trunc(d) mm=round((d-ba)*100000) ; d=imag(p3) fac2=trunc(d) b2=(d-fac2)*100000 ; d=real(p4) mi2=trunc(d) fac3=round((d-mi2)*100000) ; d=imag(p4) b3=trunc(d) mi3=round((d-b3)*100000) ; da=real(p5) t=da<0 if (t) da=-da endif start=2-t dd=trunc(da) if (dd<5) start=0 endif vb=(dd==3)+(dd==4) da=round((da-dd)*100) d=trunc(dd/10000) vb=(d==3)+(d==4)+vb dd=dd-d*10000 d=trunc(dd/1000) or1=d>5 d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) dd=dd-d*1000 d=trunc(dd/100) or2=d>5 d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) dd=dd-d*100 d=trunc(dd/10) inr1=d>5 d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) dd=dd-10*d d=trunc(dd) inr2=d>5 d=d-5*inr2 v3=(d==3) v4=(d==4) d2=(d==2)+(d==4) d=trunc(da/10) da=da-10*d ab=d>=5 d=d-5*ab bb1=(d==1) bb2=(d==2) dd=da>=5 da=da-5*dd ab=ab+dd ab1=(da==1) ab2=(da==2) ; d=imag(p5) dd=trunc(d) d=round((d-dd)*1000000) le=d>10000 da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=dd>=5 dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) if (le) freq=round((trunc(d/10000))*10) ;frequency_lake effect by S.Gallet d=d-freq*1000 level=(trunc(d/100))/100 ;water level d=d-level*10000 ampl=d/100 ;amplitude of the wave u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) d3=2*q*t rs=2*bo*(dd+flip(1))*t z2=center+(-q-bo*dd-flip(bo))*t z=pixel-z2 d=imag(conj(d3)*z)/imag(conj(d3)*rs) if (d<=level) da=level-d z=z+2*da*(1+ampl*sin(freq*da^0.2))*rs endif z=z+z2 endif if (ismand) if (vb) c=0.4*log(sqr(pixel^mm)) z=z*le else c=z*le+pixel*(le==0) z=0 endif else c=p1 z=z*le+pixel*(le==0) endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn1(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z2=z*z z=z2*z2+(p6+u)*z2+c else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif bo=|z| If (wo) t=t+1 if ((t<mi1)+(bo>b1)) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=z*le+pixel*(le==0) endif else z=z*le+pixel*(le==0) c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif bo<=ba } --------------------------------------------end---------------------------

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Re: [Fractint] "translating" animations to mpeg
by Russell Walsmith 20 Jun '03

20 Jun '03

See http://www.sonic.net/~jot/ufvp.html Cheers, Russell -- --------- Original Message --------- DATE: Fri, 20 Jun 2003 14:02:08 From: Danilo Spada <danilo.spada(a)unimi.it> To: fractint(a)mailman.xmission.com Cc: >Hello ! > >I'm a new member of this mailing list and here I am with a question. > >We are making a research in neuropsychology, and we should use the >"evolutions" of a fractal (probably "Julia"). The problem is that we >should use an animation in mpeg or avi. >Is it possible to get the output by fractint to a file.mpeg or .avi ? > >Thank You very much for any hint. > >Bye bye, >Danilo > >PS >I'm a Linux - Debian user > >-- >Dott. Danilo Spada >Istituto di Psicologia della Facolta' medica >Universita' degli Studi di Milano - Italia >(Studio) 02 / 50 31 59 91 >(Cell.) 328 / 61 78 382 > > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

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"translating" animations to mpeg
by Danilo Spada 20 Jun '03

20 Jun '03

Hello ! I'm a new member of this mailing list and here I am with a question. We are making a research in neuropsychology, and we should use the "evolutions" of a fractal (probably "Julia"). The problem is that we should use an animation in mpeg or avi. Is it possible to get the output by fractint to a file.mpeg or .avi ? Thank You very much for any hint. Bye bye, Danilo PS I'm a Linux - Debian user -- Dott. Danilo Spada Istituto di Psicologia della Facolta' medica Universita' degli Studi di Milano - Italia (Studio) 02 / 50 31 59 91 (Cell.) 328 / 61 78 382

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FOTD 18-06-03 (Ker-splash [6])
by Jim Muth 19 Jun '03

19 Jun '03

FOTD -- June 18, 2003 (Rating 6) Fractal visionaries and enthusiasts: Today's image is another scene in the East Valley area of the parent fractal of yesterday's image. Many of the same elements are there, but with the outside being rendered with the 'fmod' option, today's image is different enough to stand on its own merits. Today's rating of 6 is a big come-down from yesterday's perhaps- overblown rating of 9. It is still worth a look however. The colors, which are not nearly as finely tuned, still get the point across. When I studied the image, searching for a name, I had the impression of a Mandelbrot set being dropped into a body of colored liquid, creating a huge splash. What could I possibly have named the image other than "Ker-splash"? Curiously, if the bailout radius of today's image is raised to 10^100, the image evaporates, leaving a blank screen of all- inside points. Then, if the 'fmod' inside-fill option is applied to the blank image and the proximity is kept at 0.9, today's image will re-appear, the only difference being that instead of rendering in 13 minutes, it now takes an hour to render, and the inside of the midget now contains detail. The fastest way to observe today's inside-or-outside image is to download it in completed form from either Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's web site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Clouds hung around all day Tuesday. The sprinkles that began at 1pm turned into a steady rain by 6pm. The temperature reached 66F 19C, but what good is a pleasant temperature when rain is falling? The dynamic duo thought it was no good at all, and quickly turned sulky, demanding a treat of tuna before resuming their good spirits. Since this morning is cloudy with more rain promised, I had best stock up on the tuna. The heavy clouds do not relieve me of the duty of doing the waiting work however, so if I hope to finish, I had best get started. Until next FOTD, take care, and watch for lurking fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Ker-splash { ; time=0:13:16.68--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.02507098225420995/+0.507300152811625\ 00/24216.06/1/-60/4.61438734444818976e-011 params=1/-1.08/-1/1/0/300 float=y maxiter=1200 inside=0 proximity=0.9 outside=fmod logmap=yes periodicity=10 sound=off colors=0003tk2sh3qf3oe3mc3kb3i`4g_4eY4cX4aV4_U5YS5\ WR5VQ5TO5RN6PL6NK6LI6JH6HF7FE7DC7BB799778444767979\ B8CE9EGBHICJLDMNEOPFRSHTUIWWJYZK``LbbNeeOggPjiQliL\ wjOrkRnlTimWenY`o`XpbSqeOrgJsjFun8tm9tlAtlBtkCtkCt\ jDtiEtiFshFshGsgHsfIsfIseJseKsdLtfKseLsdLscLrbMraM\ r`Mr`Mq_NqZNqYNqXNpWOpVOpVOpUOoTPoSPoRPnQQnPQnPQnO\ QmNRmMRmLRmKRlJSlJSlISlHSkGTkFTkETjDUjDUjCUjBUiAVi\ 9Vi8Vi7Vh7Wh6Wh5Wh4Wg3Xg2Xg1Xh0Yg1Xg1Wg1Vf2Vf2Uf2T\ e2Te3Se3Re3Rd3Qd4Pd4Oc4Oc4Nc5Mb5Mb5Lb6Kb6Ka6Ja6Ia7\ H`7H`7G`7F_8F_8E_8D_1B_4CZ6CY8DXBDWDEVFEUHEUIFUJGU\ KHUKIUKJUKKUKLUKMUKNUKOUKPUKPUKQUKRUKSSKTQKUOKVMKW\ KKXKKYKKZKKYKKZKKZKK_KK_KK`KK`KK`KKaKKaKHbKFbKDcIB\ cD6eE7dF8cG9cGAbHAaIBaJC`JD_KD_LEZLFYMGYNGXOHXOIWP\ JVQJVQKURLTSMTTMSTNRUORVPQVPQWQPXROYSOYTNZTM_UM`VL\ `WKaWKbXJbYIcZIdZHe_He`GfaFgaFgbEhcDidDjdCjeBkfBlg\ AlgBlgAlgAm`AoVApPAoPAnPA } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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"CONJAG8" BUG recovery
by Jim White 19 Jun '03

19 Jun '03

Hello fractitioners! I gather from postings by Sylvie Gallet and Tim Wegner that the Fracint development team is aware of this problem. I've looked long and hard at CONJAG8 as it affects MandelbrotMix4, and I believe there is no cause for alarm, the side-effects of CONJAG8 are simply that you get a totally accurate image of the reflection of your target window. I wouldn't classify this as an artifact - the detail of the image is unaffected, only its real window. Any images you have now involving MandelbrotMix4 (and its siblings) will easily be reproduced by reflecting the corners vertically, and optionally rotating the image by 180 degrees. A simple text editor macro or program could make thse changes to batches of parameter sets using the affected formulae. >From a mathematical viewpoint, this sort of error is not likely to cause widespread artifacts. Many fractals are symmetric about the imaginary axis anyway, and your original image might simply be inverted. Getting the imaginary sign wrong doesn't affect magnitudes, which are the most common form of escape conditions. The problem with accidental reflections only becomes a nuisance if the image is not symmetric about the Y axis. Of course it is possible that we will find real artifacts in some formulae. I think they'll be quite rare, but I actually hope I find some, because that might mean finding a "lost twin" for some interesting image, and who knows what that twin is going to look like! Meanwhile, the best way to look for possibly affected formulae is to run comparison tests on a few sample images for any given formula. People can use UF or CPro, and I have my own Fractint engine emulator that I can run in debug mode, which makes it easy for me to to run a "health check" on any formula people care to nominate. I can easily test various classes of formulae to see if there is any sign of suspect behaviour. Send your requests to me! Cheers Jim White __________________________________________________ Yahoo! Plus - For a better Internet experience http://uk.promotions.yahoo.com/yplus/yoffer.html

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FOTD 19-06-03 (Cyclonic Circulation [7])
by Jim Muth 19 Jun '03

19 Jun '03

FOTD -- June 19, 2003 (Rating 7) Fractal visionaries and enthusiasts: In the northern hemisphere the atmosphere turns counter- clockwise as it is drawn into a cyclone and clockwise as it is pushed from an anticyclone. In the southern hemisphere exactly the opposite is true. But Fractal Central is located in the northern hemisphere, and since the arms of today's spiral image are moving inward in a counter-clockwise direction and curving to the left as they go, the image can only be called "Cyclonic Circulation". When the atmosphere curves to the left in the northern hemisphere, it causes low-level convergence, which forces the air upward and squeezes any available moisture from it. We have had a lot of convergence at Fractal Central over the past two months, where only 2 of the past 60 days have been clear. People are joking that the farmers prayed for rain all last year, and their prayers are being answered all this year. Now the farmers are praying for dry weather so they can work their fields. Worried about next year, my advice is for them to make their prayers more specific. On a more fractal note, the formula of today's image mixes 1.2 negative portions of Z^(1.4) with 0.3 parts of Z^(-0.8) and adds (1/C). It was calculated by the MandelbrotMix2 formula, which is identical to the MandelbrotMix4 formula, except that it includes the ability to change the automatically calculated value of initial Z. It's a rather lively image, enhanced by a brilliant palette of colors. With other color palettes, the image actually reminds me of rows of shark's teeth, but a man-eating name would give a wrong impression, so I chose the palette that reminds me of a cyclone, and rated the image at a 7. The 4-minute render time is within reason for an image that rates a 7. And as always, the completed GIF file is available for download on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Though the clouds hung tough on Wednesday, a bit of afternoon sun did manage to break through, the rain held off, and the temperature reached 75F 24C. As a result, the fractal cats were happy and I saved a can of tuna. If only today could turn out as well...but with rain having already fallen and more due, it most likely will not. The cats are still sleeping, but before long they will get up, go to the door and ask to be let out. They will then see the rain and turn moody. I fear tuna will be necessary. Finishing the day's work will also be necessary, but before I finish, I must start. Until next FOTD, take care, and keep dry, that is if possible. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ CyclonicCirclation { ; time=0:04:04.58--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=-0.74981462059503250/+0.015225453504671\ 47/3.458564e+011/1/-106/-0.0139524412207075732 params=-1.2/1.4/0.3/-0.8/0/525/0/0 float=y maxiter=500 inside=0 logmap=80 periodicity=10 colors=070070070070070070070472AAAEEHJPPPTVVWb`_id\ dqikxoqzutzzwzzzzv_uoCPg70d74b7EZ7LX7VV7bR7kPHsNRz\ J_zHizGszEszEizC_zCRzCHzA7zA7z87v87s8Co6Gk6Hg4Ld4P\ `4RZ8TTCVNEXHHYEL_8N_2Ra0Vd0Xe0`g0di0ei0bk0`m0Zo0X\ o0Vq0Ts0Ru0Pu4Nv8LxCJzGHzJGzNEzRCzVAzZ8zb6ze4zi8zg\ AzgCzgGzgHzgJzgNzgPzgRzgVzgXzgZzg`zgXzeVzdTzdRzbPz\ `Nz`LzZHzXGzXEzVCxTAvT8uR6sP2oP0mN0kL0gL0eJ0dH0aH0\ eG0iE6oCCsAGv6Lz4Pz2Vz0`z0dz0iz0mz0kz0kz6kzCkzJkzP\ kzVkz`kzgkzmkzskzxmzzozzqxzsvzuozwmsymdzmPzmAzm0zm\ 0zm0zm0zm0zm0zm6zmAzmGzqJzvPzzTzzXzzZzz`zzbzzdzzez\ zgzzizzkzzmzzmzzozzqzzszzuzzvzzxzzzzzzzzzzzzzzzzzz\ zzqzzizz`zzTzzLzzCzz4zz0zz0zz0zz0zz0zz0zz0zz6zzAzz\ GzzJzzZzzkzzgzzdzzbzzZzzXzzTzzRzzNzzLzzHzzGzzCzzAz\ z6zz4zz0zz0zz0zz2zz4zz6zz8zz8zzAzzCzzEzzGzzHzzHzzJ\ zzLzzNzzPzzRzzRzzNzzJzzHzzEzzAzz8zz4zz0zz0zz0zz0zz\ 0zz0zz4zz8zzAzzEzzHzzLzzP } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

1 0

Multifractal_4
by Albrecht.Niekamp＠t-online.de 18 Jun '03

18 Jun '03

Hi, phantastic zooming guaranteed! Fractal greetings, Al. -------------------------start-par----------------------------------------- Volcano { ; Time 2.07.11.52 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult242.frm formulaname=multifractal_4 ismand=y function=exp/exp/exp/sin passes=t center-mag=-1.23168781966593200/+0.12096646185174940/4495980/1/-17.49999\ 99991595914/-3.40947790139489726e-009 params=-0.8469801934873501/0.1406598101748711/12812.00011/40.3214026052/\ 2048.02048/384.000008/384.00024/128.0076800000001/512.0076800000001/768.\ 0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200ZVI<7>niQpjRrlS<3>ysX<25>BB7996775<3>000<24>n00p00r00<3>y00<25\ >B00900700<3>000<2>455677899ABBBCC<18>hiiijjkll<3>rss<21>HIIFGGEFF<3>677\ 455344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000111<15>XUH } Down_under { ; Time 1.58.44.34 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult242.frm formulaname=multifractal_4 ismand=y function=exp/exp/exp/sin passes=t center-mag=-1.23169094319349200/+0.12096267609571690/224799/1/-17.499999\ 9990956674/-8.80199038655327115e-010 params=-0.8469801934873501/0.1406598101748711/12812.00011/40.3214026052/\ 2048.02048/384.000008/384.00024/128.0076800000001/512.0076800000001/768.\ 0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200996<3>121000300<23>n00p00r00<3>y00<25>B00900700<3>000<2>455677\ 899ABBBCC<18>hiiijjkll<3>rss<21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es\ <3>0kz<25>09C08A068<2>022000111<24>niQpjRrlS<3>ysX<25>BB7 } Three_in_one { ; Time 1.32.14.39 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult242.frm formulaname=multifractal_4 ismand=y function=exp/exp/exp/sin passes=t center-mag=-1.23278506460602800/+0.12137156609200910/561.9975/1/-85.0000\ 000000003553/4.45664338766249557e-013 params=-0.8469801934873501/0.1406598101748711/12812.00011/40.3214026052/\ 2048.02048/384.000008/384.00024/128.0076800000001/512.0076800000001/768.\ 0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=2000bo<3>0hw0jx0kz<25>09C08A068<2>022000111<24>niQpjRrlS<3>ysX<25\ >BB7996775<3>000<24>n00p00r00<3>y00<25>B00900700<3>000<2>455677899ABBBCC\ <18>hiiijjkll<3>rss<21>HIIFGGEFF<3>677455344122000<24>0`m } Above_and_below { ; Time 1.06.53.23 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult242.frm formulaname=multifractal_4 ismand=y function=exp/exp/exp/sin passes=t center-mag=-1.23177131869359900/+0.12093733379787740/11239.95/1/-17.4999\ 999999981881/2.76966574674908372e-011 params=-0.8469801934873501/0.1406598101748711/12812.00011/40.3214026052/\ 2048.02048/384.000008/384.00024/128.0076800000001/512.0076800000001/768.\ 0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=0001221532653863A84DA5EB5HB<2>7NG8PI8RJ9TKAVNAXM<3>DdTDfVEhWFjYFl\ YGn_Gp`Prd<3>zzz<2>_ulRsgHqaHo`GmZFkXFiX<5>BYOAWMAUL9SK<4>6IC5GB5DA<3>25\ 4243121000001023025047049<5>0BL0DN0DP<4>0KZ0L`0Mb0Nd0Of0Qh<3>0Up4Yr8atCg\ vGkxKqz<3>4_s0Vq0Uo<12>0FQ0DO0DM<3>08E06C06A048046024012000100<12>R0LT0N\ V0PX0P<3>d0Wf0Yh0Z<3>p0e<3>xOtzUxyOuwIquCns6iq0g<2>k0bi0`g0_e0Z<3>Y0SW0R\ U0O<5>I0FG0EE0CC0A<3>304102010<4>0B10D10F10H20J20L20N2<2>0T40V40X3<3>0d4\ 0f50h5<3>0p6<3>WxZczeUyY<2>0s8<4>0i60g60e60c4<2>0Y40W30U4<5>0I20G20E20C2\ 0A1081<3>000010 } View_frm_the_top { ; Time 0.44.18.06 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult242.frm formulaname=multifractal_4 ismand=y function=exp/exp/exp/sin passes=t center-mag=-1.04386/0.626322/21.95303/1/-57.4999999999999574/-1.26836041\ 669520228e-013 params=-0.8469801934873501/0.1406598101748711/12812.00011/40.3214026052/\ 2048.02048/384.000008/384.00024/128.0076800000001/512.0076800000001/768.\ 0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=000A0B<6>X0a_0dc0h<3>p0w<4>_0dX0aU0Y<2>K0NH0JG0NE1R<3>7UX6`Z4h_2o\ a0wc<11>2TG2RE3OC<3>4D3<17>kkammcpoe<3>zwm<6>cYO`UKYQG<3>KA0000<43>000<4\ >000330<11>110110110<3>000KA4<7>gcOjgRmjT<3>zzc<9>UOFRKDOGA<3>A00<9>f0Ci\ 0Dl0F<3>z0K<6>Z0EV0DR0C<3>A08004000<26>000<4>000304708 } The_hat2 { ; Time 0.19.22.94 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult242.frm formulaname=multifractal_4 ismand=y function=exp/exp/exp/sin passes=t center-mag=-0.958374/0.132535/1.404994/1/-90/-1.23373533611470521e-014 params=-0.8469801934873501/0.1406598101748711/12812.00011/40.3214026052/\ 2048.02048/384.000008/384.00024/128.0076800000001/512.0076800000001/768.\ 0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=000<3>0PP0VV0``<3>0zz<3>MawRWvXQv<3>r0r<3>X0XS0SM0M<3>000<43>000<\ 3>000111333<23>nnnppprrr<3>zzz<25>CCCAAA888<2>222000000<33>000000000<3>0\ 00Z0AU00<3>d00g00j00m00<3>c0P`0VZ0`W0fT0m<3>I0MF0FA0A505000<39>qqqsssttt\ <3>zzz000 } ----------------------------------start-frm-------------------------------- FRM:Multifractal_4 { ; Albrecht Niekamp 110603 ;only integers as first input, second input 5 digits to the right ;real(p2) 5digits: shape, outside, in1, in2, in3 ; 0_off 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset digit1: +5_warp ; input2 : five digits frm2 use : 0_no 1_yes ;imag(p2) (-)digit1 : many_mods multipl. off 1_out 2_in1 3_in2 4_all ; digit2 : iter-reset 1_out 2_in1 3_in2 4_all ; input2 : many_mods_2digits frm1_2digits frm2_2digits bees_4digits ;real(p3) many_mods bailout, bailout ;imag(p3) shape : factor (fn1), outside : border-in ;real(p4) outside : factor (fn2), border-out ;imag(p4) maxiter1, factor1 (fn2) ;real(p5) maxiter2, factor2 (fn3) ;imag(p5) maxiter3, factor3 (fn4) ; da=real(p2) dd=trunc(da) da=round((da-dd)*100000)+11111 d=trunc(dd/10000) ex0=d>5 d=d-5*ex0 vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) ex1=d>0 dd=dd-d*1000 rs1=d>5 d=d-5*rs1 v1m=(d==3) v1j=(d==4) dd1=(d==2)+(d==4) d=trunc(dd/100) ex2=d>0 dd=dd-d*100 rs2=d>5 d=d-5*rs2 v2m=(d==3) v2j=(d==4) dd2=(d==2)+(d==4) d=trunc(dd/10) ex3=d>0 dd=dd-d*10 rs3=d>5 d=d-5*rs3 v3m=(d==3) v3j=(d==4) dd3=(d==2)+(d==4) ex4=dd>0 rs4=dd>5 dd=dd-rs4*5 v4m=(dd==3) v4j=(dd==4) dd4=(dd==2)+(dd==4) tt=ex0+ex1+ex2+ex3+ex4 ; d=trunc(da/10000) ab=(d==2) da=da-d*10000 d=trunc(da/1000) ab1=(d==2) da=da-d*1000 d=trunc(da/100) ab2=(d==2) da=da-d*100 d=trunc(da/10) ab3=(d==2) da=da-d*10 ab4=(da==2) ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) d=round((d-dd)*10000000000) da=trunc(dd/10) so1=((da==1)+(da==4)==0) so2=((da==2)+(da==4)==0) so3=((da==3)+(da==4)==0) dd=dd-10*da ir1=(dd==1)+(dd==4) ir2=(dd==2)+(dd==4) ir3=(dd==3)+(dd==4) ; mm=trunc(d/100000000) d=d-mm*100000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=real(p3) mb=trunc(d) ba=(d-mb)*100000 ; d=imag(p3) sfac=trunc(d) b1=(d-sfac)*100000 b0=b1/2 ; d=real(p4) ofac=trunc(d) b2=(d-ofac)*100000 ; d=imag(p4) mi1=trunc(d) fac1=(d-mi1)*100000 ; d=real(p5) mi2=trunc(d) fac2=(d-mi2)*100000 ; d=imag(p5) mi3=trunc(d) fac3=(d-mi3)*100000 ; bg=((ab+vb)==0) bg1=((ab1+v1j)==0) bg2=((ab2+v2j)==0) bg3=((ab3+v3j)==0) bg4=((ab4+v4j)==0) ; if (ismand) z=0 if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else if (bg) c=p9 else c=p1 endif z=pixel endif t=0 d3=(ismand==0) u=d3 : bo=z If (tt) t=t+1 if ((ex0)&&bo>b0) u=2*(fn1(t/sfac)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) ba=mb else c=pixel endif else z=pixel if (bg) c=p9*u else c=p1*u endif endif ex0=0 tt=tt-1 elseif ((ex1) && bo>b1 && bo<b2) u=2*(fn2(t/ofac)) rs=rs1 ab=ab1 if (dd1) if (rs) z=pixel endif vb=v1j d3=1 if (bg1) c=p9*u else c=p1*u endif else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1m if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir1) t=0 endif ex1=0 tt=tt-1 elseif ((ex2) && t>mi1) u=2*(fn2(t/fac1)) rs=rs2 ab=ab2 if (dd2) if (rs) z=pixel endif vb=v2j if (bg2) c=p9*u else c=p1*u endif d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v2m if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir2) t=0 endif ex2=0 tt=tt-1 elseif ((ex3) && t>mi2) u=2*(fn3(t/fac2)) ab=ab3 rs=rs3 if (dd3) if (rs) z=pixel endif vb=v3j if (bg3) c=p9*u else c=p1*u endif d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3m if (vb) if (so3) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir3) t=0 endif ex3=0 tt=tt-1 elseif ((ex4) && t>mi3) u=2*(fn4(t/fac3)) ab=ab4 rs=rs4 if (dd4) if (rs) z=pixel endif vb=v4j if (bg4) c=p9*u else c=p1*u endif d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v4m if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif ex4=0 tt=tt-1 endif endif if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn1(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z1=fn1(z)-c ;Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif |z|<=ba } --------------------------------end---------------------------------

1 0

Multifractal_4
by Albrecht.Niekamp＠t-online.de 18 Jun '03

18 Jun '03

Hi, this hopefully is the version I will use for some time, as everything does what I expect. The images were not possible with previous versions and are really extraordinary. The_hat is the basic image. Fractal greetings, Al. -----------------------------start-par----------------------------------- Biomorphs { ; Time 0.39.11.31 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult242.frm formulaname=multifractal_4 ismand=y function=exp/exp/exp/sin passes=t center-mag=-0.497251/0.568314/19.72387 params=-0.5/0.375/12867.00011/40.3214026052/4048.02048/384.000008/384.00\ 024/128.0076800000001/512.0076800000001/768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200III<3>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>\ 022000211<24>oiQqjRslS<3>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25\ >C00A00800<3>000<25>iiijjjlll<3>sss<20>KKK } The_heart { ; Time 0.15.45.98 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult242.frm formulaname=multifractal_4 ismand=y function=exp/exp/exp/sin passes=t center-mag=-0.06546992645160482/-0.00653500612040142/332.451/1/90/3.8857\ 8058618804789e-016 params=-0.5/0.375/12812.00011/40.3214026052/2048.02048/384.000008/384.00\ 024/128.0076800000001/512.0076800000001/768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200pqqrss<21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<25>09\ C08A068<2>022000111<24>niQpjRrlS<3>ysX<25>BB7996775<3>000<24>n00p00r00<3\ >y00<25>B00900700<3>000<2>455677899ABBBCC<22>opp } The_hat { ; Time 0.12.32.97 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult242.frm formulaname=multifractal_4 ismand=y function=exp/exp/exp/sin passes=t center-mag=-0.537836/0.38229/1.202675/1/-90/3.88578058618804789e-016 params=-0.5/0.375/12812.00011/40.3214026052/2048.02048/384.000008/384.00\ 024/128.0076800000001/512.0076800000001/768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200pqqrss<21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<25>09\ C08A068<2>022000111<24>niQpjRrlS<3>ysX<25>BB7996775<3>000<24>n00p00r00<3\ >y00<25>B00900700<3>000<2>455677899ABBBCC<22>opp } Ruins {; that the weed has overgrown ; Albrecht Niekamp June, 03 reset=2002 type=formula formulafile=mult242.frm formulaname=multifractal_4 ismand=y function=exp/exp/exp/sin passes=t center-mag=-0.368627/-0.272217/24.0535/1/-90/3.88578058618804789e-016 params=-0.5/0.375/12812.00011/40.3214025131/2048.02048/384.000008/384.00\ 024/128.0076800000001/512.0076800000001/768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200pqqrss<21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<25>09\ C08A068<2>022000111<24>niQpjRrlS<3>ysX<25>BB7996775<3>000<24>n00p00r00<3\ >y00<25>B00900700<3>000<2>455677899ABBBCC<22>opp } Windhose { Time 8.13.17 ; Albrecht Niekamp June, 03 reset=2002 type=formula formulafile=mult242.frm formulaname=multifractal_4 ismand=y function=exp/exp/exp/sin passes=t center-mag=-0.05573016812667020/+0.01426832175061791/45.21334/1/-90/-1.2\ 3373533611470521e-014 params=-0.5/0.375/12812.00011/40.3214026052/2048.02048/384.000008/384.00\ 024/128.0076800000001/512.0076800000001/768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200pqqrss<21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<25>09\ C08A068<2>022000111<24>niQpjRrlS<3>ysX<25>BB7996775<3>000<24>n00p00r00<3\ >y00<25>B00900700<3>000<2>455677899ABBBCC<22>opp } --------------------------------start-frm----------------------------------- FRM:Multifractal_4 { ; Albrecht Niekamp 110603 ;only integers as first input, second input 5 digits to the right ;real(p2) 5digits: shape, outside, in1, in2, in3 ; 0_off 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset digit1: +5_warp ; input2 : five digits frm2 use : 0_no 1_yes ;imag(p2) (-)digit1 : many_mods multipl. off 1_out 2_in1 3_in2 4_all ; digit2 : iter-reset 1_out 2_in1 3_in2 4_all ; input2 : many_mods_2digits frm1_2digits frm2_2digits bees_4digits ;real(p3) many_mods bailout, bailout ;imag(p3) shape : factor (fn1), outside : border-in ;real(p4) outside : factor (fn2), border-out ;imag(p4) maxiter1, factor1 (fn2) ;real(p5) maxiter2, factor2 (fn3) ;imag(p5) maxiter3, factor3 (fn4) ; da=real(p2) dd=trunc(da) da=round((da-dd)*100000)+11111 d=trunc(dd/10000) ex0=d>5 d=d-5*ex0 vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) ex1=d>0 dd=dd-d*1000 rs1=d>5 d=d-5*rs1 v1m=(d==3) v1j=(d==4) dd1=(d==2)+(d==4) d=trunc(dd/100) ex2=d>0 dd=dd-d*100 rs2=d>5 d=d-5*rs2 v2m=(d==3) v2j=(d==4) dd2=(d==2)+(d==4) d=trunc(dd/10) ex3=d>0 dd=dd-d*10 rs3=d>5 d=d-5*rs3 v3m=(d==3) v3j=(d==4) dd3=(d==2)+(d==4) ex4=dd>0 rs4=dd>5 dd=dd-rs4*5 v4m=(dd==3) v4j=(dd==4) dd4=(dd==2)+(dd==4) tt=ex0+ex1+ex2+ex3+ex4 ; d=trunc(da/10000) ab=(d==2) da=da-d*10000 d=trunc(da/1000) ab1=(d==2) da=da-d*1000 d=trunc(da/100) ab2=(d==2) da=da-d*100 d=trunc(da/10) ab3=(d==2) da=da-d*10 ab4=(da==2) ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) d=round((d-dd)*10000000000) da=trunc(dd/10) so1=((da==1)+(da==4)==0) so2=((da==2)+(da==4)==0) so3=((da==3)+(da==4)==0) dd=dd-10*da ir1=(dd==1)+(dd==4) ir2=(dd==2)+(dd==4) ir3=(dd==3)+(dd==4) ; mm=trunc(d/100000000) d=d-mm*100000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=real(p3) mb=trunc(d) ba=(d-mb)*100000 ; d=imag(p3) sfac=trunc(d) b1=(d-sfac)*100000 b0=b1/2 ; d=real(p4) ofac=trunc(d) b2=(d-ofac)*100000 ; d=imag(p4) mi1=trunc(d) fac1=(d-mi1)*100000 ; d=real(p5) mi2=trunc(d) fac2=(d-mi2)*100000 ; d=imag(p5) mi3=trunc(d) fac3=(d-mi3)*100000 ; bg=((ab+vb)==0) bg1=((ab1+v1j)==0) bg2=((ab2+v2j)==0) bg3=((ab3+v3j)==0) bg4=((ab4+v4j)==0) ; if (ismand) z=0 if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else if (bg) c=p9 else c=p1 endif z=pixel endif t=0 d3=(ismand==0) u=d3 : bo=z If (tt) t=t+1 if ((ex0)&&bo>b0) u=2*(fn1(t/sfac)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) ba=mb else c=pixel endif else z=pixel if (bg) c=p9*u else c=p1*u endif endif ex0=0 tt=tt-1 elseif ((ex1) && bo>b1 && bo<b2) u=2*(fn2(t/ofac)) rs=rs1 ab=ab1 if (dd1) if (rs) z=pixel endif vb=v1j d3=1 if (bg1) c=p9*u else c=p1*u endif else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1m if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir1) t=0 endif ex1=0 tt=tt-1 elseif ((ex2) && t>mi1) u=2*(fn2(t/fac1)) rs=rs2 ab=ab2 if (dd2) if (rs) z=pixel endif vb=v2j if (bg2) c=p9*u else c=p1*u endif d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v2m if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir2) t=0 endif ex2=0 tt=tt-1 elseif ((ex3) && t>mi2) u=2*(fn3(t/fac2)) ab=ab3 rs=rs3 if (dd3) if (rs) z=pixel endif vb=v3j if (bg3) c=p9*u else c=p1*u endif d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3m if (vb) if (so3) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir3) t=0 endif ex3=0 tt=tt-1 elseif ((ex4) && t>mi3) u=2*(fn4(t/fac3)) ab=ab4 rs=rs4 if (dd4) if (rs) z=pixel endif vb=v4j if (bg4) c=p9*u else c=p1*u endif d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v4m if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif ex4=0 tt=tt-1 endif endif if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn1(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z1=fn1(z)-c ;Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif |z|<=ba } -------------------------------------end-----------------------------------

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FOTD 17-06-03 (Deep in Inner Space [9])
by Jim Muth 17 Jun '03

17 Jun '03

FOTD -- June 17, 2003 (Rating 9) Fractal visionaries and enthusiasts: Does today's visionary fractal image actually rate a 9? Well, maybe not, maybe a rating of 8 would be more accurate, but I've been hard on myself lately and it's about time I give myself a break, so I decided that today's image rates a 9, which equals 'one of the all-time best'. The parent fractal was produced by subtracting Z from Z^(-1.08) and adding (1/C). The resulting image resembles a distorted and somewhat lopsided Mandeloid standing on its nose. Today's scene is located in the East Valley area of this parent, which in this case is a north valley. I named the image "Deep in Inner Space" because I'm in a rather subjective mood this morning. The picture has unusually smooth coloring, at least on my fractal monitor, with the bands being almost invisible. The overall effect is one of a serene, hazy, fantastic fractal landscape, with gossamer arms composed of clouds of invisible smaller midgets extending outward from the central midget in a star-like shape. The price to pay for all this serenity is the 1/2 hour required to render the scene from the attached parameter file. And even that price may be avoided by downloading the completed image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Lots of clouds spoiled the day here at Fractal Central on Monday, but the temperature of 73F 18C was close to perfect, and the fractal cats made the most of it. Today is starting cloudy again, with rain forecast for later in the day. The duo will have a marginal day at best. I'm having a fair to good day -- so far that is. I hope the pleasantness can continue. With any luck at all, it will. In any case, until next time, which will arrive in 24 hours, take care, and last year the farmers prayed for rain. This year their prayers are being answered. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Deep_In_InnerSpace { ; time=0:29:24.20--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.02357251356169931/+0.372397927789504\ 30/1.14291e+008/1/10/1.30309761642993793e-006 params=1/-1.08/-1/1/0/300 float=y maxiter=2500 inside=0 logmap=644 periodicity=10 colors=000EAUFBVFBVFBWFBWFBXGBXGBYGBYGBZGBZHB_HD_H\ D`HD`HDaIDaIDbIDbIDcIDcJDdJDdJDeJEeJEfJEfLEgLEgLEh\ LEhLEiMEiMEjMEjMEkMFkNFlNFlNFmNFmNFnOFnOFoOFoOFpOF\ pJGqMFqNFqOFqPFqQFpREpSEpTEpUEoVEoWDoYDoYDn_Dn_Dna\ BnaBmbBmcBmdBmeAmfAmgAmhAmiAlj9lk9ll9lm9kn9ko7kp7k\ q7jr7js7js6ju6iu6iv6iv6ix4kw6jw6iw6iw6hw6hv7hv7hv7\ gv7gv7fv7fv9ev9ev9dv9cv9cuAbuAbuAauAauAauAatB_tB_t\ B_tB_tBZsDYsDYsDXsDXsDWsDWsEVsEVsEUsEUsETtBUsDTsET\ sETrFTqFTqGTpHTpHToITnITnJTmLTmLTmMTlMTlNTkOSjOSjP\ SiPShQShRShRShSSgSSfTSfUSeUSdVSzVSzWSzpPzpQzpRzpSz\ pSbQTaPUaNUaLV_IW_FX_GW_HWaHWaIWaIWaJVaJVaLVbLVbMV\ bMVcNUcOUdOUdPUdPUeQTeQTeRTfRTfSTfSTgTSgUShUShVShV\ ShWRhWRhXRiXRiYRiYRjZQj_Qk_Qk_Qk_QlaPlaPlaPmaPmbPm\ bPmcOmdOndOneOneOofNofNogNpgNphNreMqgNphNoiOnjOmlP\ mmPlnPkoQjqQirRhsRjuPktQmtRntRpuSrvUsvTuwTvxSxySzz\ RzzRzzQzzQzzPzzPzzOzzOzzN } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 16-06-03 (Vision of a Square [7])
by Jim Muth 16 Jun '03

16 Jun '03

FOTD -- June 16, 2003 (Rating 7) Fractal visionaries and enthusiasts: Things are far more settled today here at Fractal Central, though city workers and home-owners are still cleaning up where the flash flood struck on Friday at the bottom of the fractal hill. The only problem here inside F.C. is a huge backlog of work, which must be cleared away before things will be totally back to fractal normal. Today's fractal is named "Vision of a Square". I gave it this name because the square in question, which is delineated by the blue area, is not immediately apparent, and gradually appears in the awareness, almost like a mystical vision. But even if the square eludes detection, the graceful filaments are worth a name in themselves. The parent fractal adds together 3.9 negative parts of Z^2 and Z^3 before adding 1/C. The fractal produced by this formula is a grossly oversized, double-lobed thing that requires several outzooms before it fits on the screen. Today's scene is located in a small bay on an inland shoreline near the X-axis of this parent. Much of the image consists of bof61 inside fill. This fill is the reason that the central midget is so poorly defined. But despite the poorly-defined central midget, the image rates a 7. The 6-minute render time can be avoided by downloading the completed image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Though it remained cloudy, only a few drops of rain fell here at Fractal Central on Sunday. The neighborhood Father's Day cook- outs went as planned, and the fractal cats enjoyed a pleasant afternoon outdoors in the temperature of 81F 27C. They needed no treats of tuna to put them in good moods. Today is promising to once again be pleasant. But I'll not be able to say for sure that it will be pleasant until the day and the work are behind me. Until then, anything can happen and usually does. Until tomorrow, when the next FOTD will appear, take care, and be wary of stray fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Vision_of_a_Square { ; time=0:06:29.32--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+7.70124460252959/+3.08060831519806/6.0\ 07398e+009/1/172.5/3.78867931411924763e-005 params=-3.9/2/-3.9/3/0/0 float=y maxiter=800 inside=bof61 periodicity=10 colors=000WOFSOEOODJOCFOCBOB7OA3OACLLLJWTGeaEpiCzZ\ RqPehSbeV`cYYa`W_cUYbTUaSRaRN`RK`QG_PD_PAZMCYKEXHF\ WFHWDIVAKU8MT5NS3PS1QV2OX3MZ3K`4Jb4Hd5Ff5Dh6Cj6Al7\ 8n76p85r83t91v90rC5oE9lGDiIHfLMcNQ`PUYRYVUbSWfPYjM\ _nJarIbqHbpGcoFcnEdmDdlDekCejBfiAfh9gg8gf7he7he9eb\ Ab`A_YAXWAVUASRAPPAMMAKKAHIAEFABDA9BBCECEHDGJEIQFM\ TGOVHQYIS`JUdKWiLYkM_nNarOcvLfzJkzXpzoqzvsznvmdx`W\ xPYvNZrM_nL`jK`fJ`bI`ZH`VG`RFaNEbJDZFC_CBhEAmFArGA\ wHAzI9zJ9zK9zL9UN8UO8UP8fQ8fR7fS7fT7fU7S8KP9MN9NLA\ PJAQHBSFBTCCUACW8DX6DZ4E_2E`4Ga5Hb6Ic7Jd8Kd9MeANfB\ OgCPhDQhESiFTjGUkHVlIWlSNs`FyYHjVIXSKIQL4PM5PN5OO5\ OP6OQ6NR6NS6MS7MT7MU7LV7LW8KX8KY8KY8LZALZCL_DL_FL`\ GL`IMaKMaLMbNMbOMcQMcRTfUZhWdjYjl_imYhmXgmVfnUenSd\ nRcoPboOaoM`pL_pJZpIYpHXnKWlMVjOUhRUgTTeVScYRa_Q_a\ QZcT``VbYYdV_fSbhPdjMglJinGlpDnrAqt7sv4uw2qlFmaSiR\ deHpfGqfGrfGrgGshOHcOG_OF } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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4-Dimensional Rubik's Cube
by Paul N. Lee 14 Jun '03

14 Jun '03

For those individuals interested in challenges, mathematics, or just a bit of fun, may wish to visit the following web page: http://www.superliminal.com/cube/cube.htm Windows and Linux executables (with source code) available, along with an article on how to calculate the permutations of 4D Magic Cubes. Sincerely, P.N.L. ------------------------------------------------- http://home.att.net/~Paul.N.Lee/PNL_Fractals.html http://www.Nahee.com/Fractals/

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FOTD 14-06-03 (A Midget Collision [4])
by Jim Muth 14 Jun '03

14 Jun '03

FOTD -- June 14, 2003 (Rating 4) Fractal visionaries and enthusiasts: Due to a flood and power failure, I had little time to find an honorable fractal for today. What I did find was a collision and partial merger of two midgets in the fractal created by adding portions of Z^4, Z^5. The real(p3) parameter is very critical to the shape of the combined midgets, and changing its value by as little as 0.000001 makes a noticeable change in the image. I named the image "A Midget Collision" because that's what it is. I rated it at a 4 because that's all it's worth. The render time of just over 1 minute takes some of the disappoint- ment from the FOTD. As always, the image can also be seen by visiting one of the FOTD web sites and downloading it from there. Paul's site is: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's is: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Friday, with its temperature of 86F 30C, was a fine day until 7pm when a thunder-storm of biblical proportions arose, flooding the fractal basement to a depth of 6 inches and cutting the power. (I have always wondered how a sump pump is supposed to keep the water down when the storm causes a power failure, as usually happens.) But it was far worse a couple blocks down the road, where a sudden 10-foot flood washed the neighborhood cars into a single heap of wreckage, with a Lincoln Towncar sitting proudly on top. There were numerous high-water rescues in the area. Luckily, the fractal cats were well ensconced in the darkest closet during the spectacular noise. More severe storms are forecast for later today, so we'll see how it goes. For me, I'm going to finish as many chores as possible before the next deluge and power failure. It's sunny at the present, and the cats are in the yard. All is temporarily well. Until next FOTD, take care, and be at ease. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Midget_Collision { ; time=0:01:48.75--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-10.8815/-1.72085e-015/3.908693 params=1/4/0.1/5/-0.991909/0 float=y maxiter=1200 inside=0 logmap=yes symmetry=xaxis periodicity=10 colors=000QFDNFDLECJEBGEAEDACD99C87C77C06C45C74CB3\ CE3CH6EI8FIBGIDHIFIIIJJKKJMLJPMJRNJUOKWPKYQK`RKbSK\ o`YpX`qTcrPfsLisHkpFhnEelDbiC_gBXeAUc9S`7PZ6MX5JU4\ GS3DQ2AO18R6BTBDVFGXKI_PKaTNcYPeaShfUjkWloZnt`pxbm\ wakv`hu_ftZdsZarY_qXXqWVpVToVQnUOmTLlSJkRHkRKlPMmO\ OnMQnLSoJVpIXpGZqF`rEbrCesBgt9it8ku6mv5ov4pu7puApu\ CqtFqtIqtKrsNrsPrsSsrVsrXsr_tqbtqdtqgtqiqphnpglpgi\ offofdoeaoeZndXndUncRncPmbMmbJmaHmaFk_EjYDiWCgUBfS\ AeQ8cO7bM6aK5_I4ZG3YE8_HCaJGbLLdNPePTgRYhUajWekYjm\ _nnarpcvoesmdpmcmmbkmbtoJqqKoqKloKjmKgmLemLbmL`mLY\ mMWmMTmMRmMQmLPmKOmJOmINmHMmGLmFLmEKmGJmIImKHmLGmN\ FmPEmRDmSCmUBmWAoY9qZ8s`7ub6wd5xeJzdXzcjzcnz8rzMvz\ _czeLzk2zqAznHzlPziWzgczdjzbkzalz`lz_mzZnzYnzXozWB\ zkWzbozVpzWpzXqzYqzYrzZrz_sz`sz`tzatzbwzftzbJzK`zS\ qzZkzXfzV`zUWzSQzRLzPBzHEzLGzOJzSLzVOzZQzaTzeVzhUz\ cUz_TzVTzRSzMSzIXzGUzFSzE } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 13-06-03 (Mistral [7])
by Jim Muth 13 Jun '03

13 Jun '03

FOTD -- June 13, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today is Friday the 13th here at Fractal Central as well as nearly everywhere else on earth. Because the number thirteen has always been considered unlucky, and in the middle ages criminals were usually executed on Friday, it is supposed to be an unlucky day. Well, it's not supposed to be unlucky, it's simply that many people consider it to be unlucky. This, of course, is superstition. Rational-thinking people realize that belief in superstitious things is a sign of irrational thinking. (Even though I now know that precognition exists, I am still a rational-thinking person.) Nothing in a calendar day of the week and a date that were determined by men can cause bad luck. Bad luck is nothing more than randomly distributed and often self- produced misfortune. But we now know that the world extends into regions where reason alone can no longer give all the answers. So who can say for sure that irrational thinking is always wrong and today is not somehow jinxed? Today's fractal is named "Mistral". A Mistral is not a mis- spelling of the word 'mis-trial', it is a cold north wind that blows for long periods of time in southern France. After a while, it becomes quite annoying to those not accustomed to it. I chose this name for whimsical reasons. There is nothing windy about today's image, which subtracts Z^(1.1) from Z^(-1.1) before adding (1/C). The parent consists of several scattered and distorted Mandel- oids. Today's scene lies in the East Valley area of the most prominent Mandeloid. It is a rather lively scene, which rates a 7. Its brilliant colors are fairly bubbling with activity. If I had been in a better mood, I might have rated it an 8, but sweeping water into the sump for 45 minutes is an annoying task, so the image rates only a 7. The parameter file renders in 6 minutes; the image file down- loads in less than one minute. Running the parameter file is more fun; downloading the completed image is more convenient. The individual fractalist must make the decision. The image can be found, ready for download at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> A very muggy day Thursday led to torrential and very noisy thunder-storms in the late afternoon and evening, which left an inch of water in the fractal basement. Before the rain arrived, the temperature reached 86F 30C. Luckily, the dynamic fractal cats had already satisfied their wanderlust by the time the rain began, and weathered the noisy storms hiding in the closet. When they finally came out, their fears were eased by a consol- ing treat of tuna. Today promises to be a repeat, so I expect a repeat performance from the duo. (Hopefully, not from the basement.) Until next FOTD, take care, and tomorrow I'll tell of any bad luck that might happen today. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Mistral { ; time=0:06:39.59--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.01259329587616971/+0.353654150329713\ 80/2.773255e+012/1/130/-0.000177204568416973463 params=1/-1.1/-1/1.1/0/0 float=y maxiter=1200 inside=0 logmap=130 periodicity=10 colors=000PGHTAGV4EX0CZ0Cb08d26e64g82iC0kG0mJ0oL0s\ P0uT0vX0x_0ze0zh0zm0zo0vj0m`0eV0XP0NJ0GG06A0040000\ 0000000ENGbzLZzPVuTRoXNi`JddGZgEVm6ds0mv0vz0zzczzc\ zzZzu0zk0zd8zVGzNNzEVz6bz0iz0qz0vz0sz0qz0mz0kz0iz0\ ex0du0bs0Zq0Xm0Tk2Ri4Pe6Ld8Jb8H`C2JE0460802A0AC0HG\ 0PH0VJ0VJ0TJ0TJRJLNLNHLPENR8PT4RV0RX4Tb6Tg8TmAVsCV\ xEVzHRvLPqNNkRLgVJbXGX`ETbCNeAHi8Ek48o22s00u00x00z\ 00m40bC0RL0ET02b00i00d00Z00V04P08L0AG6EACH6HJ0NN0R\ R0XT0bX0g`0mb0qZ0qX0qV0qT2qRAqPHqNPqLXqTbm`gkgmims\ guxezzdzzbzz`zzbuzdkvdbseRmgHgg8bi0Zi8NVGCHP04X00V\ 84VPGVgTVxdVzoRzsPzuLzxJzzGxzEvzCsz8oz6mz2iz0ez0dz\ 0`z0Zz0bz4dzAgzGizLkvRoqVqk`ueev`kxVqzPvzkzzusxzkq\ zdiz`bzdXzgPzkHzoAzs2zv0zz0zz0zz0zz0zz0zz0zz0zz0zz\ 0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0z\ z0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0\ zz0zz0zz0zz0zz0zzXzzRzzLz } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 12-06-03 (Your Cheating Fractal [5])
by Jim Muth 12 Jun '03

12 Jun '03

FOTD -- June 12, 2003 (Rating 5) Fractal visionaries and enthusiasts: Today's hastily-found scene is a play on the number 6. It is typical of the scenes found in fractals created by combining two negative powers of Z and adding the reciprocal of C. With so little effort behind it, the image cannot be considered rating any better than an average 5, but it still might be worth the 7 minutes required to render it. I named the picture "Your Cheating Fractal" for whimsical reasons after I heard a song with almost the same name on the fractal radio. As far as I know, fractals are not conscious, and therefore can not cheat. But I have heard it said that everything has a degree of consciousness, and since fractals are members of the set of everything, they also might be conscious, and therefore actually have an ability to cheat. The parent fractal resembles a Mandelbrot set with its East Valley missing, and surrounded by an extended field of chaos. Today's scene is located near the inland limit of the chaos field surrounding the main bud of the parent. The 7-minute render time can be avoided by downloading the image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Wednesday was a near perfect day here at Fractal Central -- at least for cats. For humans it was a bit muggy, with high humidity and a temperature of 86F 30C. The cats spent several presumably happy hours in the yard, while the humans did their human work. A heavy thunder-storm came up just after nightfall, but by that time, the cats' good day had been established. Today promises to be a repeat. I assume the cats will repeat their good mood. My mood will improve when the work is finished and the next FOTD is found, though it is not too bad as things stand now. Until next time, take care, and be faithful to your fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ YourCheatingFractl { ; time=0:07:23.53--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+6.00228958244036100/+3.223452857127679\ 00/2.140219e+009/1/-80/0.00351184647968315333 params=0.6/-0.6/0.06/-6/0/525 float=y maxiter=1200 inside=0 logmap=156 periodicity=10 colors=000rVhrSjrQkrOlqSnpVopZpoarnesnhtmlvlowlrxg\ iocag_TZVLRRCIN4APH9QU9Sf9Ts9SpARnARkBQiBPfCPdCOaD\ O_DNYDMVEMTELQFKOFKLGJJGJHGDVR7ha1vkGicUXXVW_VWaWW\ dWWfXWiXWkYWnYWpZWsZWu_Wx_Wz`Tv`RsaPpaNmbLjbJgbHcc\ F`cDYdBVd9Sd7PbENaLL`RKZYIYdGXjFVgITdLSaOQ_RPXUNUX\ MS_KPbIMeHJhFHkEEnCBqB9tGEoKJkOOfSTbWYY_bUYdWWeYVg\ _ThaSicQkdPlfNmhMojKplJqmInjIkhHifHfdGdbGa`F_ZFXWE\ UUESSDPQDNOCKMCIKtxTuuVurWuoXulYuiZuf_uc`u`auYbuWc\ nTahR_aPZWNXPLVJJUCHS6FR5FU5FX4F_4Fb3Fe3Fh2Fk2Fn2F\ q6Dk9BfCA`F8WI6QL5LK7OJ8RI9THAWGCZFD`EEcDFfCHhBIkA\ Jn9Kp8Jl8Ii7Jh7Jg7Jf7Je6Jd6Jc6Jb6Ja5K`5K_5KZ5KY4KX\ 4KW4KV4KUFdQQyNUrSYkX`dadYfgSjfTgeUdeUbdV_cWYcWVbX\ TbXQaYO`ZL`ZJ__G__EX`GUaIRbKOcMMcOJdQGeSDfUAgW8gY7\ iV7jT7kR7lO6mM6nK6pH6qF5rD5sA5t85u65v4Av5Fv5Kv5Pv5\ Uv5Zv5cv5hv5mv5lsAkpFjnKikPhiUgfZfdch_hjVmlQrnMwcN\ mTOdIOWJRXsfarcbradrZerXg } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 11-06-03 (The Past [6,7,8])
by Jim Muth 11 Jun '03

11 Jun '03

FOTD -- June 11, 2003 (Rating 6,7,8) Fractal visionaries and enthusiasts: Today's FOTD is late because, for some reason, the phone has been dead all morning. I think a truck ran into a telephone pole somewhere nearby. But whatever the problem was, it has now been eliminated and things are back to normal. (It was actually rather pleasant to have part of a morning without phone interruptions. I got a lot of work done.) Today's image rates a 6 in bright light and an 8 in subdued light. It is a very somber image created by the simplest of formulas -- Z^33+Z^2+C. The image is so somber in fact that it can be fully appreciated only in semi-darkness. When studying the image in subdued light, I get a feeling of something from the distant past -- something mysterious from long ago and far away, almost forgotten, remembered only by the feeling it once produced. What this nearly forgotten thing is I have no idea, so I named the image "The Past". The render time of 4 minutes is quite reasonable for an image that rates somewhere between a 6 and an 8 depending on the light. The small amount of effort required to download the finished GIF image from one of the FOTD web sites can eliminate even this short wait. Paul's site is: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's is: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Tuesday was another perfect day here at Fractal Central, with lots of sun and a temperature of 81F 27C. The fractal cats spent nearly 6 hours in the yard, enjoying the great weather. But they were not as lively as they once would have been in such conditions. I saw almost no zooming around the yard, scampering up the holly trees, or chasing birds. I did see lots of sitting and thinking. This is how it goes with cats approaching the geriatric stage of life. I am now thinking of the remaining work that must be done. But, unlike cats, I must do more than just think. So until 24 hours from now, take care, and where is the ultimate fractal? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Past { ; time=0:04:26.39--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.24755150217609540/-0.055896930341567\ 15/7.643967e+008/1/55/5.69510350649504726e-007 params=1/33/1/2/0/0 float=y maxiter=500 inside=0 outside=tdis symmetry=none periodicity=10 colors=000X9uRBzMGzGHz9Mz3Oz5Kz7Hw9Gh90AB9EE70N5TQ\ 9_TEfWMo`Sua_zYgzVozRrzOjzKozHrzEwz9zz5zz0zz0zz0zz\ 0zz0zz0zz3zz5zz9zzEzzHzxKzuOzpRzmVzfXzjTzmPzpMztHz\ wEzz9zz5zz0zz0zz0zz0zz0zz0zz0zz7zzKzzXzzfzzpzzmzzj\ zzhzzdzzazz_zzXzzTzzRzzOzzKzzHzzEzz9zz7zzBzzGzzKzz\ OzzRzzVzzYzzazzdzzhzzlzzozzrzzuzzxzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzztzzozzjzzdzz_\ zz9zzBzzEzzGzzHzzKzzMzzzzzwzzdzzzzzzzzxzzpzzjzzazz\ Tzz9zzBzzBzzEzzEzzGzzGzzHzzHzzKzzKzzMzzMdV00zYfzXd\ zVdxTduTdpRdmPdjPddOdaMdY0jz0hz0hz0hw0hu0ht0fp0fo0\ fm5fjwuKuuEtt5tt0or3lp7xGHhoBdmG_lHXjMThPPfTzK0tR0\ cYGY00T90PRGfX9cYEa_GY_KXaMTcORcROdTlEzcOtVXfmfxjd\ uhdtfdpcdoadl_djXdfVddTdaPd_OdXz0TtBVcRV0t00r00p00\ o05m57l9BjGGhMKfRzz0uYzr_zp_zm_zlazhawfatcapacmYcj\ XcfTdcRd_OdXGzjHzdKzaMpYrj3lh9dfGYfMRdRh0xf0ud3tc7\ ra9p_Eo_GmYKlXMjVOfTRdTTc } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Multifractal_3
by Albrecht.Niekamp＠t-online.de 10 Jun '03

10 Jun '03

Hi, Multifractal now has five frms to choose from. Beautiful new structures! Pagoda is a special zoom, as it contains all five, but no chaotic spots, and thatïs where I wanted to get at. Iïm still working on a better way to embed the new frm, "Bees" by Ray Girvan, so maybe tomorrow there is a new formula. I hope, this is alright with you, as I´m constantly trying to improve my baby.. Fractal greetings, Al. ---------------------------------START-PAR--------------------------------- Pagoda { ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult241.frm formulaname=multifractal_3 ismand=y function=exp/sin/sin/exp passes=t center-mag=0.374349/-0.833852/19.72387/1/154.999999999999972/7.671641100\ 15983169e-014 params=0.5/-0.375/12829.1001/40.3214026/4048.02048/384.000001/384.00024/\ 256.0076800000001/512.01024/768.01024 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200III<3>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>\ 022000211<22>keOmgPoiQqjRslSunT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00\ <3>z00<25>C00A00800<3>000<23>eeegggiiijjjlllnnn<2>sss<20>KKK } Mfr3_basic { ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult241.frm formulaname=multifractal_3 ismand=y function=exp/sin/sin/exp passes=t center-mag=-0.537836/4.44089e-016/0.9861933 params=0.5/-0.375/12829.1001/40.3214026/4048.02048/384.000001/384.00024/\ 256.0076800000001/512.01024/768.01024 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200III<3>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>\ 022000211<22>keOmgPoiQqjRslSunT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00\ <3>z00<25>C00A00800<3>000<23>eeegggiiijjjlllnnn<2>sss<20>KKK } ------------------------------------start-frm------------------------------- FRM:Multifractal_3 { ; Albrecht Niekamp 090603 ;only integers as first input, second input 5 digits to the right ;real(p2) 5digits: shape, outside, in1, in2, in3 ; 0_off 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset digit1: +5_warp ; input2 : five digits frm2 use : 0_no 1_yes ;imag(p2) (-)digit1 : many_mods multipl. off 1_out 2_in1 3_in2 4_all ; digit2 : iter-reset 1_out 2_in1 3_in2 4_all ; input2 : many_mods_2digits frm1_2digits frm2_2digits bees_4digits ;real(p3) many_mods bailout, bailout ;imag(p3) shape : factor (fn1), outside : border-in ;real(p4) outside : factor (fn2), border-out ;imag(p4) maxiter1, factor1 (fn2) ;real(p5) maxiter2, factor2 (fn3) ;imag(p5) maxiter3, factor3 (fn4) ; da=real(p2) dd=trunc(da) da=round((da-dd)*100000)+11111 d=trunc(dd/10000) ex0=d>5 d=d-5*ex0 vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) ex1=d>0 dd=dd-d*1000 rs1=d>5 d=d-5*rs1 v1m=(d==3) v1j=(d==4) dd1=(d==2)+(d==4) d=trunc(dd/100) ex2=d>0 dd=dd-d*100 rs2=d>5 d=d-5*rs2 v2m=(d==3) v2j=(d==4) dd2=(d==2)+(d==4) d=trunc(dd/10) ex3=d>0 dd=dd-d*10 rs3=d>5 d=d-5*rs3 v3m=(d==3) v3j=(d==4) dd3=(d==2)+(d==4) ex4=dd>0 rs4=dd>5 dd=dd-rs4*5 v4m=(dd==3) v4j=(dd==4) dd4=(dd==2)+(dd==4) tt=ex0+ex1+ex2+ex3+ex4 ; d=trunc(da/10000) ab=(d==2) da=da-d*10000 d=trunc(da/1000) ab1=(d==2) da=da-d*1000 d=trunc(da/100) ab2=(d==2) da=da-d*100 d=trunc(da/10) ab3=(d==2) da=da-d*10 ab4=(da==2) ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) d=round((d-dd)*100000000) da=trunc(dd/10) so1=((da==1)+(da==4)==0) so2=((da==2)+(da==4)==0) so3=((da==3)+(da==4)==0) dd=dd-10*da ir1=(dd==1)+(dd==4) ir2=(dd==2)+(dd==4) ir3=(dd==3)+(dd==4) ; mm=trunc(d/1000000) d=d-mm*1000000 p6=trunc(d/10000)/10 d=d-p6*100000 if (t) p6=-p6 endif p7=trunc(d/100)/10 d=d-p7*1000 p8=d/100 ; d=real(p3) mb=trunc(d) ba=(d-mb)*100000 ; d=imag(p3) sfac=trunc(d) b1=(d-sfac)*100000 b0=b1/2 ; d=real(p4) ofac=trunc(d) b2=(d-ofac)*100000 ; d=imag(p4) mi1=trunc(d) fac1=(d-mi1)*100000 ; d=real(p5) mi2=trunc(d) fac2=(d-mi2)*100000 ; d=imag(p5) mi3=trunc(d) fac3=(d-mi3)*100000 ; if (ismand) z=0 if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else c=p1 z=pixel endif t=0 d3=(ismand==0) u=d3 : bo=z If (tt) t=t+1 if ((ex0)&&bo>b0) u=fn1(t/sfac) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) ba=mb else c=pixel endif else z=pixel c=p1*u endif ex0=0 tt=tt-1 elseif ((ex1) && bo>b1 && bo<b2) u=2*(fn2(t/ofac)) rs=rs1 ab=ab1 if (dd1) if (rs) z=pixel endif c=p1*u vb=v1j d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1m if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir1) t=0 endif ex1=0 tt=tt-1 elseif ((ex2) && t>mi1) u=2*(fn2(t/fac1)) rs=rs2 ab=ab2 if (dd2) if (rs) z=pixel endif c=p1*u vb=v2j d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v2m if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir2) t=0 endif ex2=0 tt=tt-1 elseif ((ex3) && t>mi2) u=2*(fn3(t/fac2)) ab=ab3 rs=rs3 if (dd3) if (rs) z=pixel endif c=p1*u vb=v3j d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3m if (vb) if (so3) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir3) t=0 endif ex3=0 tt=tt-1 elseif ((ex4) && t>mi3) u=2*(fn4(t/fac3)) ab=ab4 rs=rs4 if (dd4) if (rs) z=pixel endif c=p1*u vb=v4j d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v4m if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif ex4=0 tt=tt-1 endif endif if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn1(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z1=sin(z)-c ;Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif |z|<=ba } -------------------------------------------------------------end-frm-------- --------------------------------

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FOTD 10-06-03 (Viofti [7])
by Jim Muth 10 Jun '03

10 Jun '03

FOTD -- June 10, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal image is named "Viofti". I have no idea what the word means. It could have a meaning in another language, though I doubt it. The word came into my head as I studied the image, searching for a name, and somehow it seems to fit the otherwise indescribable scene. The image is an 'evaporated' one, consisting totally of trapped 'inside' points made visible by the 'fmod' option. The parent fractal, which is really there when the bailout radius is more reasonable, was created by iterating the quite simple formula -0.5Z^(-6)-3(1/Z)+(1/C). There is no need to describe this parent, for in today's image it no longer exists as a real fractal. The scene of today's image is actually quite close to a ghost midget, which I might feature in a future FOTD. As it is, the surreal objects floating before a space of infinite depth have such vivid definition that I rated the image a 7 even though it holds no midget. An additional good point of today's image is its speed. The render time of 5 minutes is a welcome relief from images such as yesterday's, which took 2 hours to finish. And believe it or not, today's image produces more fractal bang in 5 minutes than yesterday's did in 2 hours. If the 5-minute wait is still not brief enough, the download of the completed image is even faster. The download can be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> A mostly sunny day here at Fractal Central on Monday, with an afternoon temperature of 79F 26C, made the fractal cats happy, and me as well. Due to the pleasant weather, they spent the entire afternoon in the yard. When the day was finished, they settled into sleep without the need for a treat of tuna or turkey. Today promises to be another near-perfect day. Could the dynamic duo possibly be angelic two days in a row? I've got a bit of work to wrap up before I can concentrate on fractals, so until next FOTD, take care, and see you in 24 hours. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Viofti { ; time=0:05:10.11--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+3.56320848149254700/-2.845364409269308\ 00/1763.087/1/-2.50000000000225331/1.1933828925059\ 2311e-011 params=-1/-6/-6/-1/-0.5/1e+100 float=y maxiter=900 inside=fmod proximity=1 symmetry=none periodicity=10 cyclerange=13/255 colors=000WbaW`bVZdUXeTVgTThh8wFyaEsdDnfChiPWhS8nP\ 8qN8sQIjTRbW_UZhMaqEWbMXcOYcPZcQ_dR`dSadTbdUceVdeW\ eeXfeYgfZhf_if`jfakgblgcmgdmgelhfkhgjhgjhhihihhihh\ jghjfhkfhlehldhmchmchnbhoahoahp`hp_hq_hrZhrYhsYhsX\ gpWfnWekVdiUcfUcdTbaSa_S`XR_VR_TQZQPYOPXLOWJNVGNVE\ MUBLT9LS6KR4KR2MP3NN3PL4QK4RI5TG5UE6WD6XB7Y97_78`6\ 8b49c29d19c3Db4Ha5La6O`7S_8W_9ZZAbYBfYCiXDmWEqWFtY\ Iu_KuaNucPueRugUviWvjYvl`vnbvpewrgwtiwvlwxnwypwuos\ qnommlilhekebjaZiZVhVRgRNfOKeKGdHCcD8bA4a61`36Z8BX\ DGVHKTMTRRXP_aNceLfiJjmHorFsuDvwBwvDuuEssFrqGooHmm\ IkkJijKgiLegMceNadO_bOY`NWZMUXLSWKQUJOSIMQHKOGINFK\ O2LO3LO4MO5MO6NP7NP8OP9OPAPPBPPCPQDQQEQQFRQGRQHSRI\ SRJTRKTRLURMURNUXUOb_IcYKcXLcWMcVNcUOcTPcSQcRRcQSc\ PTcOUcMWcLXcKYcJZcI_cH`cGacFbcEccDdcCecBfaDd`FcZHb\ YIaXK`VMZUNYTPXRRWQSVPUUNWSMYRLZQJ`PIbOHcNFeLEgKDh\ JBjIAlH9mG9gI9aJ9XK9RM9MN } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 09-06-03 (This is How Low [5])
by Jim Muth 09 Jun '03

09 Jun '03

FOTD -- June 09, 2003 (Rating 5) Fractal visionaries and enthusiasts: Today's image takes us to the bottom of the barrel, way down to the land of Z^(1.009)+C. At this abysmal depth, the sand-like fractal material has reached such a high maxiter that it is effectively beyond reach. But the areas of extreme discontinu- ities continue to multiply, and though still of a very high maxiter, are within reach for those with patience. The 'recip' function was an accident. The 'floor' function works best with this formula, but the image is good, and who's complaining. In today's fractal, the coloring makes the picture. A very broad palette is necessary to add definition to an otherwise featureless image, but when this is done, a series of feathery curving arms appears. I have named the image "This is How Low" because its exponent of Z is about as close to unity as it is possible to come and still get something other than an empty, featureless circle. I have rated the image at an average 5, more for mathematical interest than for artistic worth. If it were not for the render time of over 2 hours on my machine, the image might have rated a 6. But don't be put off by the slowness of the image. Give Paul and Scott a couple hours to render the image, then visit their web sites to download the completed image. Paul's site is: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's is: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The rain held off on Sunday here at Fractal Central. Despite a temperature that never reached 70F 21C, the fractal cats had a good day. When the cats are happy, I'm happy also, so I also had a good day. Today is actually starting with some sun, and no rain is forecast, making another good day near certain. Once the day's work is behind me, assuming the cats are happy, my day should once again be good. Tomorrow's FOTD might launch out in a new direction, or it might be a return to the MandelbrotMix4 formula and the midgets it draws. To see what happens, check back in 24 hours. Until then, take care, and hope for the best. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ This_is_How_Low { ; time=2:05:42.24--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=mandelbrotbc1 function=recip passes=1 center-mag=+0.07536313779841985/+0.000859404003554\ 35/8654862/1/51/-1.76329913170736319e-009 params=1.009/0/-182/1000 float=y maxiter=12000 inside=255 logmap=3216 periodicity=10 colors=000zlPzmQzmQzmQzmQzmRzmRymRymRymRymSxmSxmSx\ mSxmUwmTwmSwmSwmRvmRvmQvmQvmPumPumOumOumNtmNtmMtmM\ tmLslKskKsjJsiJrhIsgItfHueHvfGwfGxgFygFwhEwhEwiDwj\ CziDziDzhDzhDzgEzgEzfEzfEyeExeFwdFvdFucFtcGsbGrbGq\ aGpaGo`Hn`Hm_Hm_HmZIlZIlYIlYIlXIlXJlXJlWJlWJkVJkVK\ kUKkUKkTKkTLkSLkSLjRLjRLjQMjQMjPMjPMjONjONiNNiNNiM\ NiMOiLOiLOiKOiKPhJPhJPhJPhIPhIQhHQhHQhGQgGQgFRgFRg\ ERgERgDSgDSgCSfCSfBSfBTfATfATf9Tf9Uf8Ue8Ue7Ue7Ue6V\ e6Ve5Ve5Vg3Wf4Ve5Ve5Vd6Ud6Uc7Uc7Tb8Ta8Ta9S`AS`AS_B\ R_BRZCRYCQYDQXDQXEPWFPWFPVGOUGOUHOTHNTINSINSJMRJMQ\ KMQLLPLLPMLOMKONKNNKMOJMOJLPJLQIKQIKRIJRHISHISHHTG\ HTGGUGGVFFVFEWFEWEDXEDXECYDCYDBZD9YCBZDC_DD_DE`EF`\ EGaEHaEIbFJbFKcFLcGMdGNdGOeGQeHRfHSfHTgHUgIVhIWhIX\ iJYiJZjJ_jJ`kKakKblKclKclJblJalJalJ`lI_mI_mIZmIYmH\ YmHXmHXmHWmGVmGVmGUmGTmFTmFSnFRnFRnEQnEPnEPnEOnDNn\ DNnDMnDLnCLnCKnCJoCJoBIoB } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END 20.0 PAR-FORMULA FILE==================================

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Multifractal_2
by Albrecht.Niekamp＠t-online.de 08 Jun '03

08 Jun '03

Hi, not many words are needed about this one. Zoom out for more. There is a small modification in the formula, except that the text explanations are better and you can see, which function belongs to each factor. Yesterday`s images are not affected, so I suggest you just exchange the formula. Fractal greetings, Al. -------------------------------------start-par----------------------------- Zoomers_playground { ; Time 0.57.16.12 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult241.frm formulaname=multifractal_2 ismand=y function=exp/exp/exp/exp passes=t center-mag=-0.500313/6.66134e-016/1.173709 params=0.3102206488235115/0.9875484481337932/19182.101/41.321405/4048.02\ 048/384.000003/768.000218/256.0076800000001/512.01024/1536.01024 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200600<2>000<25>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0c\ q0es<3>0kz<25>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB7A96875<3>00\ 0400<23>o00q00s00<3>z00<27>800 } Black&white { ; ; Albrecht Niekamp June, 03 ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult241.frm formulaname=multifractal_2 ismand=y function=exp/exp/exp/exp passes=t center-mag=+0.09277978820879434/-0.47206879974324510/196.0418/0.9356/17.\ 3385926046431678/0.333924698186814028 params=0.3102206488235115/0.9875484481337932/19182.101/41.321405/4048.02\ 048/384.000003/768.000218/256.0076800000001/512.01024/1536.01024 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200600<2>000<25>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0c\ q0es<3>0kz<25>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB7A96875<3>00\ 0400<23>o00q00s00<3>z00<27>800 } -------------------------------start-frm----------------------------------- FRM:Multifractal_2 { ; Albrecht Niekamp 070603 ;only integers as first input, second input 5 digits to the right ;real(p2) 5digits: shape, outside, in1, in2, in3 ; 0_off 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset digit1: +5_warp ; input2 : five digits frm2 use : 0_no 1_yes ;imag(p2) (-)digit1 : many_mods multipl. off 1_out 2_in1 3_in2 4_all ; digit2 : iter-reset 1_out 2_in1 3_in2 4_all ; input2 : many_mods_2digits frm1_2digits frm2_2digits ;real(p3) many_mods bailout, bailout ;imag(p3) shape : factor (fn1), outside : border-in ;real(p4) outside : factor (fn2), border-out ;imag(p4) maxiter1, factor1 (fn2) ;real(p5) maxiter2, factor2 (fn3) ;imag(p5) maxiter3, factor3 (fn4) ; da=real(p2) dd=trunc(da) da=round((da-dd)*100000)+11111 d=trunc(dd/10000) ex0=d>5 d=d-5*ex0 vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) ex1=d>0 dd=dd-d*1000 rs1=d>5 d=d-5*rs1 v1m=(d==3) v1j=(d==4) dd1=(d==2)+(d==4) d=trunc(dd/100) ex2=d>0 dd=dd-d*100 rs2=d>5 d=d-5*rs2 v2m=(d==3) v2j=(d==4) dd2=(d==2)+(d==4) d=trunc(dd/10) ex3=d>0 dd=dd-d*10 rs3=d>5 d=d-5*rs3 v3m=(d==3) v3j=(d==4) dd3=(d==2)+(d==4) ex4=dd>0 rs4=dd>5 dd=dd-rs4*5 v4m=(dd==3) v4j=(dd==4) dd4=(dd==2)+(dd==4) tt=ex0+ex1+ex2+ex3+ex4 ; d=trunc(da/10000) ab=(d==2) da=da-d*10000 d=trunc(da/1000) ab1=(d==2) da=da-d*1000 d=trunc(da/100) ab2=(d==2) da=da-d*100 d=trunc(da/10) ab3=(d==2) da=da-d*10 ab4=(da==2) ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) d=round((d-dd)*1000000) da=trunc(dd/10) so1=((da==1)+(da==4)==0) so2=((da==2)+(da==4)==0) so3=((da==3)+(da==4)==0) dd=dd-10*da ir1=(dd==1)+(dd==4) ir2=(dd==2)+(dd==4) ir3=(dd==3)+(dd==4) ; mm=trunc(d/10000) d=d-mm*10000 p6=trunc(d/100)/10 d=d-p6*1000 if (t) p6=-p6 endif p7=d/10 ; d=real(p3) mb=trunc(d) ba=(d-mb)*100000 ; d=imag(p3) sfac=trunc(d) b1=(d-sfac)*100000 ; d=real(p4) ofac=trunc(d) b2=(d-ofac)*100000 ; d=imag(p4) mi1=trunc(d) fac1=(d-mi1)*100000 ; d=real(p5) mi2=trunc(d) fac2=(d-mi2)*100000 ; d=imag(p5) mi3=trunc(d) fac3=(d-mi3)*100000 ; if (ismand) z=0 if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else c=p1 z=pixel endif t=0 d3=(ismand==0) u=d3 : bo=z If (tt) t=t+1 if (ex0) u=fn1(1/sfac) if (ismand) z=0 if (vb) c=u*0.4*log(sqr(pixel^mm)) ba=mb else c=pixel*u endif else z=pixel c=p1*u endif ex0=0 tt=tt-1 elseif ((ex1) && bo>b1 && bo<b2) u=2*(fn2(t/ofac)) rs=rs1 ab=ab1 if (dd1) if (rs) z=pixel endif c=p1*u vb=v1j d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1m if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir1) t=0 endif ex1=0 tt=tt-1 elseif ((ex2) && t>mi1) u=2*(fn2(t/fac1)) rs=rs2 ab=ab2 if (dd2) if (rs) z=pixel endif c=p1*u vb=v2j d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v2m if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir2) t=0 endif ex2=0 tt=tt-1 elseif ((ex3) && t>mi2) u=2*(fn3(t/fac2)) ab=ab3 rs=rs3 if (dd3) if (rs) z=pixel endif c=p1*u vb=v3j d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3m if (vb) if (so3) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir3) t=0 endif ex3=0 tt=tt-1 elseif ((ex4) && t>mi3) u=2*(fn4(t/fac3)) ab=ab4 rs=rs4 if (dd4) if (rs) z=pixel endif c=p1*u vb=v4j d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v4m if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif ex4=0 tt=tt-1 endif endif if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn1(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z2=z*z z=z2*z2+(p6+u)*z2+c else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif |z|<=ba }

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FOTD 08-06-03 (Undersea Fantasy [7])
by Jim Muth 08 Jun '03

08 Jun '03

FOTD -- June 08, 2003 (Rating 7) Fractal visionaries and enthusiasts: With today's image, we sink all the way down to an exponent of Z^(1.015) and the hard-to-find chaos that lies in the resulting fractals. We examine this lowly fractal at a point 275 levels down the logarithmic spiral, though from the degree of disorder in the image, I assume the spiral has long since ceased to resemble the spiral shape we are familiar with. Not only is the image filled with discontinuities, but the discontinuities are discontinuous. The whole thing vaguely reminds me of an undersea scene, and I named it "Undersea Fantasy" accordingly. It's a spectacularly colored image, with colors perhaps a bit too gaudy, so I held the rating to a 7. As I warned earlier, the chaos in these very low fractals is of a very high maxiter and quite hard to bring out. The render time of 1 hour and 5 minutes for today's image demonstrates this fact. This slowness will grow only worse as we continue our descent toward our ultimate but perhaps unreachable goal of Z^(1.009). Luckily for fractalists with other things to do, the finished image of today's fractal will soon be available on the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> With the temperature hovering around 66F 19C, heavy rain fell all day here at Fractal Central on Saturday. It came to an end shortly before sunset, but by that time the cats' day had been totally spoiled. Their moods were sour, and the tuna treat only partially restored their spirits. Today is starting cloudy, but at least it is dry. If all goes well, and the forecasted showers hold off, the dynamic duo will have a better day. The fractal basement took on water in the rain, so my task for today will be to dry things out down there. Until next FOTD, take care, and how low can you go? Stay tuned to see. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Undersea_Fantasy { ; time=1:05:47.33--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-4.41217/0.0769257/4.96124/1/12.5/1.784\ 961067841095e-013 params=1.015/0/-275/10000 float=y maxiter=12000 inside=255 logmap=202 periodicity=10 colors=050LJYNJXNSXPHVPHV_HTQGTSGSSGQTGQTEPVEPVENS\ ENXDLXDKeDKYDI_BI_BH`BH`BFb9Eb9Ed9CY9Ce7AV79g79`77\ h67h65j65j64k52k52m51m51o50o50p50h50r50r50s50s50k5\ 0s50s50s50s50s50s50s50s60m60s70s70s90s90hB0sB0uD0u\ D0uE0uE0uG0uG0uH0uH0jJ0uJ0uK1uK1jM1uM1uO1wO2wP2wP2\ wR2wR2wS4wS4wU4wU4wV4wV5jX5wX5wY5wY5x_7x_7xa7xa7xc\ 7xc9xd9xd9xf9xf9xgAxgAxiAxiAxjAzl9xjAxjAwjAwjAuiAu\ iAuiAsiAsgArgArgArgApgApfAofAofAofCmdCmdCkdCkdCkcC\ jcCjcChcChcChaCgaCgaCeaCe_Ce_Cd_Cd_Eb_EbYE`YE`YE`Y\ E_XE_XEYXEYXFYVGXVHXVIVVJVVKVULTUMTUNSUOSSPSSQQSRQ\ SSPSTPRUPRVNRWNRXLPYLPZLP_KP`KOaIObIOcHOdHOeHMfFMg\ FMhEMiEKjEKkCKlCKmAKmAJmAJm9Jm9Jm7Hm7Hm7Hm5Hm5Gm4G\ m4Gm4Gm2Gm2Em1Em1Em1Em0Dm0Dm0Dm0Dm0Bm0Dm0Dm0Em0Em0\ Gm0Gm0Hm0Hm0Jm0Jm0Km0Km0Mm0Mm0Om0Om0Pm0Pm0Rm0Rm0Sm\ 0Sm0Um0Um0Vm0Vm0Xm0Xm0Xm0Ym0Ym0_m0_m0am0am0cm0cm0d\ o0do0fp0fr0gr0gs0is0iu0ju } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END 20.0 PAR-FORMULA FILE==================================

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FOTD 07-06-03 (First Flight [6])
by Jim Muth 07 Jun '03

07 Jun '03

FOTD -- June 07, 2003 (Rating 6) Fractal visionaries and enthusiasts: Today's image takes us into even lower territory -- down below yesterday's Z^(1.04) into the land of Z^(1.025)+C. Down in these depths, the chaos becomes harder to find, but as today's image shows, it is still there. The lengthy real(p2) parameter shows that the value was found by the Fractint randomizer. I could have rounded it to a 7 with little change in the parent fractal. Yesterday's image reminded me of a fleet of fantastic space craft taking off from a Martian invasion base. Today's image reminds me of jagged shards of something being swept up and away into infinite space by a sudden wind. Since the wind is the first in thousands of years to blow in this particular place, I named the image "First Flight". Today's image attempts the same effect as yesterday's superior image, but compared to that image, today's rates only a 6. But today's image is not without its interest. Despite the almost total descent into chaos, there are still traces of order in the image. The curving trails of bright debris in the background appear on the verge of organizing and creating a new class of order. I must examine this tendency of chaos to organize in fractals with exponents even closer to unity. The 16-minute render time can be avoided by downloading the completed image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> A mostly cloudy but mild day here at Fractal Central on Friday left the duo of fractal cats satisfied. After spending the afternoon enjoying the temperature of 75F 24C, they ended the day enjoying a treat of turkey. Their moods will be far less pleasant today however. It is already raining, heavy rain is forecast and a flood watch is in effect. I'm going to spend the day searching for fractals, working on the CD, or just plain watching the rain. Until next time, take care, and let's see a few Mandelbrot midgets. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ First_Flight { ; time=0:16:40.24--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=recip passes=1 center-mag=-2.62369017010877200/-0.375504820890258\ 10/91.72629/1/175/-1.06827741097603734e-012 params=1.025/0/6.942381054109317/1000 float=y maxiter=4200 inside=255 logmap=190 periodicity=10 colors=000iYDeaDa_F_XHbVHHXIjVIHVKHVKFULFULFUNDSPD\ SPDSQCQQCQSCQSASUAPUAKH9Q`APVANQANSALSCKQCKPCINCIN\ YHLDFKDFIXDIDCHDCFWADFADV9CF8AF8AH79H78H57H47H45I2\ 4I12I12I01I00K00K00K00K00I00K00L00N00P00Q00S00S00U\ 00V00X00Y00_00_00a00c00d00f00h00j00j01l01n01p01r01\ s02s02v02w02z02z04z04z04z04z04z05z05z05z05z05z07z1\ 8z28z59z79z8AzAAzCCzDCzHDzIFzKFzNHzPHzQIzUIzVKzXKz\ _LzaNzcNzfPzhPzjQwnQwpSwrSvvUvwVvzVszXszXszYqzYpz_\ oz_nzKmzAkz8izAgzCezEczGazI_wKYvMWsOUrQSpSQpUOnWMl\ YKj_IjaGhcEfdCdeAdf8cg6ah5_i6_j7Yk7Xl8Vm9Vm9UmASmC\ QmCQmDPmFNmFLmHLmIKmIImKHmLHmLFmNDmPCmPCmQAmS9mS8m\ U8mV7mV5mX4mY4nY2o_1pa0qa0rc0sd0vc0zd0zd0zd0zf0zf0\ zf0zf0zh0zh0zh0zh0zj0zj0zj0zj0zl0zl0zl0zl0zj0zj0zj\ 0zj0zh0zh0zh0zh0zh0zf0zf0zf0zf0zf0zd0zd0zd0zd0zc0z\ c0zc0zc0zc0za0za0za0za0za0z_0z_0z_0z_0zY0zY0zY0zY0\ zY0zX0zX0zX0zX0zX0zU0zS0z } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 29-05-03 (All Inside Stuff [6])
by Jim Muth 07 Jun '03

07 Jun '03

FOTD -- May 29, 2003 (Rating 6) Fractal visionaries and enthusiasts: I see on the Fractint list that the 'bug' in the program that has caused the MandelbrotMix4 formula to run incorrectly has been identified and can be fixed without too much effort. This obviously will have an impact on the upcoming FOTD-CD. Until now, I have been feeling a bit guilty about the unreason- able delay in releasing the FOTD-CD. Now however, it appears the delay will be a good thing, for it will enable me to release a disk that does not depend on a bug in the program to render the images correctly. Of course, this means a further delay in the release of the disk while any needed changes that might arise are being done, but after a delay of nearly a year, that will be of little consequence. Meanwhile, whenever I find the time, I am still working on the task of identifying and renaming the images on the disk, so that they can be matched with their corresponding discussions without confusion. And on a non-fractal topic, I'm now receiving spam snail mail. Yesterday, I received in the snail mail an air-mail letter from Zimbabwe, which is a country in the southern part of Africa. The enclosed letter was a print-out of the same fraudulent offer that I have received so many times in the e-mail. The letter tells me that a probably fictional Mr. Twala has in his posses- sion 9.2-million US dollars that he wants to transfer out of his country. To do this transfer he needs my bank account number. Once he has the account number, guess what will happen to any money in the account. I find it hard to believe that anyone would fall for such an obvious scam, but whoever is sending these letters must be finding some pigeons naive enough to fall for his scheme, because the postage on the envelope amounts to 700 Zimbabwe dollars or whatever their monetary unit is, and he must send out thousands of such letters. At least the stamps on the envelope, which picture a newly constructed dam, are attractive. Today's fractal is also attractive, though not quite as attrac- tive as the dam in Zimbabwe. It is another 'evaporated' image, this one located near the right edge of the fan of the parent fractal. I named the image "All Inside Stuff" as a description, and rated it a 6 because it is interesting but not that great. The render time of 19 minutes is somewhat slow for a 6-rated image, but immediate relief is available at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> It rained all morning here at Fractal Central on Wednesday, then the sun appeared and the afternoon was sunny. The temperature reached only 65F 18C, when 79F 26C is normal, but the dynamic pair had a great several hours in the yard, enduring the wet grass with little complaint. Today once again holds a chance of rain. It remains to be seen how the duo will adjust. I'll do my adjusting when the work is done and the next fractal is found. That time will likely be around 3pm. Until next time and next FOTD, take care, and don't give up hope for the FOTD-CD. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ All_Inside_Stuff { ; time=0:19:39.03 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+1.69799788216427200/-0.966528307188927\ 90/366675.9/1/-132.5/-9.33145443554606047e-009 params=-10/-1.1/-1/-11/0/1e+100/0/0 float=y maxiter=1200 inside=bof61 periodicity=10 colors=000eiOfhQggThfWjeZkdalccmbfoaip`lq_orZqqVoq\ SmpPkpMioJgoGenDcnAan7_l6Zk6Zj6Yh6Yg6Yf6Xd6Xc6Wb6W\ `6W_6VZ5VX5UW5UV5UT5TS5TR5SQ5SO5SN5RM5RK5QJ4QI4QG4\ PF4PE4OC4OB4OA4N84N74M64M00054M56M58M5AM6CM6EM6HM6\ JM7LM7NM7PM7RM7TM9VOAWPCXQDYRF_SG`TIaUJbVLdWMeXOfY\ PgZRh_Sj`UkaVlb000Yod_pe`qfbrgctheuifvjhwkkynixlhw\ jfvieugctebsd`sb_r`Yq_XpYVoWUnVSnTRmRPlQOkOMjM000J\ hJIhHGgGFfEDeCCdBAc97e68d79c89b9AbABaBB`CC`DD_EDZE\ EZFEV`FXHGTZGWJHVKIVLIUMJTMKTNKSOLRXLRQMQRNPSNOTOO\ UPNUPMVQMWRLXRKYSKZSJ_TI`UIaUHhVGbWGmWFdXErYEfYDrZ\ ChZCw`EiaGibIjcKjdMjeOkfQlgSlhUliWmjYmkZnl`nmbondo\ ofophpqjprlqsnqtprurrytuvsrtsoqslosjlrgjrdgraer_bq\ X`qUYqRWqPTpMRpJOpGMpERmCVjBZgAce9gb8k_7rZ6pY6oY6n\ X6mX6lW6kW6jV6hV6gV6fU6eU6dT6cT6bS6aS6_S6ZR6YR6XQ6\ WQ6VP6UP6SP6RO6QO6PN6ON6NM6MM6KL6LM6LM6MM6MN6NN6NN\ 6ON6OO6PO6PO6PO6QP6QP6cjL } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

3 2

Multifractal_2
by Albrecht.Niekamp＠t-online.de 06 Jun '03

06 Jun '03

Hi, hereïs what kept me silent the last days. This formula has a new structure, as I found out, how to check and uncheck all options and still they are executed in the correct order and the switching sequence is terminated after the last checked item. Also distorted structures are down to a minimum. I think this is the best one so far. Fractal greetings, Al. --------------------------------------------------------------------------- Janusbird4 { ; Time 0.33.16.49 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult241.frm formulaname=multifractal_2 ismand=y function=exp/exp/exp/exp passes=t center-mag=-0.500313/6.66134e-016/1.173709 params=0.3102206488235115/0.9875484481337932/10182.101/40.321405/4048.02\ 048/384.00004/768.00032/256.0076800000001/512.01024/1536.01024 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200600<2>000<25>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0c\ q0es<3>0kz<25>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB7A96875<3>00\ 0400<23>o00q00s00<3>z00<27>800 } Rubberboat { ; ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult241.frm formulaname=multifractal_2 ismand=y function=cos/exp/exp/exp passes=t center-mag=-0.48/6.66134e-016/1.103753 params=0.3102206488235115/0.9875484481337932/10189.101/40.321402/4048.02\ 048/384.00004/768.00032/256.0076800000001/768.01024/1536.01024 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200600<2>000<25>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0c\ q0es<3>0kz<25>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB7A96875<3>00\ 0400<23>o00q00s00<3>z00<27>800 } -------------------------------start-frm------------------------------------ FRM:Multifractal_2 { ; Albrecht Niekamp 040603 ;only integers as first input, second input 5 digits to the right ;real(p2) 5digits: shape, outside, in1, in2, in3 ; 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset digit1 +5_warpeffect ; input2 : five digits frm2 use : 0_no 1_yes ;imag(p2) (-)digit1 : many_mods multipl. off 1_out 2_in1 3_in2 4_all ; digit2 : iter-reset 1_out 2_in1 3_in2 4_all ; input2 : many_mods_2digits frm1_2digits frm2_2digits ;real(p3) many_mods bailout, bailout ;imag(p3) shape : factor, border ;real(p4) outside : factor, border ;imag(p4) maxiter1, factor1 ;real(p5) maxiter2, factor2 ;imag(p5) maxiter3, factor3 ; da=real(p2) dd=trunc(da) da=round((da-dd)*100000)+11111 d=trunc(dd/10000) ex0=d>5 d=d-5*ex0 vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) ex1=d>0 dd=dd-d*1000 rs1=d>5 d=d-5*rs1 v1m=(d==3) v1j=(d==4) dd1=(d==2)+(d==4) d=trunc(dd/100) ex2=d>0 dd=dd-d*100 rs2=d>5 d=d-5*rs2 v2m=(d==3) v2j=(d==4) dd2=(d==2)+(d==4) d=trunc(dd/10) ex3=d>0 dd=dd-d*10 rs3=d>5 d=d-5*rs3 v3m=(d==3) v3j=(d==4) dd3=(d==2)+(d==4) ex4=dd>0 rs4=dd>5 dd=dd-rs4*5 v4m=(dd==3) v4j=(dd==4) dd4=(dd==2)+(dd==4) tt=ex0+ex1+ex2+ex3+ex4 ; d=trunc(da/10000) ab=(d==2) da=da-d*10000 d=trunc(da/1000) ab1=(d==2) da=da-d*1000 d=trunc(da/100) ab2=(d==2) da=da-d*100 d=trunc(da/10) ab3=(d==2) da=da-d*10 ab4=(da==2) ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) d=round((d-dd)*1000000) da=trunc(dd/10) so1=((da==1)+(da==4)==0) so2=((da==2)+(da==4)==0) so3=((da==3)+(da==4)==0) dd=dd-10*da ir1=(dd==1)+(dd==4) ir2=(dd==2)+(dd==4) ir3=(dd==3)+(dd==4) ; mm=trunc(d/10000) d=d-mm*10000 p6=trunc(d/100)/10 d=d-p6*1000 if (t) p6=-p6 endif p7=d/10 ; d=real(p3) mb=trunc(d) ba=(d-mb)*100000 ; d=imag(p3) sfac=trunc(d) b1=(d-sfac)*100000 ; d=real(p4) ofac=trunc(d) b2=(d-ofac)*100000 ; d=imag(p4) mi1=trunc(d) fac1=(d-mi1)*100000 ; d=real(p5) mi2=trunc(d) fac2=(d-mi2)*100000 ; d=imag(p5) mi3=trunc(d) fac3=(d-mi3)*100000 ; if (ismand) z=0 if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else c=p1 z=pixel endif t=0 d3=(ismand==0) u=d3 : bo=z If (tt) t=t+1 if ((ex0) && bo>b1) u=2*(fn1(t/sfac)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) ba=mb else c=pixel endif else z=pixel c=p1*u endif ex0=0 tt=tt-1 elseif ((ex1) && bo>b2) u=2*(fn1(t/ofac)) rs=rs1 ab=ab1 if (dd1) if (rs) z=pixel endif c=p1*u vb=v1j d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1m if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir1) t=0 endif ex1=0 tt=tt-1 elseif ((ex2) && t>mi1) u=2*(fn2(t/fac1)) rs=rs2 ab=ab2 if (dd2) if (rs) z=pixel endif c=p1*u vb=v2j d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v2m if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir2) t=0 endif ex2=0 tt=tt-1 elseif ((ex3) && t>mi2) u=2*(fn3(t/fac2)) ab=ab3 rs=rs3 if (dd3) if (rs) z=pixel endif c=p1*u vb=v3j d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3m if (vb) if (so3) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir3) t=0 endif ex3=0 tt=tt-1 elseif ((ex4) && t>mi3) u=2*(fn4(t/fac3)) ab=ab4 rs=rs4 if (dd4) if (rs) z=pixel endif c=p1*u vb=v4j d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v4m if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif ex4=0 tt=tt-1 endif endif if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn1(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z2=z*z z=z2*z2+(p6+u)*z2+c else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif |z|<=ba } ---------------------------------------------------------------------end---- -----------

1 0

FOTD 06-06-03 (Martian Take-Off [8])
by Jim Muth 06 Jun '03

06 Jun '03

FOTD -- June 06, 2003 (Rating 8) Fractal visionaries and enthusiasts: For today's image we return to the chaos along the shoreline of the Z^(1.04)+C Mandeloid. I really should not say *THE* shoreline, I should say *A* shoreline, because the Z^(1.04)+C Mandeloid has an infinity of shorelines, and the shoreline in question is but one of that infinity. The shoreline is actually part of the parent as it appears in the slice 40 turns up the logarithmic spiral. As the exponent of Z is lowered ever closer to unity, the chaos in the more remote logarithmic slices of fractals first grows more chaotic, with large areas of what I call sand. The sand is present down to an exponent of around 1.01, where, due to its increasingly high maxiter, it becomes so hard to reveal that it is impractical to explore. Below this point, the Mandeloid fractals resemble mere jagged pieces of rock. The amount of sand peaks at an exponent of around 1.1, where it sometimes contains quite interesting sub-patterns. As the exponent is raised, the sand never really disappears, but becomes confined ever closer to the shoreline. By stretching my imagination, I saw in today's image a scene on a fantastic Planet Mars. Using a bit more imagination, aided by the film "War of the Worlds", I saw a fleet of space ships taking off on their way to invade earth, and named the image "Martian Take-Off". I assume that, thanks to its bacteria, the earth will survive the invasion of the fractal space craft. There is something about the image that I like. Maybe it's the jagged rust-colored rocks and space ships, maybe it's the blue of the Martian sky. Whatever it is, I rated the image at a much- above-average 8. With the help of a little imagination, the invasion fleet can be seen by running the parameter file and eagerly waiting for 15 minutes. The fleet can also be seen by downloading the pre- rendered image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Fine sunny weather and a temperature of 77F 25C here at Fractal Central on Thursday made for contented cats. The aging duo made the most of the situation by spending the day in the yard, watching for the new grey-and-white cat who moved in up the hill a couple weeks ago. Luckily for someone, the cat never showed up, and the once-dynamic duo had a restful day. Today is starting sunny again, which should assure the duo another good day. My day will be busy as I finish the work I failed to finish yesterday. And when the work is finished, I'll launch the search for the next FOTD fractal. Until next time, take care, and is there earth life on Mars? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Martian_Take-Off { ; time=0:15:11.76--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-7.03071/1.76031/1.456008/1/30/1.657771\ 14258247593e-013 params=1.04/0/40/1000 float=y maxiter=1800 inside=255 logmap=26 periodicity=10 colors=070zzTzzQzzQzyQqwOosOlqOioMgmMdkMaiKYgKXeKT\ cIQaIOYIKWHIUHFSHDNF9OF7MF5KDPMDRHDSOB0AB07BUP9079\ 079XU7ZR7Z77K77P79U79Z79c79Z79U79Z79K79F79A79c7907\ 9U7927B07B57B77B97BB7BD7BF7BH7BI7BK7BM7BO7BQ7DT7DV\ 7DX7DY7D_7Da7Dd7De7Dg7Di7Dl7Dn7Di7He7Ia7MY7OV7TTAV\ VDXXH__KadOeeSggWgl`doc_tgXvkTxoOzsKzwHzzDzz9zzBzz\ BzzDzzDzzFzzFxyHxyHvyItwItwKquKouKouMnsMlsOisOiqQg\ qQeqTeoTdoVaoVamX_mXYkXYkYXkYVi_Vi_TiaQgaOgdOgdMee\ KeeKegIcgHcgHaiFaiDalD`lB`n9`n9Yo7Yo5Yq3Wq3Wt2Wt0U\ t0Uv0Sv0Sx0Sx0Qz0Qz0Qz0Oz0Oz0Oz0Mz0Mz0Mz0Kz0Jz0Jz0\ Hz0Hz0Fz0Fz0Dz0Dz0Bz0Bz0Az08z08z07z07z07z07z07z07z\ 07z07z07z07z07z07z07z07z07z07z07z07z07z07z07z07z07\ x07x07x07x07x07x07x07x07x07x07x07x07x07x07x07v07v0\ 7v07v07v07v07v08v0Av0Bv0Dv0Dv0Fv0Fv0Hv0Ht0Jt0Jt0Kt\ 0Kt0Mt0Mt0Ot0Ot0Qt0Qt0St0St0Ut0Ut0Wq0Wq0Yq0Yq0`q0`\ q0aq0aq0cq0cq0eq0eq0gq07m } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END 20.0 PAR-FORMULA FILE==================================

1 0

Multifractal_1 par
by Lee H. Skinner 06 Jun '03

06 Jun '03

Here is a most unusual image - a zoom into Al's Mixdown. Bon_Voyage { ; Cruise Ship ; t= 3:06:40.91 on a P4 2Gh at ; 1600x1200 Image Copyright 2003 ; by Lee H. Skinner ver=2002 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=fractint.frm formulaname=multifractal_1 ismand=n function=exp/sin/exp/cosxx passes=1 center-mag=-0.08292638608437355/+0.15195752455824630/\ 3171.241/1/17.5000000000002487/6.87387646802761765e-0\ 13 params=-0.2724234748374889/0.09260841170049135/384.00\ 001/3072.4505/128.0256000000001/768.0256000000001/256\ .0256000000001/768.0307200000001/12298.7/2.16 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 symmetry=none periodicity=0 rseed=-2436 cyclerange=2/253 colors=000000U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6Zc7`c7aa7c_7\ eY<3>FcgHciJbl<3>S_v<3>civflvinvlqvotvsww<2>zzz<3>rwz\ ovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<4>XCAaB9fB7<3>zA0<13>S\ A1QA1NA1<3>D92<3>NN7PQ8SU9<3>`fDhrI<3>UnXRm_NlcJkgFfp\ Aaz<3>PJoSFlWAi_5fc0ce7_jFRoNIzb0<2>zz1zzC<2>zzz<3>jq\ dfo_blU<3>Mb8<3>LQ8KM8KJ8<2>I88H44G00<3>TA5WD6ZF7aI8e\ LAhMBiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz3<8>zY4zV5zS5<3>\ zE6wE6tD6<10>w8Px8Rx7S<3>z5_<3>f5Ma5IW4E<2>_4H<3>P3DN\ 2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>u1mt1n\ s1or2q<2>v2u<4>Z6`600enG } FRM:Multifractal_1 { ; Albrecht Niekamp 270503 ;only integers as first input, second input 5 digits to the right ;real(p2) factor1, border1 ;imag(p2) (-)bailout,input bas.frm1_2digits input bas.frm2_2digits ;real(p3) maxiter2, border2-in ;imag(p3) factor2, border2-out ;real(p4) maxiter3, border3-in ;imag(p4) factor3, border3-out ;real(p5) 1digit_shape only 5digits: shape,out1,out2,in1,in2 ; 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset (not shape) <0_no in/out1 ; optional basic frm2 digit1: 1_out1 2_out2 3_both +5_shape ; digit2: 1_in1 2_in2 3_both ;imag(p5) digit1 : many_mods multipl.shutoff 1_in/out1 2_in/out2 3_both ; digit2 :1_iter1reset 2_iter2reset 3_both +5_shape effect ; input2: Number of sides 2 digits (many_mods L.Allison) ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=d<0 if (da) d=-d endif ba=trunc(d) d=round((d-ba)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) mi2=trunc(d) b2=(d-mi2)*100000 ; d=imag(p3) fac2=trunc(d) ob2=(d-fac2)*100000 ; d=real(p4) mi3=trunc(d) b3=(d-mi3)*100000 ; d=imag(p4) fac3=trunc(d) ob3=(d-fac3)*100000 ; da=real(p5) t=da<0 if (t) da=-da endif start=2-t dd=trunc(da) da=round((da-dd)*100) if (dd<5) start=0 vb=(dd==3)+(dd==4) else d=trunc(dd/10000) vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) dd=dd-d*1000 or1=d>5 d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) d=trunc(dd/100) dd=dd-d*100 or2=d>5 d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) d=trunc(dd/10) dd=dd-d*10 inr1=d>5 d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) inr2=dd>5 dd=dd-inr2*5 v3=(dd==3) v4=(dd==4) d2=(dd==2)+(dd==4) endif ; d=trunc(da/10) da=da-10*d ab=d>=5 d=d-5*ab bb1=(d==1) bb2=(d==2) ab1=(da==1) ab2=(da==2) ; d=imag(p5) dd=trunc(d) mm=round((d-dd)*100) da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=dd>=5 dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) ; if (ismand) z=0 if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else c=p1 z=pixel endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn4(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z2=z*z z=z2*z2+(p6+u)*z2+c else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif bo=|z| If (wo) t=t+1 if (bo>b1) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else z=pixel c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2&&bo<ob2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3&&bo<ob3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif bo<=ba }

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32k
by bill ragette 06 Jun '03

06 Jun '03

help! can any one help me to get fractinct to use the new disk video mode supposedly 32k x 32k? the biggest option appears to be 2048 x 2048 i've tried fooling with makefcfg, but can't get that option to appear i have a brand new laptop with tons of memory thanks easy _________________________________________________________________ Protect your PC - get McAfee.com VirusScan Online http://clinic.mcafee.com/clinic/ibuy/campaign.asp?cid=3963

2 1

FOTD 05-06-03 (Low-Low Textures [5])
by Jim Muth 05 Jun '03

05 Jun '03

FOTD -- June 05, 2003 (Rating 5) Fractal visionaries and enthusiasts: In yesterday's FOTD I wrote that I had once found a midget in the Z^(1.04)+C fractal. The graph of Z^1.04 is nearly a straight line, and since linear functions do not make fractals, it should not be expected to create a fractal. But in today's image, we wander far from the principal image, and at the remote level 100 turns up the logarithmic spiral, Z^(1.04)+C produces an interesting parent fractal -- a sprawling oversized bay with much chaos on the southern shoreline and a smaller amount of chaos on the northern shoreline. Today's image is a scene in the chaos along the northern shore- line of the parent. I have named the image "Low-Low Textures", since the exponent of Z is so small and the image consists of nothing more than a simple texture, with the elements endlessly repeated at smaller scales. Yes, I once did find a real midget that did not vanish when the maxiter was increased in one of the Z^(1.04)+C Mandel fractals. I have no idea where I found it. There could be an infinity of midgets in today's image, in fact there certainly are, but in the range of 1.04 they are so tiny and buried so deeply, with no hint of symmetry around them, that they are virtually impossible to find. I rated today's image at a perfectly average 5. If I had actually found one of those impossible-to-find midgets, I might have rated the image a 6. The render time on my worn-out fractal machine is 1/100 second less than 6 minutes. It will be faster on more vigorous units. The fastest way of all to see the texture in today's image is to download the completed GIF image file from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The rain continued through the day here at Fractal Central on Wednesday. The temperature hovered at 57F 14C. The two fractal cats had no time at all in the great outdoors, and as a result, were unhappy cats. A treat of tuna in the evening made them less unhappy, but fish is no substitute for a trip to a great place. The feline duo ended the day in a mood of resignation. I finished yesterday's work on time, and hope to do the same today. The next fractal will arrive in 24 hours. Until then, take care, and hidden jewels are sometimes found in the lowly places. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Low-Low_Textures { ; time=0:05:59.99--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-6.563247556907927/+1.425281219594758/2\ 66.6667/1/-5/9.7999386383662568e-013 params=1.04/0\ /100/1000 float=y maxiter=600 inside=255 logmap=116 symmetry=none periodicity=10 colors=000LJWMKXMLYMNYNOZNP_NQ`OSaOTbOUbPVcPXdPYeQ\ ZfQ`gQagRbhRciRejSfkSglShlTjmTknTloUmpUoqUpqVqrVrs\ VttWuuWvvWwvVvuVuuVutVttVstVssVrsUqsUqrUprUprUoqUn\ qUnqTmpTlpTlpTkoTjoTjoTinTinShnSgmSgmSfmSelSelSdkR\ ckRckRbjRbjRajR`iR`iR_iQZhQZhQYhQXgQXgQWgQWfPVfPUf\ PUePTePSePSdPRdOSePRdPRdQRdQQdRQdRQdSPcSPcSPcTOcTO\ cUOcUNbVNbVNbVNbWMbWMbXMbXLaYLaYLaYKaZKaZKa_J`_J``\ J``J``I`aI`aI`bH_bH_cH_cG_cG_dG_dFZeFZeFZfEZfEZfEZ\ gEZgDYhDYhDYiCYiCYiCYjBXjBXkBXkAXlAXlAXj9TlAXmA`oB\ cpBgqCksCntDovCpuDquDruDsuDttDutDvtDwtExsEysEzsEzs\ EzrEzrEzrFzrFzrFzqFzqFzqFzqFzpGzpGzpGzpGzoGzoGzoGz\ oHznHznHznHznHznHzmHzmIzmIzmIzlIzlIzlIzlIzkJzkJzkJ\ zkJzjJzjJzjJzjKzjKziKziKziKziKzhKzhLzhLzhLzgLzgLzg\ LzgLziKzgLzfLzeLzdLzcLzbLzaMz`Mz_MzZMzYMzXMzWNzVNz\ UNzTNzRNzQNzPNzOOzNOzMOzLOzKOzJOzIPzHPzGPzFPzEPzI7\ zJ9zJAzJBzKDzKEzKFzLGzLIz } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END 20.0 PAR-FORMULA FILE==================================

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FOTD 04-06-03 (All Cracked-up [7])
by JimMuth＠aol.com 04 Jun '03

04 Jun '03

FOTD -- June 04, 2003 (Rating 7) Fractal visionaries and enthusiasts: I have named today's unusually somber excursion into the land of fractal discontinuity "All Cracked-up", though it really gives no impression of being unusually discontinuous. The outstanding feature is the preponderance of deep blues, with only a few spots of brilliant relief from the overall depressed mood. (Maybe it's mimicking the fractal cats.) In keeping with the unintentional theme of the month, today's image is once again part of one of the infinity of fractals created by the simple formula Z^(1.5)+C. This time it is the fractal found 12 turns up the complex logarithmic spiral, which itself is a total abstraction. In low-order fractals such as today's, as the exponent of Z drops ever farther below the value of 2, the midgets become ever more difficult to find. When the exponent is 1.5, the midgets are rather difficult to track down, though it is still reason- ably simple to do. In fact, the task of finding midgets is doable down to an exponent of 1.2. Below that value, finding them is a matter of luck. The lowest-order midget I have yet found is one with an exponent of something like 1.04. In this range, midgets are nothing more than irregular, circular holes, with no bays and no organized patterns surrounding them, though the parent fractals are filled with large fields of interesting and discontinuous chaos. Today's image has been rated by me at a 7. Actually, the rating of 7 is true only in a dimly-lit room. In bright light it rates only a 5 or 6. The render-time from the attached parameter file is a reasonable 6 minutes. By downloading the completed GIF image from one of the FOTD web sites, the time can be made even more reasonable. The FOTD web sites can be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The rains set in on schedule Tuesday afternoon here at Fractal Central. The temperature reached 63F 17C. The cats' moods deteriorated as expected, and the customary treat of tuna only partially restored their good spirits. The rain, which is still falling this morning, will likely continue intermittently into tonight. I feel sorry for the sulky duo. I've got my own problems to sulk about. Customers who want more material on a single page than can possibly fit there are a real nuisance. But I'll work it out. Until next cracked FOTD, take care, and where do fractals end? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ All_Cracked-up { ; time=0:06:44.25--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=+0.69857471108285760/-0.230797030040254\ 00/1.203615e+009/1/42.5/-6.40805482036294061e-006 params=1.5/0/12/0 float=y maxiter=1600 inside=0 logmap=120 periodicity=10 colors=00049F48Q47L47G03C34G65J96NC6QE7TH8PK8_N9cC\ AfJAaOJaLKbIKcFKdCKe8Kf4Hg0Ig3Lh6Nj9OmCQpESsHUvKWy\ NYzQ`zSczZCidEZpGPkOMzWJmcGzrDbXTSJhH6wG4pF3jF2dE1\ ZE0TF3RF6QG8PGBOHENHGMIKLIPJJUIJZHKcGKhFLmELmDLmCE\ mH7hM0cQ5ZW9U`EPfIQkMWqR`vVfzZkz`jzajzbjzcizdizeiy\ fixghvhhuihtjhsifoiekicgibci``i_XiYTiXPiWMmYNpZNt_\ Ow`OuYRtWUsTXqR_pPboMemKhlHkkFnjDqeFjaHdYIYTKSPMLL\ NFHYPDhY9sfgGZeI`dJabKbaMc`NdZOeYPfWRgVShUTiSUjRWk\ PXlOYmNZnMXkLVhKTeJRbJQ_KUYLXXM`WNcVOgUPjSQnRRqQSu\ PSxOAanDYkGViJSgMPePLbSI`VFZYCXZGZ_J``MaaPcbTdcWfd\ ZgeaifejghlhkminoiqpkoqmlsnitpfvrdwsayuZzvXzwUwwRs\ wPowMkwKhwHdxF`xCXxAUx7Qx5Mx2Ix0Fw2Gx4Gy6Gz7Gz9GzB\ GzCHzEHzGHzHHzJHzLHzMHzMIzMIzMJzMJzMKzMKzMLzMLzMLz\ MMzMMzMNzMNzMOzMOzMOzLNzLMzKMzKLzJKzJKzIJzIIzHIzHH\ zHHzGFzFEzEDzDCzCBzBAzA9zBDzCHzDLzEPzESzFWzWaz_azb\ azRpzFzzExzDszCnzBizBdzA_ } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END 20.0 PAR-FORMULA FILE==================================

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Multifractal_1
by Albrecht.Niekamp＠t-online.de 04 Jun '03

04 Jun '03

Hi, summer in the city and lots of ways to have fun, but nevertheless I found a basic image which is unique sofar. I succeeded to use the many_mods frm as inside for the hybrid julia, which has no inside. The result is a complete mix, even the basic structure. I think, this is fascinating. Fractal greetings, Al. -----------------------------start-par----------------------------------- Mixdown { ; Time 0.39.12.83 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal_1 ismand=n function=exp/sin/exp/cosxx passes=t center-mag=-0.0315457/2.22045e-016/0.9303941 params=-0.2724234748374889/0.09260841170049135/384.00001/3072.4505/128.0\ 256000000001/768.0256000000001/256.0256000000001/768.0307200000001/12298\ .7/2.16 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<24\ >oiQqjRslS<3>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3\ >000<25>iiijjjlll<3>sss<26>999 } --------------------------------start-frm----------------------------------- FRM:Multifractal_1 { ; Albrecht Niekamp 270503 ;only integers as first input, second input 5 digits to the right ;real(p2) factor1, border1 ;imag(p2) (-)bailout,input bas.frm1_2digits input bas.frm2_2digits ;real(p3) maxiter2, border2-in ;imag(p3) factor2, border2-out ;real(p4) maxiter3, border3-in ;imag(p4) factor3, border3-out ;real(p5) 1digit_shape only 5digits: shape,out1,out2,in1,in2 ; 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset (not shape) <0_no in/out1 ; optional basic frm2 digit1: 1_out1 2_out2 3_both +5_shape ; digit2: 1_in1 2_in2 3_both ;imag(p5) digit1 : many_mods multipl.shutoff 1_in/out1 2_in/out2 3_both ; digit2 :1_iter1reset 2_iter2reset 3_both +5_shape effect ; input2: Number of sides 2 digits (many_mods L.Allison) ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=d<0 if (da) d=-d endif ba=trunc(d) d=round((d-ba)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) mi2=trunc(d) b2=(d-mi2)*100000 ; d=imag(p3) fac2=trunc(d) ob2=(d-fac2)*100000 ; d=real(p4) mi3=trunc(d) b3=(d-mi3)*100000 ; d=imag(p4) fac3=trunc(d) ob3=(d-fac3)*100000 ; da=real(p5) t=da<0 if (t) da=-da endif start=2-t dd=trunc(da) da=round((da-dd)*100) if (dd<5) start=0 vb=(dd==3)+(dd==4) else d=trunc(dd/10000) vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) dd=dd-d*1000 or1=d>5 d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) d=trunc(dd/100) dd=dd-d*100 or2=d>5 d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) d=trunc(dd/10) dd=dd-d*10 inr1=d>5 d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) inr2=dd>5 dd=dd-inr2*5 v3=(dd==3) v4=(dd==4) d2=(dd==2)+(dd==4) endif ; d=trunc(da/10) da=da-10*d ab=d>=5 d=d-5*ab bb1=(d==1) bb2=(d==2) ab1=(da==1) ab2=(da==2) ; d=imag(p5) dd=trunc(d) mm=round((d-dd)*100) da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=dd>=5 dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) ; if (ismand) z=0 if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else c=p1 z=pixel endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn4(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z2=z*z z=z2*z2+(p6+u)*z2+c else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif bo=|z| If (wo) t=t+1 if (bo>b1) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else z=pixel c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2&&bo<ob2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3&&bo<ob3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif bo<=ba } ---------------------------------------end-----------------------------

2 1

Re: [Fractint] test
by Jim Muth 04 Jun '03

04 Jun '03

At 04:52 PM 6/3/03 -0700, J. Wilson wrote: >Jim, > >This is one of your most outstanding tests. > >Congratulations. I enjoy simplicity! Jim M.

2 1

test
by Jim Muth 03 Jun '03

03 Jun '03

test...

2 1

FOTD 03-06-03 (Unity and a Half [6])
by Jim Muth 03 Jun '03

03 Jun '03

FOTD -- June 03, 2003 (Rating 6) Fractal visionaries and enthusiasts: We seem to be developing a theme for the month of June. I had no intention of having two 'theme' months in a row, but sometimes fractals have a will of their own, and a theme of midgets in the many Z^(1.5)+C fractals seems to be developing. Today's image is the third consecutive scene in the set of fractals created by the formula Z^(1.5)+C. As the lengthy real(p2) parameter shows, the parent fractal was found by the evolver feature. I could have rounded off this parameter to -46.7 with little change in the resulting image. Fractals with exponents in the X.5 range are the most prone to the type of discontinuities that fill today's image. Fractal discontinuities decrease in significance as the exponent nears integer values, and vanish entirely when the exponent is an integer. I normally use the <floor> function with the MandelbrotBC1 formula, but for a change, I used the <recip> function in today's image. In today's image, which lies in the most-discontinuous range of exponents, the attractive symmetrical patterns that surround midgets in the classic Mandelbrot set are totally absent. Today's half-midget is surrounded by a kind of star-burst with an obvious break in the upper part. This break totally destroys any pretense of symmetry, though it does make an interesting feature. To add more interest, I rendered the image with the outside set to < fmod > and the proximity set to 0.5. The other outside options also make interesting variations of the basic scene, and are worth checking. I named the image "Unity and a Half" as a description of the exponent. I could rate the final result at only a 6. The rating is held down by the coloring, which could have used a bit more work. At least, the render time of 6 minutes is reasonable. The download of the finished image file is even more reasonable. That download can be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Another perfect day here at Fractal Central on Monday produced perfect cats. The not-quite-dynamic duo spent the better part of the day in their porch chairs, watching the world, enjoying the temperature of 73F 23C, and remembering the days when they were actually dynamic. Today, unfortunately, is starting cloudy, with rain promised by afternoon. For me, it will be just another workday. Until next time and next fractal, take care, and sometimes fractals are not all they're cracked out to be. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Unity_and_a_Half { ; time=0:06:08.50--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=recip passes=1 center-mag=-0.73254313764763500/+0.180334958341697\ 00/4.605696e+007 params=1.5/0/-46.74114200262459/0 float=y maxiter=4200 inside=0 proximity=0.5 outside=fmod symmetry=none periodicity=10 colors=000CvNBnPBfRBZTASVAKXACZA5`WSZpnYokZnhZmeZl\ bZk_ZjX_iU_hR_gO_fL_eI_TFYHCXMIYQNYVSYZXYbaYgfYkkY\ opYkk`gfccae_XhXSjTNmPIpLDrH8uE4wF6rF7mG9hGAcO8TV6\ Ia47WGFQSMKcUEo`9zgBxcCv`DtYErVGpSHnPIlMJjJKiGPlJU\ nMZpPcrShtVmvYks_ipagmcfjedggbdi`ak_ZmYWoWTqUQsTNu\ RPrPQoOSmMTjLUhJWeIXcGY`E_YD`WBaTAcR8dO7eMBcOEaPI`\ RLZSOYTNTRMPPWnaSoYOpVJqRFrNBsK7tG3tD5qE6nF8lG9iHB\ gICdJEaKF_KHXLIVMKSNLPONNPOKQPIQY9Kf1Fg7DgCCgIBhNA\ hT9hY8ic7ih6im5ciAYfFScJN`OHYTBVX5Sa0Pe3Of6Og9OhBO\ iEOjHOkJOkMOlPOmROnUOoXOpZOp_Kl_Hh_Dd`A``6X`3T`0Qb\ 2Td3Ve4Xg6_h7aj8ckAfmBhoCjpEmrFosGquItvJvxKxyLzwOy\ vQxuSwtVvsXurZtqaspcroeqnhpmjollnkomjqlislngkrWkUg\ W6sGBcSGOcL8nODmQHlTMkVRjYWi__iadhdhgfmfiqekudiwib\ vkbti_odWj_TfVQaQMXLJTGFOBCJ69F1BE2CE3ED3FD4HC4IC5\ JB5LB6MA7OA7P98R98S89T89SBBSDCSGESIFSKHRNIRPKRRLRU\ MRWOQZPQ`RQbSQeUQgVQiWJpR } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END 20.0 PAR-FORMULA FILE==================================

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FOTD 03-06-03 (Unity and a Half [6])
by Jim Muth 03 Jun '03

03 Jun '03

FOTD -- June 03, 2003 (Rating 6) Fractal visionaries and enthusiasts: We seem to be developing a theme for the month of June. I had no intention of having two 'theme' months in a row, but sometimes fractals have a will of their own, and a theme of midgets in the many Z^(1.5)+C fractals seems to be developing. Today's image is the third consecutive scene in the set of fractals created by the formula Z^(1.5)+C. As the lengthy real(p2) parameter shows, the parent fractal was found by the evolver feature. I could have rounded off this parameter to -46.7 with little change in the resulting image. Fractals with exponents in the X.5 range are the most prone to the type of discontinuities that fill today's image. Fractal discontinuities decrease in significance as the exponent nears integer values, and vanish entirely when the exponent is an integer. I normally use the <floor> function with the MandelbrotBC1 formula, but for a change, I used the <recip> function in today's image. In today's image, which lies in the most-discontinuous range of exponents, the attractive symmetrical patterns that surround midgets in the classic Mandelbrot set are totally absent. Today's half-midget is surrounded by a kind of star-burst with an obvious break in the upper part. This break totally destroys any pretense of symmetry, though it does make an interesting feature. To add more interest, I rendered the image with the outside set to < fmod > and the proximity set to 0.5. The other outside options also make interesting variations of the basic scene, and are worth checking. I named the image "Unity and a Half" as a description of the exponent. I could rate the final result at only a 6. The rating is held down by the coloring, which could have used a bit more work. At least, the render time of 6 minutes is reasonable. The download of the finished image file is even more reasonable. That download can be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Another perfect day here at Fractal Central on Monday produced perfect cats. The not-quite-dynamic duo spent the better part of the day in their porch chairs, watching the world, enjoying the temperature of 73F 23C, and remembering the days when they were actually dynamic. Today, unfortunately, is starting cloudy, with rain promised by afternoon. For me, it will be just another workday. Until next time and next fractal, take care, and sometimes fractals are not all they're cracked out to be. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Unity_and_a_Half { ; time=0:06:08.50--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=recip passes=1 center-mag=-0.73254313764763500/+0.180334958341697\ 00/4.605696e+007 params=1.5/0/-46.74114200262459/0 float=y maxiter=4200 inside=0 proximity=0.5 outside=fmod symmetry=none periodicity=10 colors=000CvNBnPBfRBZTASVAKXACZA5`WSZpnYokZnhZmeZl\ bZk_ZjX_iU_hR_gO_fL_eI_TFYHCXMIYQNYVSYZXYbaYgfYkkY\ opYkk`gfccae_XhXSjTNmPIpLDrH8uE4wF6rF7mG9hGAcO8TV6\ Ia47WGFQSMKcUEo`9zgBxcCv`DtYErVGpSHnPIlMJjJKiGPlJU\ nMZpPcrShtVmvYks_ipagmcfjedggbdi`ak_ZmYWoWTqUQsTNu\ RPrPQoOSmMTjLUhJWeIXcGY`E_YD`WBaTAcR8dO7eMBcOEaPI`\ RLZSOYTNTRMPPWnaSoYOpVJqRFrNBsK7tG3tD5qE6nF8lG9iHB\ gICdJEaKF_KHXLIVMKSNLPONNPOKQPIQY9Kf1Fg7DgCCgIBhNA\ hT9hY8ic7ih6im5ciAYfFScJN`OHYTBVX5Sa0Pe3Of6Og9OhBO\ iEOjHOkJOkMOlPOmROnUOoXOpZOp_Kl_Hh_Dd`A``6X`3T`0Qb\ 2Td3Ve4Xg6_h7aj8ckAfmBhoCjpEmrFosGquItvJvxKxyLzwOy\ vQxuSwtVvsXurZtqaspcroeqnhpmjollnkomjqlislngkrWkUg\ W6sGBcSGOcL8nODmQHlTMkVRjYWi__iadhdhgfmfiqekudiwib\ vkbti_odWj_TfVQaQMXLJTGFOBCJ69F1BE2CE3ED3FD4HC4IC5\ JB5LB6MA7OA7P98R98S89T89SBBSDCSGESIFSKHRNIRPKRRLRU\ MRWOQZPQ`RQbSQeUQgVQiWJpR } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] FOTD 02-06-03 (Burbles [7])
by Tim Wegner 03 Jun '03

03 Jun '03

Jim M wrote: > The FOTD for June 2 once again takes advantage of the multi- > valued nature of the complex log function. Jim, it was silly of me to request that someone make a fractal that illustrates the discontinuities of some of the transcendental functions like Log(). The examples are already legion in your work and an the work of many of the other fractal artists. Burbles has clear and obvious discontinuities. A fractal like the classic Mandelbrot has none, and cannot, because the underlying formula has no discontinuities. Tim

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FOTD 02-06-03 (Burbles [7])
by Jim Muth 02 Jun '03

02 Jun '03

FOTD -- June 02, 2003 (Rating 7) Fractal visionaries and enthusiasts: The FOTD for June 2 once again takes advantage of the multi- valued nature of the complex log function. The iterated expres- sion is a very simple Z^(1.5)+C. The trick in the MandelbrotBC1 formula is that an unlimited number of different images can be produced by the expression Z^(1.5), depending on which of the infinity of returned log values are chosen. The real(p2) parameter of the formula makes the choice. Today's image is part of the particular Z^(1.5) fractal that results when the real(p2) parameter of the MandelbrotBC1 formula is set to -31. The amorphous thing at the center is a midget of order 1.5. I have no idea what the jagged-edged colored disks surrounding the midget are. I have never seen anything quite like them. I have named the picture "Burbles". Those disks reminds me of something bubbling. The rating of a 7 seems correct for the image, which has more math interest than artistic worth. To see these truly unique fractal burbles, run the attached parameter file and wait 5 minutes, or download the finished GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Sunday started blustery and chilly here at Fractal Central, but by afternoon, the sun appeared, the wind slacked off, and the temperature rose to 66F 19C. The cats had a good day. This morning is starting much better. The cats will likely have another good day. For me, it's several hours work before my day will be good. Until next time, take care, and keep blowing those burbles. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Burbles { ; time=0:05:06.76--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=+0.72523926124837650/+0.172183551614105\ 20/488923/1/-62.5/9.1405363139562823e-010 params=1.5/0/-31/0 float=y maxiter=12000 inside=0 logmap=105 symmetry=none periodicity=10 colors=000GstKptNmuQkuThvXev_cwb`weYxiWxlTyoQyrOyo\ NvmNskMpiMmgMjeLgcLdaLa_KZYKWWJTUJQSJNQIKOIHMIEOJG\ QJISJJUJLVJMXJOZJQ`KRbKTcKUeKWgKYiKZkK`lKajRdhYgfd\ jdkmbrp`xsYvrWtrUsqRqqPppNnpKmoIkoGjnDhnBgm9em6dl4\ bl2al3bk3cj3di3ei4fh4gg4hf4hf5ie5jd5kc5lc6mb6na6o`\ 6o`5la5ia5fa5ca5`a5Yb5Vb5Sb5Pb5Mb9PcDSdGVeKYfN`gRc\ hVfiYijalkdolhrmlunoxoszpvzpozahyNaw9aw9aw9aw9aw9b\ vAbuBbuBctCctDcsDcsEdrFdrFdqGdqHepHepIepIeoJeoJfnK\ fnLfmLfmMglNgkNgkOgjPhjPhiQhiQhhRihSigSigTifUjfUje\ VjeWjdWkdXkcYkcYkbZla_la_l``m`am_am_bmZcnZcnYdnYen\ XeoXfoWfoWgoVhpVhpUipUjpTjqSkqSlqRlqRmrQnrQnrPorPp\ sOpsOqsNrsNrtMstMttLttLuuKvuKvuJwuJwsJwqKwoLwmMwkN\ wiOwgPweQweRweSwfTwfTwgSwgSwgSwgSuhRwiRwiRwjQwjQwk\ QwkQwkPwlPwlPwmOwmOwnOwnNwnNwoNwoNwpMwpMwqMwqLwrLw\ rLwrLwsKwsKwtKwtJwuJwuJwvJxvJywJzwJzxJzxJzyJzyJzzJ\ zzJzzJzzJzzJzzJzzJzzJzzJz } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END 20.0 PAR-FORMULA FILE==================================

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FOTD 01-06-03 (Curlers [5])
by Jim Muth 01 Jun '03

01 Jun '03

FOTD -- June 01, 2003 (Rating 5) Fractal visionaries and enthusiasts: We've been talking about multi-valued functions a lot lately, so here's a formula and an image that takes advantage of multiple values. It's not a new formula; I have posted many FOTD images created by it in the past. But it gives an example that good things can sometimes come from fractured fractals. The formula being iterated is Z^(1.06)+C, a formula that normally would produce nothing but a tiny featureless dot in the center of the screen. (Change the real (p2) parameter to pi to see this dot.) But thanks to those multiple values and today's formula, which takes advantage of them, the tiny dot has been transformed into an immense cigar with many fields of chaos around its edges. Today's scene is a blow-up of the edge of one of those fields of chaos. I have named the image "Curlers" because of the many loops that fill it. Not really impressed with the image, I have rated it at only a 5. The render time of 1/2 hour is almost entirely expended on the top inch or so of the image, so don't be concerned when nothing much happens for a while. Those who prefer not to wait the 1/2 hour can download the finished image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Rain fell off and on all day Saturday here at Fractal Central, while the temperature reached 73F 23C. A thunder-shower at 6pm climaxed the day's events as well as the cats' dis-satisfaction. Needless to say, a good treat of tuna was needed. Today is starting cloudy, windy and chilly, with occasional bursts of light rain -- not a good sign for fractal cats. For me, it's a sign I might not be able to trim the grass, but may have to go along on a shopping trip. Until next time, take care, and don't get broken up over fractured fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Curlers { ; time=0:38:53.19--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-6.07363/12.6745/0.4719481/1/72.5/-1.23\ 3735336114705e-014 params=1.06/0/121.2/3000 float=y maxiter=4200 inside=0 symmetry=none periodicity=10 colors=0007EXCCZHB`M9bR7dW6f`4hd3je7feAceE`eHYfLVf\ OSfSPfVLfZIgaFgeCgh9gl6go3dl5bi6`f8Zc9W`BUYCSVEQSF\ NPHLMIJJKHGLFDMHHPJKSLNVMQXOT_QWbRZdTagVdjWglXgmYf\ mxSuxRvsSsoSpjTmfTjaUhYUeTVbPV_KWXGWVFYQF_ME`IEbDD\ c9De5Df1Fc5Ga9H_DIXHJVLKTPLRTMOXNM`OKdPHhQFlRDpSBs\ PAnM9iJ8dH7_E6VB5Q94L63G32B116D3NP5c`7tZ8qY9oXAmWB\ kVCiUDgTEeSFcRGaQH_PIYOJWNJUPMTQPSSRSTURUWRWZQX`QZ\ cP_eP`hObjOcmNdoNbmMalL`jKZiJYhIXfHWeGUcFTbESaDR_C\ PZBOXANW9MV9OXBPZDQ`ERaGScIUeJVgLWhNXjOYlQZmR_kP`i\ OagNbeMccLdaKd_JeZLeYNfXPfWRgVThUVhTXiSZiR`jQbkPdk\ OflNhlMj`VqQcxSerUflWgfYi`ZjW`kQbmKdnEeo9`n8Wn7Sn6\ Nn5In4En39n24n10n09j4Ig8QdCOeAMf9Kg7Ig6Gh5Ei3Cj2Bj\ 1bl6hn9moCrqFwrItnJrkKphKmdLkaLiZMfVNdSNbPO_LOYIPW\ FQTBQR8RP5RKGPFRNBaL6lJ2wI4wJ6wJ7wK9wKBwKCwLEwLFwL\ EvNEuOEtPDsRDrSDqTCpVCoWCnXBmZBl_Bk`AjbAicAhdAheDk\ cGmbJoaMq_PsZSuYVwX4IT2GU } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END 20.0 PAR-FORMULA FILE==================================

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FOTD 31-05-03 (The Final Fling [8])
by Jim Muth 31 May '03

31 May '03

FOTD -- May 31, 2003 (Rating 8) Fractal visionaries and enthusiasts: I am still watching with interest the debate about the Fractint bug that might or might not be a bug. Being no expert in complex functions and how they are calculated by computer programs, I will offer no opinion. My feeling is that, if the only effect of the 'bug' is to cause the program to draw reversed images with certain formulae, it should be left as is, because correcting it could cause more problems than it solves. It is a different story if other so far unrecognized more serious problems are being caused by the 'bug'. Today's image is the last trip into the mayparent fractal. It is an 8-rated image that I have named "The Final Fling". Starting with tomorrow's FOTD we'll have images from a new parent fractal every day. But this is not necessarily a policy fixed in stone. If I come upon another fractal as rich as the mayparent, I may spend another month or so exploring it. The scene illustrated in today's image lies near the tip of the filament extending south from the southern bud of the Mandeloid feature of the parent. It is a scene of unusually smoothly curving, twisting elements. Actually, most of the curving lines are due to the coloring, as a new color palette will show. The render time of 16 minutes makes the parameter file a slow one. But take heart, the completed GIF image is available at the two FOTD web sites: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Friday turned out to be the most pleasant day of the month here at Fractal Central, and the fractal duo enjoyed it to the utmost. The warm sun and temperature of 79F 26C brought out the very best in both of them. They spent the entire afternoon on the porch, behaving like angels in disguise. But today is again starting threatening, with heavy rain forecast. I hope the duo's angelic ways can withstand the challenge. My challenge is to finish the little bit of work and search for a new parent fractal. Until next time, take care, and may only good fractals come your way. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Final_Fling { ; time=0:16:34.70--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=-0.51776427347768130/-3.488176830655431\ 00/78974.62/1/135/-3.99629947189783508e-010 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=1200 inside=0 periodicity=10 colors=000o2PoAPp0Pq3Oq5Nr7Mr9LsBKsDJtFIuHHvJGwLFx\ NEyPDzSCzUBzWAzY9z_8za7zc6ze5zg4zi3zk2zm2yl6xl9xlD\ wkGwkKvkNujRujUtjYti`sidsignhhjhhfhibhiZhjVhjXggYf\ dZfa_eZ`dWbdTccQdbNebKfaHh`Ei`Bj_8kZ5mY1lZ2kZ2jZ3i\ _3h_4g_4f_5e`5d`5c`6ba6aa7`a7_a8Zb8Zb8Yb9Xc9WcAVcA\ UcBTdBSdCRdCQeCPeDOeDNeEMfELfFKfFJhEKfFKeFKdFKcGKb\ GKaGK`HK_HKZHKYHKXIKWIKUIKTJKSJKRJKQJKPKKOKKNKKMLK\ LLKKLIIKKJLLKLNKMOLMQMNRMNTNOUOOWOPXPPZPQ_QQaRRbRR\ dSSeTSgTThUTjUUkVUmWVnWVpXWqYWsYXtZXuZXs`Zra_qb`od\ anebmfclgdjieijfhkgglhenidojcpkarl`sm_tnZuoXwpWxqV\ yrUzsVxnWwjWvfXuaYtYYsUZqP_pL_oH`nCam8al4eqMivbjsd\ kpekmflkglhhmejmckn`loYmoWnpTppQqqOrqLsrItrGuqHsqI\ rpJqpKooLnoMmnNknOjmPimQglRflSelTckUbkVajW_jXZiYYi\ ZWh_Vh`UgaSgbRgcQebPdaPb`Oa`O__NZZNXYMWYMVXMTWLSWL\ QVKPUKNTJMTJKSIJRIMONGQHFPHDOGCOGANF9PF8MFCPUGRRKT\ WOVaSXfWUl_PhaKceFZiAUm5P } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

3 2

Multifractal_1
by Albrecht.Niekamp＠t-online.de 31 May '03

31 May '03

Hi, here is another zoom into Janusbird3, for me itïs one of my best, and a repeat of the "gallery" and the "basket"image, as there was a bug (own production!) in the first version. -------------------------start-par----------------------------------------- Chinese_fantasy { ; Time 1.57.37.86 ; Albrecht Niekamp May, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult240.frm formulaname=multifractal_1 ismand=y function=exp/exp/exp/exp passes=t center-mag=-0.65303667287728500/-0.09362771308668312/265.3586/1/15.00000\ 00000004601/-1.64999958141009984e-013 params=-0.2724234748374889/0.09260841170049135/384.00001/2048.4505/768.0\ 256000000001/768.0256000000001/1025.0256/1536.0256/12284.5/11.16 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200pppqqqsss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08\ A068<2>022000211<22>keOmgPoiQqjRslSunT<2>zsX<25>CB7A96875<3>000400<23>o0\ 0q00s00<3>z00<25>C00A00800<3>000<28>nnn } Gallery { ; Time 1.50.48.79 ; Albrecht Niekamp May, 03 ; Version 2002 Patchlevel 5 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=220503a.par formulaname=multifractal_1 ismand=y function=exp/exp/exp/exp passes=t center-mag=0.981945/-0.000647375/18.72659/1/-90/-1.23373533611470521e-01\ 4 params=-0.1738944669942329/-0.3000579851680044/384.00004/2048.1133/768.0\ 0008/768.00128/1024.00256/1536.01024/18166.01/0.32 float=y maxiter=2048 inside=maxiter outside=tdis logmap=yes periodicity=0 rseed=-2436 colors=200BBB<3>444222000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<22\ >keOmgPoiQqjRslSunT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C0\ 0A00800<3>000<23>eeegggiiijjjlllnnn<2>sss<24>DDD } --------------------------------start-frm----------------------------------- FRM:Multifractal_1 { ; Albrecht Niekamp 270503 ;only integers as first input, second input 5 digits to the right ;real(p2) factor1, border1 ;imag(p2) (-)bailout,input bas.frm1_2digits input bas.frm2_2digits ;real(p3) maxiter2, border2-in ;imag(p3) factor2, border2-out ;real(p4) maxiter3, border3-in ;imag(p4) factor3, border3-out ;real(p5) 1digit_shape only 5digits: shape,out1,out2,in1,in2 ; 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset (not shape) <0_no in/out1 ; optional basic frm2 digit1: 1_out1 2_out2 3_both +5_shape ; digit2: 1_in1 2_in2 3_both ;imag(p5) digit1 : many_mods multipl.shutoff 1_in/out1 2_in/out2 3_both ; digit2 :1_iter1reset 2_iter2reset 3_both +5_shape effect ; input2: Number of sides 2 digits (many_mods L.Allison) ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=d<0 if (da) d=-d endif ba=trunc(d) d=round((d-ba)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) mi2=trunc(d) b2=(d-mi2)*100000 ; d=imag(p3) fac2=trunc(d) ob2=(d-fac2)*100000 ; d=real(p4) mi3=trunc(d) b3=(d-mi3)*100000 ; d=imag(p4) fac3=trunc(d) ob3=(d-fac3)*100000 ; da=real(p5) t=da<0 if (t) da=-da endif start=2-t dd=trunc(da) da=round((da-dd)*100) if (dd<5) start=0 vb=(dd==3)+(dd==4) else d=trunc(dd/10000) vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) dd=dd-d*1000 or1=d>5 d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) d=trunc(dd/100) dd=dd-d*100 or2=d>5 d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) d=trunc(dd/10) dd=dd-d*10 inr1=d>5 d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) inr2=dd>5 dd=dd-inr2*5 v3=(dd==3) v4=(dd==4) d2=(dd==2)+(dd==4) endif ; d=trunc(da/10) da=da-10*d ab=d>=5 d=d-5*ab bb1=(d==1) bb2=(d==2) ab1=(da==1) ab2=(da==2) ; d=imag(p5) dd=trunc(d) mm=round((d-dd)*100) da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=dd>=5 dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) ; if (ismand) z=0 if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else c=p1 z=pixel endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn4(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z2=z*z z=z2*z2+(p6+u)*z2+c else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif bo=|z| If (wo) t=t+1 if (bo>b1) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else z=pixel c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2&&bo<ob2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3&&bo<ob3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif bo<=ba } ---------------------------------------end-----------------------------

2 2

It's all a bit complex, isn't it!
by Jim White 31 May '03

31 May '03

Tim Wegner wrote: > 1. The "bug" is not a bug!!! > 2. Fractint is cleared of the unjust accusation! The verdict: INNOCENT! An interesting and entertaining analysis, Tim! But hang on just one minute!!!! We agree that log(x+iy) = (1/2)log(x^2 + y^2) + i(atan2(y,x) + 2kPi) (I'll use "atan2(y,x)" because it's less ambiguous) It's standard practice in mathematical libraries that when a single-valued result is required, the "principal value" is returned, which in this case is to set k=0. (aka "2*PI normalisation"). So for everyday single-valued use, the formula becomes log(x+iy) = (1/2)log(x^2 + y^2) + i * atan2(y,x) > log(-5.0, 0.0) > The assembler log function gives: > (1.6094379124341,-PI) > Coding by hand in C gives: > (1.6094379124341, PI) > BOTH ANSWERS ARE RIGHT!!! The imaginary parts differ by 2*PI, which is acceptable. I'm sorry, I can't agree! atan2(0,-5) is (by ANSI definition), +PI. A value of -PI is of course "correct", but not the "principal value". It corresponds to selecting k = -1 in the log function, a strange choice indeed. And I've plotted log(-5) with (in both int and float modes) in Fractint using that plotting formula, and it gives the right answer in both cases! > Jim's fatal mistake was when he assumed that, given > a = 1, b = -5, g = 1, h = -1 > that (-a*b*g*h) is -5. Yes, it's very close to -5 In 30 years of programming, I've yet to come across a system that does not produce EXACTLY -5 from these values. So, IMHO, Fracint does have a problem, and as far as I can see, the POWER operator is still under suspicion. Ball's in your court, Tim! Cheers Jim White __________________________________________________ Yahoo! Plus - For a better Internet experience http://uk.promotions.yahoo.com/yplus/yoffer.html

3 3

Re: [Fractint] It's all a bit complex, isn't it!
by Jim Muth 30 May '03

30 May '03

At 06:34 PM 5/30/03 +0100, Jim White wrote: >It's standard practice in mathematical libraries that >when a single-valued result is required, the >"principal value" is returned, which in this case is >set to k=0. I assume this means that the MandelbrotMix4 images are in fact 'correct' as they now stand, but if the 'maybe bug' were fixed, the formula would draw images that are "more correct" (whatever that means). Jim M.

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FOTD 30-05-03 (The Dried-Out Lake [6])
by Jim Muth 30 May '03

30 May '03

FOTD -- May 30, 2003 (Rating 6) Fractal visionaries and enthusiasts: I should have realized it. I see from the Fractint list that the 'bug' in the program is not a bug at all, but actually a result of the multi-valued nature of the complex log function. It turns out that the mirror images that result from switching the (p1) and (p2) parameters in the MandelbrotMix formulas are both correct. In fact, an infinity of other 'correct' images could be drawn from the same basic formula. I have a formula in my collection named MandelbrotBC1, (BC stands for branch cuts), which takes advantage of the multi- valued complex log function. I have posted quite a few FOTD images created by this formula. I also have a formula hidden somewhere which raises a complex exponent of Z to a power, then extracts the same root. Because of the two multi-valued steps, the final image has little resemblance to the starting image. Today's image is what I call a 'dry-lake', a term invented by Lee Skinner, who first drew my attention to these features. The symmetry is there, but the midget at the center is not. What has happened is that the slice of today's image has passed very close to a midget, but has not cut through it. By changing the (p4) parameter, the slice could be moved until it cuts the now-invisible midget. This is the reason I added the extra para- meter. But finding the skimmed midget is not as easy as it seems. The C value changes along with the Z value, and, when the (p4) parameter is changed, the center of the dry lake must be chased as it moves off the screen. Today's image lies in the north branch of the East Valley area of the prominent Mandeloid feature located to the northeast of the 'fan' of the parent fractal. The elements in this area are very skeletal, consisting largely of inside points, so to produce a good picture, I set the inside to < atan > and let the iterations add up. The resulting image rates a 6 -- not bad, but with lots of room for improvement. The render time of 48 minutes could certainly be improved, and this improvement may be gained by visiting Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> and downloading the image from there. The forecast rain never appeared here at Fractal Central on Thursday, and the temperature reached 75F 24C. As a result, the dynamic duo had an exceptional day in the outdoors. They even managed to stay out of trouble, (which isn't very difficult for near-13-year-old cats). Today is actually starting sunny, with a forecast of sun all day. It should be a good day for the cats. For me, it will be a good day when the work is finished. And in order to finish, I must start. So until next time, take care, and beware of multiple values. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Dried-Out_Lake { ; time=0:48:07.99--SF5 on a P200 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=allinone.frm formulaname=mandelbrotmix2 function=recip passes=1 center-mag=+1.28250208122812600/-3.009422644531135\ 00/4914106/1/95.0004599045420264/1.230095661228919\ 33e-005 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=1200 inside=atan periodicity=10 colors=000JTSMYXQc`TgcYmg`rlcvojjrp_uvPxzDzz1zz0zz\ 0yz3rz9lzFdzJ_uMclOgdPjXQoOTsGVv7Xz0Yz0_z0Sr0La3DM\ 766A007306704C03G01L00P00T00Y00a00f00j00g00f11d64c\ C7aGA`MD_SGYXJXaMVfPTlSSrVQvYPz`OzcQzfSziTzjVzmSxo\ QurPrsOovMlxLizJfzIczG`zF_zA`x7`s3`o0`j0`f0`a0`d0Y\ g0Vi1Sl6QoAOpDLsIIvMGxPDzTAzY7z`6zd3zi0zl0zo3zp7zs\ CzuFyxJvyOszSrzVfuSXmQMfOCYM1QJ0JI0IJ0GJ4FJ9DJDCJI\ CJMAJQ9JV7J_6Ja6Jc9DcC9dD3dG0dI0aO0_T6X_CVcISiOPoS\ MuYLycIziFzoDzsFzuGpvIdvJTxLIxY0j70IC0GG0GL4GP7GTC\ GYFG`JGdMGiQGmTGrYGv`GzdGzgGzdIzaJz_LzYMzVOzSPcQQy\ OScQQxJVxGXxDYvC_v9`v6av4au7Ys9VsASrDOrFLpGIoIFoLA\ mM7mO4lP1jS0jT0iV0iX0d_0aa0_c0Vf3Sg6PjALlDIoIFpLAs\ O7uS4xV1yYCzSLzMTzGczAlz4uz0zz0vx0pv0iu0cs0Xp0Qo0L\ m0Dl07i00g00f00d00g00i60jC0mG0oM0pS0sY0ua0vg0ym0zs\ 0zx1zz3zz3zz6zz9zzCzzFzzIyzLxzOvzQsyTrxXpu_osamrdl\ pgjoPmg6p`0sT3ua9FGCJLGPP } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Multifractal
by Albrecht.Niekamp＠t-online.de 29 May '03

29 May '03

Hi, i dont intend to push anyone "to extend the limits", but what good is a composition tool if it isïnt used as such? It would be sad, if the only reason is that the inputs are not clear. Also Iïm not an artist and definetly there is much more to it than I can explore. First some remarks about the basic structure as John suggested. The main loop consists of 3 parts, the iteration loop, the part defined by the variable "wo" and the part defined by the variable "start". The iteration loop checks if "VB"is set, which means one of the 2 hybrid frms is to be used, if "zero" one of the 2 basic frms is used. The "d3" variable checks if it is a Julia (1) or a mandel-type (0).In case of the hybrid frms it`s the hybrid Julia, otherwise many_mods. If "vb" is zero itïs one of the 2 basic frms, but as Julia. The default basic frm, just like the hybrid Julia gets more complexity by use of the warp-factor "u". The "ab" variable determins which one of the 2 basic frms is to be used. The "wo" part supplies the initial value to warp the basic shape if it is checked. When the border or maxiter values are reached, iteration restarts from zero but warped. The difference can easily be checked with the speed test image. The "start" variable determines if one or two in/out options are used. If zero, only the main loop and the "wo" part (if checked) is active. If "1", only in/out2 options are active. It is counted down from 2 to zero, so that finally, at high iteration, only the iteration loop is used. Regard the border and maxiter values as imaginary bailout points where the iteration switches to the next selected frm. The warpeffect like it says somehow bends the look of the next iteration part, how - depends on the type. The internal counter "t" of the previous part(s) is used for itïs calculation. It needs outside=tdis and a colourmap which supports "3d"looks. BUD2.map is my favorite as it supports "3d" in 3 basic colors. To create a new image from the scratch firstly you decide which basic frm (I call it shape) to use. There are 6 options, the 4 frms and the Julia variation of the 2 basic frms. Ismand has the precedence, so if frm3 (many_mods) is checked and Ismand is "no" the hybrid julia (4) is used. To start off you use the real(p5) 1digit input, 1 to 4. Set image(p5) to 5 if you want to warp it. Having done that you add the other 4 digits, in the following order: (shape), out1, out2, in1, in2. Of course the outside options are used also for the inside parts and vv, if the conditions are met. Now the explanation of the inputs in their order: P1 is the Julia seed, it is used for all julia variations and it is shared by the basic frm1. Get the values using the evolver or take them from any other image. Real (p2) factor1, is used for the shape-warpeffect. Set it to maxiter1 or higher. A good example is one third above. After the dot the border1 input. Select the value and divide it by 100000, a value of 1.234 appears as -.00001234. It is the same with the other secondary inputs, except where a number of digits is requested, see the text. If the shape is a basic mandel or Julia, any value between 1 and 4 makes sense, for the other ones itïs a matter of try and error and experience. Use low resolutions for that purpose. Image(p2) is maxiter1, select a relatively low value, maybe 256. The secondary input has 4 digits, the first 2 are used for frm1, the other 2 for frm2. The first one also accepts a negative input. A "-" will be applied to this one only. If you have found the julia seed, see what image you get and modify it with these inputs. Use the evolver, set max mutation f.e to 0.5 for frm1 and to 0.003 for frm2. Higher figures generate smaller shapes. Frm2 supplies a big variety of shapes, mirrored mandels or 2 mandels combined to one shape, it even can be quadratic. This one is used in todayïs image. Real(p3) is the general bailout, use a really high value if you want to fill those black holes, which are typical for many_mods.The second input is the "number of sides" created by many_mods; a high number generates smaller structures, f.e. 4 to 32. The format is the same as border1. This value is doubled if m_m is called as in/out option and again, if called twice. This leads to very high complexity, sometimes chaotic spots, so it can be shut off (-later). Image(p3) is factor 2, take a value higher then maxiter2, just like factor1. Border2 is fractional, same format as border1. For a basic mandel or Julia a value between 4 and 32 makes sense, of course all other values are possible. Modify this figure, so that nothing of the basic shape is covered, if it is a mandel (and you want that), 9.1 is a good example. Real(p4) is maxiter2, it makes sense to double the value of maxiter1 or any higher value. The second input, factor 3 is used for in/out2, any value well above maxiter 3, f.e. one third or double. Image(p4) is border3, this one is not fractional, any value below bailout. The second input, maxiter3 should be well below the general maxiter on the x-screen in order to leave enough iterations for in/out2. If you want to use the in-options exclusively set the border values higher then bailout, and vv the maxiter values higher then general maxiter. Real(p5): As explained use 1 digit only to create just the shape and add the other 4 digits later. Add 5 to each selection, except the shape, in order to reset it. Resetting generally adjusts the selected part to the screen instead of the surrounding, if itïs m_m, it creates circular shapes and helps avoid chaotic spots. If this value is negative in/out1 is shut off. The figures are as follows: 1_basic mandel, 2_basic julia, 3_many_mods, 4_hybrid Julia. The second input is optional and determines where the basic frm2 is used, regardless if itïs Julia or mandel. Type the number of the out-option you want to use it for and the number of the in-option, zero if none. Type 3 to use it on both. One digit only defines the out-option, add 5 to the first or second digit, to use frm2 as shape. Precedence has the primary real(p5) input, so these values must correspond to it, to be active. One example: 18212.71 (or 18212.26) uses frm2 as shape, out2 and in1. Out1 is m_m with a reset, out2 is basic julia2, in1 is basic mandel2,in2 is basic julia1. This may sound complicated, but you`ll manage after a couple of times. An earlier version of this formula was much heavier. Image(p5): Optional, 1 digit: "1" resets the iteration counter after the "wo" calculations, "2" after in/out1, "3" after both. This effects the calculation of the warp-factor. Add "5" or just type "5" to use the warpeffect on the shape. 2 digits: the first digit shuts off the m_m multiplication, "1" at the in/out1 switch, "2" at the in/out2 switch, "3" completely. Second input: Optional, used for the lake-effect variables. 6 digits, 2 digits for each one: Example 324151 means a frequency of 320, a level of 41% and an amplitude of 0.51. Any valid input activates the lake effect. The functions are used for the calculation of the warpeffect, if you use a different one, possibly the corresponding factor must be changed. For some Julias "sin" is a must. Fn1 is shared by m_m and the basic image, so if that is not warped, it is free to use. The m_m rendering changes dramatically. Fn2 is used for in/out1 fn3 is used for in/out2 Thatïs it. I hope itïs understandable and not too chaotic. Fractal greetings, Al. ----------------------------start-par------------------------------------- Easter_eggs { ; Time 0.29.47.49 ; Albrecht Niekamp May, 03 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/exp/exp passes=t center-mag=-0.464607/-4.44089e-016/0.5117907 params=-0.8940855128635518/0.8105868709372235/384.00001/256.1133/2048.00\ 008/768.0003400000001/768.01536/2560.01025/18934.5/5 float=y maxiter=3072 inside=maxiter outside=tdis logmap=7 periodicity=0 rseed=-2436 colors=200444222000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<24>oiQqj\ RslS<3>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<2\ 5>iiijjjlll<3>sss<25>BBB999777555 } Wonderland { ; Albrecht Niekamp May, 03 ; Time 1.09.00.09 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/exp/exp passes=t center-mag=-1.5922/0.155851/14.26617/1/95/1.31075705844807544e-014 params=-0.8940855128635518/0.8105868709372235/384.00001/256.1133/4094.00\ 016/768.0003400000001/768.0076800000001/256.01024/18937.52/5 float=y maxiter=3072 inside=maxiter outside=tdis logmap=7 periodicity=0 rseed=-2436 colors=200444222000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<24>oiQqj\ RslS<3>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<2\ 5>iiijjjlll<3>sss<25>BBB999777555 } -------------------------------start-frm----------------------------------- FRM:Multifractal {; Albrecht Niekamp 16.5.01 ;only integers as first input, second input 5 digits to the right ;real(p2) factor1,border1 ;imag(p2) (-)maxiter1,input bas.frm1_2digits input bas.frm2_2digits ;real(p3) bailout,hyb.mandel: number of sides (Many_mods L.Allison) ;imag(p3) factor2,border2 ;real(p4) maxiter2,factor3 ;imag(p4) border3,maxiter3 ;real(p5) 1digit_shape only 5digits: shape,out1,out2,in1,in2 ; 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset (not shape) <0_no in/out1 ; optional basic frm2: out-nbr 1digit in-nbr 1digit 3_both +5_shape ;imag(p5) 1digit : 1_iter1reset 2_iter2reset 3_both +5_shape effect ; 2digits : many_mods multipl.shutoff +10_in/out1 +20_in/out2 +30_both ; optional input2: frequency_2digits level_2digits amplitude_2digits ; d=real(p2) ;factor1 , border1 fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=d<0 ;p6 negative (frm1) if (da) d=-d endif mi1=trunc(d) ;maxiter1 d=round((d-mi1)*10000) p6=trunc(d/100)/10 ;init. value frm1 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ;init. value frm2 ; d=real(p3) ba=trunc(d) ;bailout mm=round((d-ba)*100000) ;m_mods nbr of sides ; d=imag(p3) fac2=trunc(d) ;factor2 b2=(d-fac2)*100000 ;border2 ; d=real(p4) mi2=trunc(d) ;maxiter2 fac3=round((d-mi2)*100000) ;factor3 ; d=imag(p4) b3=trunc(d) ;border3 mi3=round((d-b3)*100000) ;maxiter3 ; da=real(p5) t=da<0 ;in/out2 only if (t) da=-da endif start=2-t ;inout1+inout2: start=2 dd=trunc(da) if (dd<5) start=0 endif vb=(dd==3)+(dd==4) ;shape hybrid frm_1digit input da=round((da-dd)*100) d=trunc(dd/10000) vb=(d==3)+(d==4)+vb ;shape hybrid frm_5digits input dd=dd-d*10000 d=trunc(dd/1000) or1=d>5 ;reset out1 d=d-5*or1 vv1=(d==3) ;hybrid frm out1_mandel vv2=(d==4) ;hybrid frm out1_julia dd1=(d==2)+(d==4) ;julia out1 dd=dd-d*1000 d=trunc(dd/100) or2=d>5 ;reset out2 d=d-5*or2 vv3=(d==3) ;hybrid frm out2_mandel vv4=(d==4) ;hybrid frm out2_julia dd2=(d==2)+(d==4) ;julia out2 dd=dd-d*100 d=trunc(dd/10) inr1=d>5 ;reset in1 d=d-5*inr1 v1=(d==3) ;hybrid frm in1_mandel v2=(d==4) ;hybrid frm in1_julia d1=(d==2)+(d==4) ;julia in1 dd=dd-10*d d=trunc(dd) inr2=d>5 ;reset in2 d=d-5*inr2 v3=(d==3) ;hybrid frm in2_mandel v4=(d==4) ;hybrid frm in2_julia d2=(d==2)+(d==4) ;julia in2 d=trunc(da/10) da=da-10*d ab=d>=5 ;shape frm2 d=d-5*ab bb1=(d==1) ;frm2 out1 bb2=(d==2) ;frm2 out2 dd=da>=5 ;shape frm2_second digit da=da-5*dd ab=ab+dd ab1=(da==1) ;frm2 in1 ab2=(da==2) ;frm2 in2 ; d=imag(p5) dd=trunc(d) d=round((d-dd)*1000000) le=d>10000 ;lake effect on da=trunc(dd/10) so1=((da==1)+(da==3)==0) ;m_m multiplication off_in/out1 so2=((da==2)+(da==3)==0) ;m_m multiplication off_in/out2 dd=dd-10*da wo=dd>=5 ;shape warpeffect dd=dd-5*wo ir1=(dd==1)+(dd==3) ;iter reset in/out1 ir2=(dd==2)+(dd==3) ;iter reset in/out2 if (le) ;lake effect freq=round((trunc(d/10000))*10) ;frequency_lake effect by S.Gallet d=d-freq*1000 level=(trunc(d/100))/100 ;water level d=d-level*10000 ampl=d/100 ;amplitude of the wave u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) d3=2*q*t rs=2*bo*(dd+flip(1))*t z2=center+(-q-bo*dd-flip(bo))*t z=pixel-z2 d=imag(conj(d3)*z)/imag(conj(d3)*rs) if (d<=level) da=level-d z=z+2*da*(1+ampl*sin(freq*da^0.2))*rs endif z=z+z2 endif if (ismand) if (vb) ;many_mods c=0.4*log(sqr(pixel^mm)) z=z*le else c=z*le+pixel*(le==0) z=0 endif else ;julia c=p1 z=z*le+pixel*(le==0) endif t=0 d3=(ismand==0) u=d3 ;warpeffect initial value : if (vb) if (d3) ;julia z=(z*z-real(c))^(z*u+imag(c)) ;hybrid julia else z2=fn1(z)+c ;hybrid mandel L.Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;basic frm2 Pusk.s Istv.n elseif (d3) z2=z*z z=z2*z2+(p6+u)*z2+c ;basic frm1 as julia else z2=z*z ;basic frm1 Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif bo=|z| ;bailout value If (wo) ;shape warp effect t=t+1 if ((t<mi1)+(bo>b1)) u=2*(fn1(t/fac1)) ;warpeffect if (ismand) z=z*u if (vb) ;hybrid frm c=0.4*log(sqr(pixel^mm)) ;init m_m else c=z*le+pixel*(le==0) endif else z=z*le+pixel*(le==0) ;init julia c=p1*u endif wo=0 if (ir1) ;iter reset t=0 endif endif elseif (start) ;0_shape only t=t+1 if (start==2) ;in/out1 + in/out2 if (bo>b2) ;z > border2 ? u=2*(fn2(t/fac2)) rs=or1 ;reset ab=bb1 ;frm2 if (dd1) ;julia? if (rs) z=pixel endif c=p1*u vb=vv2 ;hybrid d3=vb ;julia else ;mandel d3=0 z=z*u c=z if (rs) ;reset z=0 endif vb=vv1 if (vb) if (so1) ;m_m multiplication mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ;m_m init endif start=1 endif elseif (t>mi2) ;counter > maxit2 u=2*(fn2(t/fac2)) ;warpeffect rs=inr1 ab=ab1 ;frm2 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) ;reset z=0 endif vb=v1 if (vb) if (so1) ;m_m multiplication mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3) ;start=1 z>border3 u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) ;start=1 counter>maxiter3 u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 ;mainloop only endif endif bo<=ba ;z<=bailout } ----------------------------end-------------------------------------------

4 16

FOTD 29-05-03 (All Inside Stuff [6])
by JimMuth＠aol.com 29 May '03

29 May '03

FOTD -- May 29, 2003 (Rating 6) Fractal visionaries and enthusiasts: I see on the Fractint list that the 'bug' in the program that has caused the MandelbrotMix4 formula to run incorrectly has been identified and can be fixed without too much effort. This obviously will have an impact on the upcoming FOTD-CD. Until now, I have been feeling a bit guilty about the unreason- able delay in releasing the FOTD-CD. Now however, it appears the delay will be a good thing, for it will enable me to release a disk that does not depend on a bug in the program to render the images correctly. Of course, this means a further delay in the release of the disk while any needed changes that might arise are being done, but after a delay of nearly a year, that will be of little consequence. Meanwhile, whenever I find the time, I am still working on the task of identifying and renaming the images on the disk, so that they can be matched with their corresponding discussions without confusion. And on a non-fractal topic, I'm now receiving spam snail mail. Yesterday, I received in the snail mail an air-mail letter from Zimbabwe, which is a country in the southern part of Africa. The enclosed letter was a print-out of the same fraudulent offer that I have received so many times in the e-mail. The letter tells me that a probably fictional Mr. Twala has in his posses- sion 9.2-million US dollars that he wants to transfer out of his country. To do this transfer he needs my bank account number. Once he has the account number, guess what will happen to any money in the account. I find it hard to believe that anyone would fall for such an obvious scam, but whoever is sending these letters must be finding some pigeons naive enough to fall for his scheme, because the postage on the envelope amounts to 700 Zimbabwe dollars or whatever their monetary unit is, and he must send out thousands of such letters. At least the stamps on the envelope, which picture a newly constructed dam, are attractive. Today's fractal is also attractive, though not quite as attrac- tive as the dam in Zimbabwe. It is another 'evaporated' image, this one located near the right edge of the fan of the parent fractal. I named the image "All Inside Stuff" as a description, and rated it a 6 because it is interesting but not that great. The render time of 19 minutes is somewhat slow for a 6-rated image, but immediate relief is available at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> It rained all morning here at Fractal Central on Wednesday, then the sun appeared and the afternoon was sunny. The temperature reached only 65F 18C, when 79F 26C is normal, but the dynamic pair had a great several hours in the yard, enduring the wet grass with little complaint. Today once again holds a chance of rain. It remains to be seen how the duo will adjust. I'll do my adjusting when the work is done and the next fractal is found. That time will likely be around 3pm. Until next time and next FOTD, take care, and don't give up hope for the FOTD-CD. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ All_Inside_Stuff { ; time=0:19:39.03 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+1.69799788216427200/-0.966528307188927\ 90/366675.9/1/-132.5/-9.33145443554606047e-009 params=-10/-1.1/-1/-11/0/1e+100/0/0 float=y maxiter=1200 inside=bof61 periodicity=10 colors=000eiOfhQggThfWjeZkdalccmbfoaip`lq_orZqqVoq\ SmpPkpMioJgoGenDcnAan7_l6Zk6Zj6Yh6Yg6Yf6Xd6Xc6Wb6W\ `6W_6VZ5VX5UW5UV5UT5TS5TR5SQ5SO5SN5RM5RK5QJ4QI4QG4\ PF4PE4OC4OB4OA4N84N74M64M00054M56M58M5AM6CM6EM6HM6\ JM7LM7NM7PM7RM7TM9VOAWPCXQDYRF_SG`TIaUJbVLdWMeXOfY\ PgZRh_Sj`UkaVlb000Yod_pe`qfbrgctheuifvjhwkkynixlhw\ jfvieugctebsd`sb_r`Yq_XpYVoWUnVSnTRmRPlQOkOMjM000J\ hJIhHGgGFfEDeCCdBAc97e68d79c89b9AbABaBB`CC`DD_EDZE\ EZFEV`FXHGTZGWJHVKIVLIUMJTMKTNKSOLRXLRQMQRNPSNOTOO\ UPNUPMVQMWRLXRKYSKZSJ_TI`UIaUHhVGbWGmWFdXErYEfYDrZ\ ChZCw`EiaGibIjcKjdMjeOkfQlgSlhUliWmjYmkZnl`nmbondo\ ofophpqjprlqsnqtprurrytuvsrtsoqslosjlrgjrdgraer_bq\ X`qUYqRWqPTpMRpJOpGMpERmCVjBZgAce9gb8k_7rZ6pY6oY6n\ X6mX6lW6kW6jV6hV6gV6fU6eU6dT6cT6bS6aS6_S6ZR6YR6XQ6\ WQ6VP6UP6SP6RO6QO6PN6ON6NM6MM6KL6LM6LM6MM6MN6NN6NN\ 6ON6OO6PO6PO6PO6QP6QP6cjL } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

1 0

Multifractal 1600/1200 Bug
by Albrecht.Niekamp＠t-online.de 28 May '03

28 May '03

Hi, I spend a lot of time trying to find a workaround for that bug and that is no fun anymore. I was kinda shocked when I read yesterdays message by Jim White. Imagine, working for years with a formula that only generates artefacts produced by a fractint bug -if it is true. Also Jonathans remark that the formula possibly will be broken by just that forces me to stop working with multifractal, at least until that bug is tracked down, if ever. So I tried to reproduce the Janusbird3 image with the new formula Multifractal_1. It should be no problem, as the relevant code is identical and only the iteration counter is used for switching. The result is identical except that tesseral (passes=t) does not produce error pixels anymore. But--it was not possible with Lee`s image which is a zoom with identical settings. In the frame of the basic image there are mandeloids which definetly are artefacts produced by misreading of the input values. The artefacts cannot be reproduced by changing of the settings. For me it is now certain, that fractint under certain conditions misreads the inputs and causes the error pixels when there is a conflict between the original settings and the misreadings. Mfx_testz is Lee`s image without the artefacts. -------------------------------start-par----------------------------------- mfx_testz { ; reproduced with Multifractal_1 ; 1600x1200 Image Copyright 2003 ; by Lee H. Skinner ver=2002 reset=2002 type=formula formulafile=mult240.frm formulaname=multifractal_1 ismand=y function=exp/exp/exp/exp passes=t center-mag=-1.41631/0.116469/5.602624/1/-87.4999999999999716/-1.14117049\ 143658278e-013 params=-0.2724234748374889/0.09260841170049135/384.00001/2048.4505/768.0\ 256000000001/768.0256000000001/1025.0256/1536.0256/12284.71/11.16 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 symmetry=none periodicity=0 rseed=-2436 cyclerange=2/255 colors=000000hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi_5fc0ce7_jFRoNIzb0<2>zz\ 1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhM\ BiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5zP5zL6zI6zE6wE6tD6<6\ >vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW4E<2>_4H<3>P3DN2CK2A<3>805G0BO0G<3\ >g0Ul0Xq0`v0d<2>y0fz0gy0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4K\ W0Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvlqvotvsww<2>zzz<3\ >rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<4>XCAaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<\ 4>QR8SU9UXAW`BYcC<2>enG } Janusbird3a { ; reproduced with Multifractal_1 ; original settings ; ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult240.frm formulaname=multifractal_1 ismand=y function=exp/exp/exp/exp passes=1 center-mag=-0.488627/4.44089e-016/1.086909 params=-0.2724234748374889/0.09260841170049135/384.00001/2048.4505/768.0\ 256000000001/768.0256000000001/1025.0256/1536.0256/12284.5/11.16 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200pppqqqsss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08\ A068<2>022000211<22>keOmgPoiQqjRslSunT<2>zsX<25>CB7A96875<3>000400<23>o0\ 0q00s00<3>z00<25>C00A00800<3>000<28>nnn } --------------------------------start-frm----------------------------------- FRM:Multifractal_1 { ; Albrecht Niekamp 270503 ;only integers as first input, second input 5 digits to the right ;real(p2) factor1, border1 ;imag(p2) (-)bailout,input bas.frm1_2digits input bas.frm2_2digits ;real(p3) maxiter2, border2-in ;imag(p3) factor2, border2-out ;real(p4) maxiter3, border3-in ;imag(p4) factor3, border3-out ;real(p5) 1digit_shape only 5digits: shape,out1,out2,in1,in2 ; 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset (not shape) <0_no in/out1 ; optional basic frm2 digit1: 1_out1 2_out2 3_both +5_shape ; digit2: 1_in1 2_in2 3_both ;imag(p5) digit1 : many_mods multipl.shutoff 1_in/out1 2_in/out2 3_both ; digit2 :1_iter1reset 2_iter2reset 3_both +5_shape effect ; input2: Number of sides 2 digits (many_mods L.Allison) ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=d<0 if (da) d=-d endif ba=trunc(d) d=round((d-ba)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) mi2=trunc(d) b2=(d-mi2)*100000 ; d=imag(p3) fac2=trunc(d) ob2=(d-fac2)*100000 ; d=real(p4) mi3=trunc(d) b3=(d-mi3)*100000 ; d=imag(p4) fac3=trunc(d) ob3=(d-fac3)*100000 ; da=real(p5) t=da<0 if (t) da=-da endif start=2-t dd=trunc(da) da=round((da-dd)*100) if (dd<5) start=0 vb=(dd==3)+(dd==4) else d=trunc(dd/10000) vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) dd=dd-d*1000 or1=d>5 d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) d=trunc(dd/100) dd=dd-d*100 or2=d>5 d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) d=trunc(dd/10) dd=dd-d*10 inr1=d>5 d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) inr2=dd>5 dd=dd-inr2*5 v3=(dd==3) v4=(dd==4) d2=(dd==2)+(dd==4) endif ; d=trunc(da/10) da=da-10*d ab=d>=5 d=d-5*ab bb1=(d==1) bb2=(d==2) ab1=(da==1) ab2=(da==2) ; d=imag(p5) dd=trunc(d) mm=round((d-dd)*100) da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=dd>=5 dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) ; if (ismand) z=0 if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else c=p1 z=pixel endif t=0 tt=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn4(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z2=z*z z=z2*z2+(p6+u)*z2+c else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif bo=|z| If (wo) t=t+1 if (bo>b1) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else z=pixel c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2&&bo<ob2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3&&bo<ob3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif bo<=ba } ---------------------------------------end-----------------------------

2 1

FOTD 28-05-03 (In the Oort Cloud [8])
by Jim Muth 28 May '03

28 May '03

FOTD -- May 28, 2003 (Rating 8) Fractal visionaries and enthusiasts: What is the outer limit of the solar system? Is it the planet Pluto? No, Pluto, which is hardly worthy of being called a planet, is not the end of the solar system. Are a few icy rocks a short distance beyond Pluto the limit of the solar system? No. What then is the end? The end of the solar system is the Oort cloud of comets, which surrounds the sun and extends nearly halfway to the nearest star. These distant chunks of rocky ice drift lazily along in their orbits at a rate of perhaps one meter per second, taking many millions of years to complete one revolution. Today's image reminds me of a cloud of comets, such as the Oort cloud. The resemblance inspired the name "In the Oort Cloud". Of course, the actual comets in the Oort cloud are totally dead. They are not surrounded by a coma of ejected gases, nor are they as crowded together as the 'comets' in the image, but the image bears enough of a resemblance to a cloud of comets to justify its name. At this time, I must make a minor confession. At the beginning of the month, I stated that I would post no 'evaporated' images during the month. Until today, I have posted none. But the 'normal' version of today's image that I originally found became so much better when it was evaporated that I could not keep it secret. The entire image is composed of < bof60 > inside fill. The scene of today's image is located inland, near the discon- nected area of chaos south of the main body of the mayparent fractal. Of course, since the scene is an evaporated one, the parent fractal is no longer there. When the time came to rate the image, I had no trouble deciding on an 8. The image truly is an exceptional one (as FOTD images go). The render time of 16 minutes is not so exceptional, but this minor annoyance can be eliminated by downloading the completed GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Though the clouds were heavy, the expected rain failed to materialize here at Fractal Central on Tuesday, and as a result, the Fractal Central cats had an enjoyable day. The temperature of 61F 16C was a bit chilly for their sensitive whiskers, but at least the grass was dry when they ventured into the yard for their afternoon exploration. This morning is once again cloudy and rain is once again threatening. The duo will have as good a day as they can. My day will be as good as the work permits and as good as I make it. Until next FOTD, take care, and give those Fractint bugs a shot of Raid. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ In_the_Oort_Cloud { ; time=0:16:13.23--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=-0.79387328486147/+2.42904310788191/3.7\ 3372e+008/1/-5/-1.9083425896814e-005 params=-10/-1\ .1/-1/-11/0/1e+100/0/0 float=y maxiter=1200 inside=bof60 outside=iter periodicity=10 colors=000zzzzyyzxxxwwwvvuuusttqssorrmqqjppgoodnna\ mmZmlWkkTkjQjiNihKhgHgfEfeDdaCbXB`TAZP9WL8TGNRCAMA\ ZF9l77y06t7CoDHjJMeQS`WXWaaYZ`_X_aVZcTYeQYgOXiMWkK\ VmHVoFUqDTsBSt9SsEWsJZrObrTerYuqbw000QpdRoQSoQTpRU\ pRUpSVpSWpTXpTYpUZpU_pV_pVXqTVqSSrRQrQNsPLsNItMGtL\ DuKBuJ9uI8tK8sL8rM8qN8pO8oP8nQ8mR8lS8kT8jU8iV8hW8g\ X8fY8eZ8d_8c`8ba8ab8`c8_d8Ze8Yf8Xg8Wh8Vi8Uj8Tk8Sl8\ Rm8Qn8Po8Op8Nq8Mr8Ls8Kt8JuchIR_hS_iT`jU`kV`kWalXam\ YanZao_bp`bpabqbbrccsdctecufcud`rcZpbXn`Vl_TjZQgXO\ eWMcVKaTI_SFXRDVPBTO9RN7PM5NP9RSCUUFYXI`ZLcaOgcRjf\ UmhXqk_tmbwmcwndxnfxogxoixojxRrbRraSs`St_TuZTuYUvX\ UwWUwWSsVRpUPlTOiSNfRLbQK_PIWPHTOGQNEMMDJLBFKACJ99\ JAAIAAIBAHBAHBBGCBGCBFCBFDBFDCEDCEECDECDEDCFDCFDBF\ DBGDBGEAGEAHE9HE9HF8IF8IF8IF7JF7JG6JG6KG5KG5KH4LH4\ LH4LH3MH3MI2MI2NI1NI1NI1OK4PL6PM9QNBROERPGSQJSRLTT\ OUUQUVTVWVWXYWY_XZbX_d_Xf } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] BUG - (all MandelbrotMix images are reflections!)
by Jim Muth 27 May '03

27 May '03

At 08:27 PM 5/26/03 +0100, Jim White wrote: <snipped> >....all images using MandelbrotMix4 are accidental >reflections!.... I have long realized that all is not mathematically correct with the way the MandelbrotMix4 (and MandelbrotMix2) formulas are handled by the Fractint program. This is quite obvious when the order of the parameters is reversed and (a*z1)+(b*z2) does not equal (b*z2)+(a*z1). But what can be done about it now? If the bug were corrected, many of the older parameter files would not work. Jim M.

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Re: Fractint Digest, Vol 3, Issue 21
by JackOTradez 27 May '03

27 May '03

Yes! ""When you are dealing with endless repetitions (specifically, iterations) on infinitesimal quantities anything can and does happen. Who can say what is right and what is wrong?"" Can you say "CHAOS" ? (I know you can . . .. ... ..... ........ ) Ain't it cool!? JoTz

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Re: [Fractint] FOTD 23-05-03 (Isolated Minibrot [8])
by Jim Muth 27 May '03

27 May '03

At 01:24 PM 5/27/03 -0400, Mike Traynor wrote: <snipped> >...in a broader sense, the definition [of a fractal] >is recognizing that we haven't yet formalized the >description of the kinds of similarities fractals >display. Fortunately, we've got a terrific pattern- >recognizing computer that doesn't need to have things >like "the same 'type' of structures" formalized. >It is, of course, the human brain. ...which takes us back to my original statement that it is ultimately up to we human beings to decide what is and what is not a fractal. Jim M.

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Re: CONJ/Float Bug
by Jim White 27 May '03

27 May '03

Hello everybody > (Jonathan) Have you tried the command line option debugflag=322? I tried including "debugflag=322" in the PAR files. It seems to make no difference to ANY of the tests. > (Jim Muth) If the bug were corrected, many of the older parameter files would not work. I know just what you mean! It's a real pain in the proverbial! Nevertheless, I'd make the following points: 1. Fractint appears to me to be be a bit of an icon (!) in the fractal generation arena. Its formula parser represents a de-facto standard by which users of different packages (and home-grown engines like mine) can share images. In the home-grown case, I use fractint as a benchmark to test my program (which is how I came to discover the bug) 2. While packages will vary in their approach to interface issues and rendering techniques, it is surely critical that the underlying mathematical "signature" of an image (as encapsulated by the formula + the target window) should be both consistent and accurate. 3. Accidental artifices that produce desirable effects can be retained, where it's deemed desirable and practicable, by having the package support an option to allow the former bug to be activated (as I understand was done with cos/cosxx). 4. Mathematical bugs cut both ways - they might produce interesting images that otherwise would never be found, but they might also conspire to prevent discovery of others! 5. Corrections to parameter files for images based on MandelbrotMix4 would only require window-reflection, a relatively simple task. But what if the reflections we are seeing here are NOT the only symptom of this bug? What if other artificial side-effects are going undetected? This itself is a good argument for fixing the bug, and checking samples of the various formula types. In other words, I hate to be a pain the arse, but I don't see that we have a choice! Cheers Jim White __________________________________________________ It's Samaritans' Week. Help Samaritans help others. Call 08709 000032 to give or donate online now at http://www.samaritans.org/support/donations.shtm

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Re: [Fractint] FOTD 23-05-03 (Isolated Minibrot [8])
by Jim Muth 27 May '03

27 May '03

At 09:45 AM 5/27/03 -0500, Prog. Dude wrote: <sippped> >Doesn't "fractal" have a *mathematical* definition? Yes. I now quote from page 1101 of the second edition of the CRC Concise Encyclopedia of Mathematics: [A fractal is] "An object or quantity which displays SELF-SIMILARITY, in a somewhat technical sense, on all scales. The object need not exhibit *exactly* the same structure at all scales, but the same 'type' of structures must appear on all scales. A plot of the quantity on a log-log graph versus scale then gives a straight line, whose slope is said to be the FRACTAL DIMENSION." IMO, words such as 'somewhat' and 'not exactly' and 'same type' in this definition leave it open to individual interpretation. Jim M.

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Re: [Fractint] FOTD 23-05-03 (Isolated Minibrot [8])
by Jim Muth 27 May '03

27 May '03

On Sat, 24 May 2003 at 12:38:52 Albrecht Niekamp wrote: <snipped> >If a seemingly irregular structure turns out to be part of a >bigger structure that isnt chaotic at all and maybe a structure >that you havent seen before, then what is a fractal if this >isnt? The entire concept of the entities we now know as 'fractals' was invented by human beings, and it is up to each individual to decide what is or is not 'a fractal'. To me, a fractal is something that resembles the images that I first saw in 'Sci. Am.' magazine around 18 years ago. This is my personal decision. IMO, when things such as multiple layers and transforms are applied to an image, what results is computer art based on fractal formulae. There is nothing wrong with calling this art 'a fractal' or 'fractal art' or anything else the creator wishes. I simply choose not to call it a fractal. >Tell me what's missing. Nothing is missing. >Purity as such is meaningless in this context, unless it is >part of your message. 'Fractal purity' is also a human invention. No two people will agree on what it is. >And another question: If Lee detects hidden beauty within a >seemingly uninteresting scene, what better could you say about >a fractal artist? I could say nothing better. I am most certainly not suggesting that everyone limit themselves to my definition of fractals or fractal art. >After all we are trying to do the same thing: Create images >that make people look twice and maybe take a closer look. True. >And maybe there is a smile on their face when they see beauty. >As for me, we are covering a different part of the spectrum... True. There is nothing wrong with that, especially in light of how I have narrowed my spectrum. >and if you feel attacked... I do not feel attacked. I think you misread the word 'aggressive', which was intended as a joke much as the phrase 'sexy fractals' would have been. ...thats exclusively your own problem. No problem. >I'm happy that a fresh wind is blowing in Fractalia and that I >could do my part to keep it alive. Regards, Keep up the good work. Things that do not change with the times soon become things of the past. Jim M.

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FOTD 27-05-03 (Red and Green [7])
by JimMuth＠aol.com 27 May '03

27 May '03

FOTD -- May 27, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today's FOTD image has nothing to do with a certain Canadian back-woodsman. I named it "Red and Green" because those colors are most prominent in the image. The red-green area is surrounded by an extended area of lavender chaos, which sets it off quite nicely, earning the whole thing a rating of 7. The scene is located in an area of chaos near a small and very distorted Mandeloid just beyond the northern edge of the 'fan'. The trip back out to the surface of the mayparent fractal is quite interesting, and can be done most quickly in a smaller view window. Before starting the trip, set the passes to < g > and turn off the logmap. I have been aware for quite some time that the Fractint program, (and from what I hear, apparently the UltraFractal program as well), does not calculate the MandelbrotMix formulas correctly. It is a small deficiency but it is there. To see the 'bug' in operation, bring today's image to the screen and switch the (p1) and (p2) parameters. This should change nothing, since a+b is equal to b+a, but when it is done, the calculated image totally changes. It becomes a solid blue screen with an iteration count of 107. What has happened is that the parent fractal has become a mirror image of itself. I have never mentioned this bug because of the backward compat- ibility problem, and also because the formula does do what it was intended to do, which is set initial Z to a critical point of the formula, so that the image the formula draws will contain intact midgets. My opinion is to leave well enough alone and live with the minor inaccuracy, which if corrected, would cause more problems than it eliminates. And speaking of eliminating problems, the problem of the 20-minute wait to render today's image can be eliminated by downloading the completed image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The cat duo had a better day than expected on Monday. The rain ended later in the morning and we actually had a bit of sun in the afternoon. When the temperature reached the trigger point of 66F 19C the duo snapped out of their lethargy, leaped to their feet, and came running, demanding to be let out. They enjoyed a two-hour romp in the yard, (if sitting and watching birds can be called a romp), before they realized how wet their paws were getting. This morning, the clouds in advance of the next rain have already moved in, and the rain is due by afternoon. If the duo expects to go out today, they had better wake up this morning and get active. As for me, I've got enough work lined up to keep me active most of the day. And then, there is the next FOTD to find and write about. So until next time, take care, and watch for unexpected fractal bugs. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Red_and_Green { ; time=0:20:26.98--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+4.29791870853377400/-2.096657547867527\ 00/1.096168e+010/1/-160/-8.91246113253474359e-006 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=2400 inside=0 logmap=370 periodicity=10 colors=000QTkRRjSPiSMgTKfUIeUGcVEbWCaWA`XCaXDbYFcY\ GcYHdZJeZKf_Mf_Ng_Oh`Qi`RiaTjaUkaVk7aSBcUFeWJgYNi_\ Qk`UmbYndapfdrghtilvkpxmsynukmvYmwKlx7ls7ko7jk7jg7\ ic7i_7hW7gS7gO7fK7fJBbIF_HJXGNUFRREVNDZKCbHBfEBjBC\ gFDdJEaMEZQFWUGTXHQ`HNdIKgJHkJEnIHlIJkIMiIOhIQgHTe\ HVdHYbH_aHa`K`bM_cOZdQZfSYgUXhXWjZWk`VlbUndTofTpgU\ ogVohWohXohYoiZoi_oi`ojaojbokcokdokeolfolgolzoOnZ0\ wI1rJ2pJ3mK4jK5hK6eL7cL8`M9ZMAWMBUNCRNCPN000XLLgKL\ pIKzXKyIJyJIyKHzXGxMFxNExNDwOCwPBwQAvR9vS8vT7vT6nR\ BfQFZPKROOJNTBMXzL`zYRziIzmJzmJzzJzvUzrdzmYzhRzcLz\ ZNzUOwPQtKRqFSmAUh9Vg7Wg5Yg3Zg2_d3Za4Y_4YX5XV5XS6W\ Q6WN7VL7VI8UG8UF7TE7TE6TD6SC6SC5SB5SA5RA4R94R94RC6\ TF7VI8XL9ZOA`RBbUDdXEf_FhbGjeHlhInjJoDbcCdjBfqDgmE\ hjFifGjcHk`JlZKmYLnWNoVOpTPqSRrRSsPTtOVuMWvLXwKVxJ\ TyJRzJPzINzILzIJzIHzHFzHDzHCzHYzBsz5izD_zLQzTHz`Bz\ T5zL0zEHzhJzgNzqOzoPznQzm } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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[Fractint] BUG - Float=y Calculation Error! (all MandelbrotMix images are reflections!)
by Jim White 27 May '03

27 May '03

Greetings, everyone I've caught Fractint red-handed getting its sums wrong! The proof is simple but irresistible. It turns out that Jim Muth's excellent image, Fractal_Medallion, is in fact a reflected image of the reflection of his window. In fact all images using MandelbrotMix4 are accidental reflections! In a nutshell, Fracint sometimes gets the imaginary sign wrong. Where you think you are getting -5 ^ x, you might actualy be getting conj(-5 ^ x). A little scary, yes? I've provided a detailed account of my investigations below: 1. Bug Description 2. Bug Demonstration 3. Bug Analysis 4. Bug Impact 5. Bug demo formula/par I hope you all find it interesting, and I look forward to feedback. Regards Jim White =================================================================== 1. Bug Description In the formula, MandelbrotMix4, the initial value of Z is set using this expression z = (-a*b*g*h)^j Now, in Jim Muth's Fractal_Medallion (FOTD V3) the parameters are a = 1, b = -5, g = 1, h = -1, j = 1/6 The initial value of Z should therefore be z = -5 ^ (1/6) The correct answer is z = (1.13246720041135087, .653830243005915296) But Fracint is actually returning the conjugate! z = (1.13246720041135087, -.653830243005915296) 2. Bug Demonstration The formula CONJ-BUG-1 (attached) draws the X and Y axes, and also draws "axis lines" through 2 points, z and z2, where z and z2 are the result of a fixed calculation. It sets a, b, g, h and j as above, then calculates z = (-a*b*g*h)^j z2 = b^j Given the parameter values, clearly -a*g*h is 1, so z and z2 should be identical. The display has a grey background, and the axis lines are displayed as follows: (0,0) in black z in yellow z2 in dark red Where z and z2 correspond, the axis lines are blended. The result should be a pair of blended red/yellow lines through z = (1.13246720041135087, .653830243005915296) Run the parameter set CONJ-OK to verify this result. It specifies float=n In CONJ-BUG, however, float=y and the horizontal red and yellow lines are separated. The yellow line (imag(z)) has been reflected! 3. Bug Analysis a. Fractint appears to maintain a separate sign-bit for float values, but suffers from the rather disturbing condition that (n,0) and (n,-0) are two different numbers! This can be verified by substituting j = 1/6 z = -5^j z2 = conj(-5)^j into the CONJ-BUG formula. With float=y you get 2 different answers. b. The conditions under which a value (x,0) gets its sign-bit conjugated appear to be related to the use of the unary "-" operator. Try the CONJ-BUG formula with j = 1/6 b = -5, z = b^j b = 5, z2 = (-b)^j Here Z is correct, but Z2 is conjugated. c. !!!!! Late Extra !!!!! it's getting weird! NOW GET THIS! Simply changing the order of the 2 statements above affects the result! So if we have j = 1/6 b = 5, z2 = (-b)^j b = -5, z = b^j We get Z and Z2 in agreement, BUT both are wrongly conjugated!!!!! 4. Bug Impact Well, I've spent so bloody long just identifying this bug that I haven't had much time to consider the ramifications. I only stumbled across it because when I ran Jim Muth's Fractal Medallion on my home-grown Windows-based Fractint emulator - I got nothing at all, just a solid block of colour 9. I spent several days assuming my program was at fault until I discovered the "reflection" syndrome, and several more days before I was convinced my program was right, and Fractint was wrong. The MandelbrotMix4 formula just happens to be one that delivers a reflected image if the initial Z value is replaced with conj(Z), and just happens to have a particular expression for this initial value that is vulnerable to the "CONJ bug". There may of course be other formulae that are infected in more subtle ways. The fact that conj(x,0) and (x,0) can differ in a calculation is disturbing, but the most worrying aspect of all is that final test I ran (3.c above) which demonstrates that the occurrence of conjugation errors is by no means predictable, and can even be affected by the order of otherwise independent statements! 5. The Demo Formula/Params CONJ-BUG {; Dr Memory's CONJ bug demo ; ; plot axis lines ; (0,0) in colour 8 (black) ; z in colour 14 (yellow) ; z2 in colour 4 (dark red) ; all other points in colour 7 (grey) ; ; z and z2 axes plots are interlaced, so if z and z2 agree, ; the answer will be shown with mixed red/yellow axes. ; Any disagreement will be indicated by solid red/yellow lines ; ; Calculate Z and Z2 here! a = 1, b = -5, g = 1, h = -1, j = 1/6 z = (-a*b*g*h)^j ; the expression in question ; -a*g*h = 1, so z = b^j [i.e. -5 ^ (1/6)] z2 = b^j ; correct answer ; Axis-plot code - Set colour values according to pixel co-ordinates axis = real(p1) ; line thickness (in window co-ords) colour = 7 ; default bgnd colour ; always plot (0,0) in black (8) x = real(pixel), y = imag(pixel) if (abs(x) < axis) colour = 8 elseif (abs(y) < axis) colour = 8 endif ; plot z in yellow (14) if (abs(x - real(z)) < axis) colour = 14 elseif (abs(y - imag(z)) < axis) colour = 14 endif ; plot z2 in dark red (4) (blend with yellow if z/z2 agree) colour2 = 4 if (colour == 14) if (whitesq) colour2 = 14 endif endif if (abs(x - real(z2)) < axis) colour = colour2 elseif (abs(y - imag(z2)) < axis) colour = colour2 endif loopn = 0 : loopn = loopn + 1 loopn < colour } CONJ-BUG { ; CONJ bug demo PAR type=formula formulafile=??? formulaname=CONJ-BUG passes=1 float=y corners=-2.25/1.75/-1.75/1.25 params=0.01/0 maxiter=16 inside=0 symmetry=none map=default.map } CONJ-OK { ; CONJ bug avoided, float=n type=formula formulafile=??? formulaname=CONJ-BUG passes=1 float=n corners=-2.25/1.75/-1.75/1.25 params=0.01/0 maxiter=16 inside=0 symmetry=none map=default.map } __________________________________________________ It's Samaritans' Week. Help Samaritans help others. Call 08709 000032 to give or donate online now at http://www.samaritans.org/support/donations.shtm

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1600x1200 bug
by Lee H. Skinner 26 May '03

26 May '03

In the past few days, I've run into a bug over a dozen times while exploring with the multifractal formula. I've also recently upgraded to patch level 5 of Fractint version 2002. It appears most often at 1600x1200 resolution, occasionally other resolutions. At 1600x1200, the following par illustrates the bug. It only does 2 or 3 lines at passes=1, and barely gets started at passes=t before it stops generating the picture. A showdot continues to move, but nothing else is generated. This is similar to a save and restore gif bug discovered several years ago, but no save and restore is necessary this time. It may have something to do with a buffer size since it occurs much more frequently with higher resolutions. Bug_Test { ; ; t= 0:01:28.42 on a P4 2Gh at ; 1600x1200 Image Copyright 2003 ; by Lee H. Skinner ver=2002 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=0from_ml.frm formulaname=multifractal ismand=n function=exp/exp/exp passes=t center-mag=-6.52603785028786300/-0.01400828975779934/\ 404.3077/1/77.5000000000016342/-4.47783476964502825e-\ 012 params=-0.1740997192297128/-0.2996141087069308/384.00\ 004/256.1106/2048.00016/768.00009/768.01536/256.01025\ /28974.5/12 float=y maxiter=2048 inside=maxiter outside=tdis logmap=yes symmetry=none periodicity=0 rseed=-2436 cyclerange=2/255 colors=000000zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8K\ J8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9\ vq8xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5zP5zL6zI6zE6wE6tD6<6\ >vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW4E<2>_4H<3>P3DN\ 2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>u1mt1n\ s1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6Zc7`\ c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvlqvotvsww<2>z\ zz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<3>SCCXCAaB9<3>\ uA2zA0xA0<12>SA1QA1NA1<3>D92<6>UXAW`BYcC<3>hrI<3>UnXR\ m_NlcJkgFfpAaz<3>PJoSFlWAi_5fc0ce7_jFRoNIzb0zj0zr0 } -------------------------------start-frm----------------------------------- FRM:Multifractal { ;Albrecht Niekamp May, 03 ;only integers as first input, second input 5 digits to the right ;real(p2) factor1,border1 ;imag(p2) (-)maxiter1,input bas.frm1_2digits input bas.frm2_2digits ;real(p3) bailout,hyb.mandel: number of sides (Many_mods L.Allison) ;imag(p3) factor2,border2 ;real(p4) maxiter2,factor3 ;imag(p4) border3,maxiter3 ;real(p5) 1digit_shape only 5digits: shape,out1,out2,in1,in2 ; 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset (not shape) <0_no in/out1 ; optional basic frm2: out-nbr 1digit in-nbr 1digit 3_both +5_shape ;imag(p5) 1digit : 1_iter1reset 2_iter2reset 3_both +5_shape effect ; 2digits : many_mods multipl. shutoff +10_in/out1 +20_inout2 +30_both ; optional input2: frequency_2digits level_2digits amplitude_2digits ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=(d<0) if (da) d=-d endif mi1=trunc(d) d=round((d-mi1)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) ba=trunc(d) mm=round((d-ba)*100000) ; d=imag(p3) fac2=trunc(d) b2=(d-fac2)*100000 ; d=real(p4) mi2=trunc(d) fac3=round((d-mi2)*100000) ; d=imag(p4) b3=trunc(d) mi3=round((d-b3)*100000) ; da=real(p5) t=(da<0) if (t) da=-da endif start=2-t dd=trunc(da) if (dd<5) start=0 endif vb=(dd==3)+(dd==4) da=round((da-dd)*100) d=trunc(dd/10000) vb=(d==3)+(d==4)+vb dd=dd-d*10000 d=trunc(dd/1000) or1=(d>5) d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) dd=dd-d*1000 d=trunc(dd/100) or2=(d>5) d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) dd=dd-d*100 d=trunc(dd/10) inr1=(d>5) d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) dd=dd-d*10 d=trunc(dd) inr2=(d>5) d=d-5*inr2 v3=(d==3) v4=(d==4) d2=(d==2)+(d==4) d=trunc(da/10) ab=(d>=5) d=d-5*ab da=da-10*d bb1=(d==1) bb2=(d==2) d=da ab=(d>=5) d=d-5*ab ab1=(d==1) ab2=(d==2) ; d=imag(p5) dd=trunc(d) d=round((d-dd)*1000000) le=(d>10000) da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=(dd>=5) dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) if (le) freq=round((trunc(d/10000))*10) ;frequency_lake effect by S.Gallet d=d-freq*1000 level=(trunc(d/100))/100 ;water level d=d-level*10000 ampl=d/100 ;amplitude of the wave angle=real(rotskew*pi/180) t=exp(-flip(angle)) h=1/real(magxmag) q=h/0.75*imag(magxmag) tanskew=tan(imag(rotskew*pi/180)) w=2*q*t v=2*h*(tanskew+flip(1))*t z3rd=center+(-q-h*tanskew-flip(h))*t z=pixel-z3rd s=imag(conj(w)*z)/imag(conj(w)*v) if (s<=level) da=level-s z=z+2*da*(1+ampl*sin(freq*da^0.2))*v endif z=z+z3rd endif if (ismand) if (vb) c=0.4*log(sqr(pixel^mm)) z=z*le else c=z*le+pixel*(le==0) z=0 endif else c=p1 z=z*le+pixel*(le==0) endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) ;frm: Albrecht Niekamp else z2=fn1(z)+c ;frm: Many_mods Linda Allison sqz2=cos(z2) z=c*(1-sqz2)/(1+sqz2) endif else if (ab) z=z*z+c+c*c-p7 ;frm: Puskás István else z2=z*z ;frm: Puskás István modified z=z2*z2+(p6+u)*z2+c-p1*(d3==0) endif bo=|z| If (wo) t=t+1 if ((t<mi1)+(bo>b1)) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=z*le+pixel*(le==0) endif else z=z*le+pixel*(le==0) c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif bo<=ba } -------------------------------------------end-----------------------------

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FOTD 26-05-03 (Evaporation [7])
by Jim Muth 26 May '03

26 May '03

FOTD -- May 26, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today's image, with its three-dimensional effect and its monochrome color palette, takes us to the a small spot of chaos in the center of the 'fan' feature of the mayparent fractal. Actually, the scene is located in a spot in a spot in a spot. When I zoomed into the original spot, I chose not the most obvious place that might hold a midget, but a less obvious feature off to the side. When rendered in the normal manner, the scene is relatively boring, consisting of large flat areas of color, so to increase interest, I rendered the scene with the outside areas set to < fmod > and the proximity set to 10. This choice greatly narrows the color palette, but adds interest to an otherwise humdrum image. The picture reminds me of a thick, viscous fluid in the process of evaporating. I named the image "Evaporation". The image impresses me as above average. It might not be that much above average, but it is different enough to warrant a rating of 7. The render time of 12 minutes is a bit slow. A faster way of seeing the image is to download it from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> A few rays of sun broke through on Sunday here at Fractal Central, but enough showers fell between the hints of sun to keep things wet and keep the dynamic duo confined to the indoors. However, after so much confinement, the duo pretty much took their confinement in stride. With the temperature at 61F 16C, they barely thought of going out. It is raining again this morning, so the duo will likely have a repeat. For me, I expect a reasonably peaceful day. Until next FOTD, take care, and don't miss the byways of life. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Evaporation { ; time=0:12:45.00--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+2.95955458582929700/+0.046213892587742\ 94/3.236004e+010/1/97.5/0.000545378124574120993 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=1200 inside=0 proximity=10 outside=fmod logmap=yes periodicity=10 colors=000`uz_rzWozSlyOixKfwGcuC`s8Yq9VoASlBPiDMfE\ JcFG`GJYIMXKPWMSWOVVQYUS_UUbTWdTYgS_iRalRcnQdpQcnS\ cmTblUbjVaiWahY`fZ`e_`d`_ba_acZ`dZZeYYfYXgYWhfkSnz\ BouZoqvplqqhmrdir_esWatSYtNUuJQvFMvBIoJJhQJaXKVdKO\ kLIrLEi4oDfkJbIS97b2GbAObIWbQcbYkbd_gRPkDKaAGT8BK6\ 7B4322V8CvELrDKoDJlCJhCIeCIbBH_BHWBGTAGQAFNAFT8NZ6\ Vc5b_BaXH`UN_RS_NYZKcYHiXEnXHoYKoYMoZPpZSpZUp_Xp__\ q_aq`dq`fq`gnYgkWghUgeRgbPg_NgXLgUIgRGgOEgLCbSMYYW\ TdeOjoKpxJosJonJojJoeJoaJoXIoTIoOIoKIoFIoBIo6Io2Mk\ 7PhBSdFWaJZYNaVReRVhOZkKboHfrDjuAnx7r7m5RSqPNxOJmN\ FcMBUM7KLBNKFPJJRINTHRWGVYFZ_EbaDfdCjfBnhBqjPtZbvN\ oxCnvCmtCmsClqCkoCknCjlCjkCiiChgChfCgdCfbCfaCe_CeZ\ Cc_Fa`I_aKYaNWbQUcSScVRdXPe_NebLfdJggHgjFhlDioCiqE\ jnGjlIjiKjgMjdNkbPk_RkYTkVVkTWkREQzHUqJYiL`aNdTPhL\ RkDMa_ISuMOrQLoUIlYFi`Cfd9ch6`l3Yo0VX5sWBtVHtVNtUT\ tTZuTduSjuRpuRvuPsuNquLou } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Multifractal_1
by Albrecht.Niekamp＠t-online.de 25 May '03

25 May '03

Hi, this is a new formula, not an update, as it is not compatible. If it does what I expect, I still need some testing, itïs a major step forward, because now two way border values are available, which means, there also is an out-border. When this point is reached, the previous iteration is in use again. I did this in order to have a better separation and to a certain degree avoid distorted structures. Theoretically it should be possible to define the size of the inside image with pixel accuracy, as all border values are fractional. Therefor I skipped the lake effect, it was not compatible with most images anyway. The tricky real(p5) input is now easier to handle and the initial routine is more effective. That BUG still was there in the beginning, but when I changed all border inputs to be fractional (secondary inputs), it seemed to be gone. "Gallery" is a zoom into one "neuralgic" spot and renders ok. In the previous frm I had to use "round" functions to get rid of the "artefacts" which fractint adds to the inputs. I think in some rare events these caused a different value of a variable and the consequent errors. Jonathan, does this sound reasonable? Anyway I keep my fingers crossed and will do some more testing. Fractal Greetings, Al.

3 4

New gallery
by Sylvie Gallet 25 May '03

25 May '03

Hi All, I just updated my Fractal of the Week and added a gallery (#42) with 15 new fractals. All these fractals are one or two layer images made with Ultra Fractal, one layer for the fractal (dmj-fBmNovaMandel) and one for the light. Cheers, - Sylvie _________ ________ _______ ______ _____ ____ ___ __ _ E-mail address: sylvie.gallet1(a)libertysurf.fr Web site: in English : http://www.fractalus.com/sylvie/homepage.htm in French : http://www.fractalus.com/sylvie/homepagf.htm _________ ________ _______ ______ _____ ____ ___ __ _

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Partiton Magic
by James R. McKenzie 25 May '03

25 May '03

If you go to www.abilitywholesale.com you can get PM 8 for about $30 USD. It's an OEM site and I've ordered alot of stuff from them. They are very fast and have alots of other stuff too. Just trying to help fellow cheap-skates. 8-{> James R. McKenzie jimmckenzie(a)earthlink.net

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Multifractal
by Albrecht.Niekamp＠t-online.de 25 May '03

25 May '03

Hi, this is a major update for the Multifractal formula. The inputs are a lot easier and a problem is solved that in some cases caused that the inside options were not executed. This means, this update is not completely compatible, so dont remove the previous version. To avoid confusion it has a different name. The images all use the same shape, but with different insides. A lot of interesting border zooms are guaranteed. Janusbird3 uses passes=1 as passes=t causes coloring errors. Fractal Greetings, Al. --------------------------------start-par---------------------------------- Janusbird { ; Albrecht Niekamp May, 03 ; Time 0.39.46.32 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractalx ismand=y function=exp/sin/exp passes=t center-mag=-0.488627/4.44089e-016/1.086909 params=-0.2724234748374889/0.09260841170049135/384.00001/255.4505/2048.0\ 0008/768.0256000000001/768.01536/2560.01025/12297.72/0 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200pppqqqsss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08\ A068<2>022000211<22>keOmgPoiQqjRslSunT<2>zsX<25>CB7A96875<3>000400<23>o0\ 0q00s00<3>z00<25>C00A00800<3>000<23>eeegggiiijjjlllnnn } Janusbird2 { ; Julia as inside ; Albrecht Niekamp May, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractalx ismand=y function=exp/exp/exp passes=t center-mag=-0.488627/4.44089e-016/1.086909 params=-0.2724234748374889/0.09260841170049135/384.00001/255.4505/2048.0\ 0008/768.0256000000001/768.01536/2560.01025/12224.71/0 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200pppqqqsss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08\ A068<2>022000211<22>keOmgPoiQqjRslSunT<2>zsX<25>CB7A96875<3>000400<23>o0\ 0q00s00<3>z00<25>C00A00800<3>000<23>eeegggiiijjjlllnnn } Janusbird3 { ; Inside many_mods and julia mix ; Albrecht Niekamp May, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractalx ismand=y function=exp/exp/exp passes=1 center-mag=-0.488627/4.44089e-016/1.086909 params=-0.2724234748374889/0.09260841170049135/384.00001/255.4505/2048.0\ 0016/768.0256000000001/768.01536/2560.01025/12284.71/11 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200pppqqqsss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08\ A068<2>022000211<22>keOmgPoiQqjRslSunT<2>zsX<25>CB7A96875<3>000400<23>o0\ 0q00s00<3>z00<25>C00A00800<3>000<23>eeegggiiijjjlllnnn } ----------------------------------------start-frm-------------------------- FRM:Multifractalx { ; Albrecht Niekamp Update 260503 ;only integers as first input, second input 5 digits to the right ;real(p2) factor1,border1 ;imag(p2) (-)maxiter1,input bas.frm1_2digits input bas.frm2_2digits ;real(p3) bailout,hyb.mandel: number of sides (Many_mods L.Allison) ;imag(p3) factor2,border2 ;real(p4) maxiter2,factor3 ;imag(p4) border3,maxiter3 ;real(p5) 1digit_shape only 5digits: shape,out1,out2,in1,in2 ; 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset (not shape) <0_no in/out1 ; optional basic frm2 digit1: 1_out1 2_out2 3_both +5_shape ; digit2: 1_in1 2_in2 3_both ;imag(p5) digit1 : many_mods multipl.shutoff 1_in/out1 2_in/out2 3_both ; digit2 :1_iter1reset 2_iter2reset 3_both +5_shape effect ; optional input2: frequency_2digits level_2digits amplitude_2digits ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=d<0 if (da) d=-d endif mi1=trunc(d) d=round((d-mi1)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) ba=trunc(d) mm=round((d-ba)*100000) ; d=imag(p3) fac2=trunc(d) b2=(d-fac2)*100000 ; d=real(p4) mi2=trunc(d) fac3=round((d-mi2)*100000) ; d=imag(p4) b3=trunc(d) mi3=round((d-b3)*100000) ; da=real(p5) t=da<0 if (t) da=-da endif start=2-t dd=trunc(da) da=round((da-dd)*100) if (dd<5) start=0 vb=(dd==3)+(dd==4) else d=trunc(dd/10000) vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) dd=dd-d*1000 or1=d>5 d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) d=trunc(dd/100) dd=dd-d*100 or2=d>5 d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) d=trunc(dd/10) dd=dd-d*10 inr1=d>5 d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) inr2=dd>5 dd=dd-inr2*5 v3=(dd==3) v4=(dd==4) d2=(dd==2)+(dd==4) endif ; d=trunc(da/10) da=da-10*d ab=d>=5 d=d-5*ab bb1=(d==1) bb2=(d==2) dd=da>=5 da=da-5*dd ab=ab+dd ab1=(da==1) ab2=(da==2) ; d=imag(p5) dd=trunc(d) d=round((d-dd)*1000000) le=d>10000 da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=dd>=5 dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) if (le) freq=round((trunc(d/10000))*10) ;frequency_lake effect by S.Gallet d=d-freq*1000 level=(trunc(d/100))/100 ;water level d=d-level*10000 ampl=d/100 ;amplitude of the wave u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) d3=2*q*t rs=2*bo*(dd+flip(1))*t z2=center+(-q-bo*dd-flip(bo))*t z=pixel-z2 d=imag(conj(d3)*z)/imag(conj(d3)*rs) if (d<=level) da=level-d z=z+2*da*(1+ampl*sin(freq*da^0.2))*rs endif z=z+z2 endif if (ismand) if (vb) c=0.4*log(sqr(pixel^mm)) z=z*le else c=z*le+pixel*(le==0) z=0 endif else c=p1 z=z*le+pixel*(le==0) endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn1(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z2=z*z z=z2*z2+(p6+u)*z2+c else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif bo=|z| If (wo) t=t+1 if ((t<mi1)+(bo>b1)) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=z*le+pixel*(le==0) endif else z=z*le+pixel*(le==0) c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif bo<=ba } -------------------------------------end-------------------------------

1 0

Re: Multiboot
by JackOTradez 25 May '03

25 May '03

Tony (and other folks) - Your very sophisticated technique might be a bit intimidating for some. Let me offer an alternative. One that I used and works. My Dell P4-2Gig originally came with Win2K which I hated from day one. I wanted my old trusty Win98SE and DOS back for much work including Fractint. It is very difficult to install a lower version of windows/DOS after Win2K or XP is already installed. But it can be done, as with your method, or this: Get "Partition Magick" utility. It only costs about $50. from any computer store. Install it. It is very sophisticated in what it does and can do, and is also very user friendly. You don't have to be a techie-geek. With it, you can alter/change/create/delete/modify partitions on your HD without loss of any data! You can create a partition, load DOS or Win98 on it completely isolated from 2000 or XP, and then use the included boot-loader to set up a multiboot system. At boot-up, you can select any OS you want. You can also install Linux on it's own partition for a Linux/Windows/DOS multiboot - which I did on my old P2-300! I did this succesfully (and very easy) and put Win98SE and DOS622 next to Win2K for a triple boot. This was over a year ago when I was researching fractint and optimizing - I found that the P4 chip sucks for fractint or any DOS app. I have since loaded XP on my P4 system and use my P3-733 (Win98SE) for fractint - which works the best. I hope this can help someone. BTW - I do NOT receive any kickbacks from PowerQuest! :) JoTz

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FOTD 25-05-03 (Sapphire Jewel [8])
by Jim Muth 25 May '03

25 May '03

FOTD -- May 25, 2003 (Rating 8) Fractal visionaries and enthusiasts: My e-mail address certainly gets around. This morning I found 26 letters in my e-mailbox, with the word 'jamth' in the subject line. I don't know why the senders do this. Most likely it is an effort to make their ads appear personal, but all it does is make the unwanted ads easier to recognize and delete. I also am seeing more and more nonsense words such as 'tghs df6szzhs' in the subject lines. I assume this is an attempt to defeat the programs that automatically delete e-mail spam. And speaking of spam, I recently saw on the BBC-America channel the original Monty Python skit that inspired the word. Now if only a way could be found to eliminate spam itself. Today's image, which is located in a valley of a distorted bud on the northern fringe of the 'fan' of the may-parent fractal, is striking for the intensity of its colors, especially the blues. I have named it "Sapphire Jewel" accordingly. The unusual shape of the fractal elements alone would rate a 6 or 7. When this is added to the unusually brilliant colors, the sum of the two easily rates the 8. Unlike the past two images, today's is very slow. It takes 43 minutes to render on my machine. Since my machine is an aging clunker, the image will render in considerably less time on most units. And if even the speediest fireball screamer is too slow, the completed GIF image can be found on the internet at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> and downloaded from there. Occasional rain much of the day Saturday here at Fractal Central kept the dynamic duo of fractal cats confined to quarters. The temperature of 59F 15C helped not a bit. Their moods were lighter than expected however. Maybe they're getting used to being unable to go out. The clouds are still hanging around this morning, with a rather dense fog added to make things even more unpleasant for cats. Regardless, I'm ready to have a relaxing day doing pretty much nothing but searching for the next fractal. Until I find it, take care, and enjoy the other images. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Sapphire_Jewel { ; time=0:43:28.30--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+5.30940846654323200/-2.048115157663139\ 00/1197664/1/-82.5/4.63141944379019677e-008 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=32767 inside=0 periodicity=10 colors=000i0zi0z0X0GLLdAfz0zz6yzCyzIyyMyxSyxYyvcyu\ gyumyssysxyosylpyglycgy`cyX_ySVyPSyOQvMQuLQrJQpIQm\ GQlFQiDQgCPdAPc9P`7P_6PX4PV3PS1PQ0OO0OM0OJ0OI0OF0O\ D0OA0O90SC1VF7YID`LIcOOfQTiS_lVdoYir`oucuxfzzizzjz\ zizygzvfzufyrdxpcxmcvlaui`ug`sf_rcYpaXp_XoYVmVTmTT\ lQSjPQjOQmSYpXcr`iudoviuymzzrzvpzsozpozmmzimzflzcl\ y`jxYjxTivQguOguLfsGfrDdrAdp7co4co1Vm0Ol0Gj09j0Ci1\ Di4Gg6Ig9LfAMfDPdFQdITcJVcLXcJVaJVaIVaIVaIVaGVaGVa\ FVaFVaFVaDVaDV`CV`CV`CV`AV`AV`9V`9V`9V`7V`7V`7V`AX\ _CY_D_YG`YIaXJcXMdVOfVPgTSiTTjSVlSYmQ_oQ`pPcrPdsOf\ uOivMjxMlyLmzLiyIfxGcvD_uCXsATr7Pp6Mo4Jm1Fl0Cj09i0\ 4g01f00d00c00d04d09d0Dd1If6Mf9QfCVfF_gJcgMggPlgSvJ\ OrVSsJQu6Pp0Op0Mm0Lj3Jf6Ic9G`CFXDDTGCQJAOMAJP9GS7D\ V69X46_33a10d00g00j00l00j10i41g74fA9dDCdGFcJJaMM`P\ Q_STYVXYYYV`YSa_Qc_Od`Mf`JgaIiaFlcDmcAod9pd6rf4sf1\ ug0xg0yi0zi0zj0zj0zj0zi0z } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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[Fractint] Fractint Multi-Boot Menu On Win98, Win2K, and WinXp Revisited
by Tony Parker 24 May '03

24 May '03

Some member of this list e-mailed me recently for information on Multiboot Menus for Win98, Win2K, and WinXP. Here's an e-mail message that I posted posted to this list Monday, November 25, 2002. Further to the recent message traffic about the problems that some members of this list have had trying to load Fractint in a Dos Box on Win98, Win2K or WinXp, I've gone and done some research on the matter. Here are my results of some tweaking and "kludgeing" on my own systems. I have installed Multi-Boot Menus on my 2 Win98 Work Stations and a Multiboot DOS/Win2000/WinXP Menu system on my Win2000 Profesional Work Station and they all work fine. The basic idea is to install a simple Multiboot Menu System that can allow you to boot and reboot between MSDOS and Win2000/WinXp on the same hard drive FAT32 File System partition. This method requires that you have access to the various files found on a working Win95/98 system and on a working Win2000/Xp sytem. You may also need A Win95/98 and a Win2000/WinXp Installation CD-ROM. It is also understood that you have installed the Win2000/WinXp system on a FAT32 File system. It is possible to install a multiboot system that can span different File systems like FAT16, FAT32, and NTFS, on different partitions, but that job is even more complicated, and will only be dealt with in a later article if Fractint E-Group members ask me to. 1.) Floppy Boot Disk Method - Several Fractint E-Group members have already discussed this Floppy Boot Disk method of booting a Win2000/WinXp system with a DOS boot Floppy disk. Hopefully you installed Win2K or WinXp on a FAT32 file system. All my multiboot menus assume that you installed Windows 2000 or WinXp with a FAT32 files system. A simple Win98 Boot Floppy disk can be generated from the Win98 Format dialog box when you check the "Copy system files". That method works ok, but I found that I needed more resources so I created autoexec.bat and config.sys files, and I edited the msdos.sys file to suit my requirements. The boot disk method works fine, but I was always misplacing the boot disk, and I felt that having everything accessible from a boot menu on my hard drive was neater and quicker. 2.) Multiboot Hard Drive Menu - I had once used a MultiBoot Menu on my old MSDOS & Win3.xx system, so I figured that the same type of menu system on a Win98, Win2K, or WinXp system ought to be feasible. On Win 95/98 you have to edit the Msdos.sys file to allow for a multiboot menu and some other features that will speed up the loading of Windows as well. You also have to edit your autoexec.bat and config.sys files to create your different sytems configurations. You need to download the file olddos.exe from microsoft.com, or find the "tools\oldmsdos\" sub-directory on your Win95/98 CDROM. You should copy those files to the Windows\command\ subdirectory. I have found such features like smartdrv.exe really enhance fractint's performance. You will also need to locate himem.sys, and emm386.exe in either "c:\windows", "c:\windows\command" or the "tools\oldmsdos\" sub-directory in the Windows95/98 installation CD-ROM. Once you located these files then it's not a difficult task to edit your msdos.sys, config.sys, and autoexec.bat files to give you a multiboot system that will boot both Windows95/98 and Dos 7.01. I think I've already provided fairly complete instructions and examples how to do this in earlier e-mails to this E-Group, but if anybody wants, I can repost them again to this e-group. 3.) Once you've gotten a multiboot system to work on a Win95/98 system that let's you boot to either DOS or Win95/98, you're about half of the way to a multiboot system on a Win2000 or WinXp system. Make sure that you have a Win95/98 Set-up disk. Go to Start > Settings > Control Panel > Add/Remove Programs Properties > Startup Disk > and click on the Create Disk radial button, to create a Win98/Dos 7.01 a Start-up disk. Create and Label this disk as you will need this disk later on. 4.) Now we are ready to start work on our Win2000 and/or WinXp system. We will also need to make a complete set of the Win2000 Startup Disks, and Emergency repair disk. To make the Win200 startup disks, go to the "\BOOTDISK\" subdirectory on our Win2000 Installation CDROM, and load makeboot32.exe. If you have followed the directions properly you should have 4 Win2000 Startup disks. Label them and put them aside. You will definitely need them later. To make a Win2000 "Emergency Repair Disk" go to Start > Programs > Accessories > System Tools > Backup and click the "Emergency Repair Disk" radial button. Check the registry backup feature, and insert a floppy disk, and click "OK". Label and save the disk, you will need it later on in this process. WARNING: Do not try this "Tweak" until you have created the 4 Win2000/WinXp Startup Disks, and the Win2000/WinXp Emergency Repair disk. 5.) On your Windows 2000 system, create c:\dos, c:\windows and a c:\windows\command subdirectories even though you may not want to install a full blown windows95/98. Now copy or transfer all the files that you will need for launching DOS 7.01 files that you have located on your Win95/98 system in c:\windows, c:\windows\command\, "olddos.exe, and "oldmsdos". Copy your working Win95/98 multi-boot menu files, i.e, msdos.sys, autoexec.bat, and config.sys onto a floppy and label it. 6.) On your Windows 2000 either create or edit a file "boot.ini" thusly: [boot loader] timeout=15 default=multi(0)disk(0)rdisk(0)partition(1)\WINNT [operating systems] multi(0)disk(0)rdisk(0)partition(1)\WINNT="Microsoft Windows 2000 Professional" ' /fastdetect C:\bootsect.dos="Msdos 7.01" /win95dos I've tried to make this Win200 boot menu really simple, but once you get his working you can tweak it and make it as fancy as you want. 7.) Now comes the really serious stuff. Do not proceed any further until you have really created your Win2000 startup disks AS WELL AS your Win2000 Emergency Repair Disk, otherwise you will really have a mess on your hands. 8.) Insert your Windows95/98 Startup Floppy Disk into the Win2000 System , and go to Start > Shutdown > make sure you have selected Restart before you click "OK". You will now boot from your Floppy a win95/98 DOS 7.01system. >From the DOS 7.01 command line, type in the DOS command "SYS c:". You will then be copying your vanilla dos system to the Win2000 system. Now enter the following from the DOS command line. Debug<ENTER> L 100 2 0 1<ENTER> N C:\BOOTSECT.DOS<ENTER> R BX<ENTER> 0<ENTER> R CX<ENTER> 200<ENTER> W<ENTER> Q<ENTER> Congratulations! You have just created a special file called bootsect.dos. For the really courageous I have attached a file "bsread.txt" which allows you an automated method of creating this file. You will need to have the file "bsread.txt" copied onto the c: drive of your C; drive. For an automated creation of the "bootsect.dos" file, enter the following command. "c:\debug <bsread.txt<ENTER>" 9.) Remove the Win95/98 Startup floppy and enter "CTL, ALT, DELETE" simultaneously to reboot your system. The PC will now boot a vanilla DOS system. Now insert the floppy to which you had previously copied your edited "msdos.sys", "autoexec.bat", and "config.sys" files from your Win95/98 multi boot system in Step 5. Copy "msdos.sys", "autoexec.bat", and "config.sys" files to your C: drive. Remove the floppy. Reboot your system and you will now have your Ms-Dos Multiboot Menu installed on your system. For the system to be able to Multiboot between Win95/Win98/DOS and Win2000WinXp, we have to re-install your Win2000/WinXp boot sector onto your C: drive. 10.) Insert your Win2000 Startup disk and reboot your system with "CTL, ALT, DELETE" and then follow the directions. You will have to insert the other 3 Win2000 Startup Disks to enable the Win2000 Startup system. When you finally reach Windows 2000 Setup Menu, enter "R". At the next menu enter "R" again. At the next menu enter "F". When the Menu asks you for the Emergency Repair disk, ENTER, and then insert the Emergency repair disk, and follow the directions until the end. 11.) Remove the floppy disk, and reboot. If everything was done correctly, you will first see the Windows 2000/XP Multiboot menu giving you a choice between booting Windows 200 or DOS, then, if you select DOS, you will then see your DOS Multiboot menu. To switch back and forth between systems simply shutdown and reboot and then select the appropriate menu option(s). Hope you got it all to work for you! Just to make life easier for you all. I've attached my msdos.sys, autoexec.bat, config.sys, boot.ini, and bsread.txt, which you will need to edit and change to work on your system. Let me know if any of this has worked for you! All the best, Tony

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Re: Fractint Digest, Vol 3, Issue 16
by JackOTradez 24 May '03

24 May '03

I gotta hand it to you, Al - some of those new multifractal images are ACE+ way-cool! The "Underground Mandelbrot" is my favie. I am not able to generate the "Mountain Garden" however - it gets about a third done then the whole rest of it is solid blue. I think this is that "bug" everyone's been talking about. BTW - Xfractint runs in Linux. When you install it on a system which already has windoze, you are given the option of setting up a multiboot configuration. But I'm sure Natalie knew that <g>. JoTz

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Multifractal_1
by Albrecht.Niekamp＠t-online.de 24 May '03

24 May '03

Hi, not many words today.Iïm still testing. Fractal greetings, Al. ---------------------------------start-par------------------------------- Explosion { ; Albrecht Niekamp May, 03 ; Time 0.05.03.03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult240.frm formulaname=multifractal_1 ismand=y function=exp/sin/exp/exp passes=t center-mag=-0.06119726357949132/-2.00383650309781000/2422.48/1/100.00000\ 0000004448/-9.79223646613291976e-013 params=-0.1738944669942329/-0.3000579851680044/384.00004/2048.1133/768.0\ 0008/768.00128/1024.00256/1536.01536/18922.01/10.32 float=y maxiter=2048 inside=maxiter outside=tdis logmap=yes periodicity=0 rseed=-2436 colors=200O00<14>q00<3>x00z00x00<24>C00A00800<3>000<25>iiijjjlll<3>sss<2\ 5>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<24>o\ iQqjRslS<3>zsX<25>CB7A96875<3>000400<8>M00 } ----------------------------start-frm------------------------------------- FRM:Multifractal_1 { ; Albrecht Niekamp 240503 ;only integers as first input, second input 5 digits to the right ;real(p2) factor1, border1 ;imag(p2) (-)bailout,input bas.frm1_2digits input bas.frm2_2digits ;real(p3) maxiter2, border2-in ;imag(p3) factor2, border2-out ;real(p4) maxiter3, border3-in ;imag(p4) factor3, border3-out ;real(p5) 1digit_shape only 5digits: shape,out1,out2,in1,in2 ; 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset (not shape) <0_no in/out1 ; optional basic frm2 digit1: 1_out1 2_out2 3_both +5_shape ; digit2: 1_in1 2_in2 3_both ;imag(p5) digit1 : many_mods multipl.shutoff 1_in/out1 2_in/out2 3_both ; digit2 :1_iter1reset 2_iter2reset 3_both +5_shape effect ; input2: Number of sides 2 digits (many_mods L.Allison) ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=d<0 if (da) d=-d endif ba=trunc(d) d=round((d-ba)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) mi2=trunc(d) b2=(d-mi2)*100000 ; d=imag(p3) fac2=trunc(d) ob2=(d-fac2)*100000 ; d=real(p4) mi3=trunc(d) b3=(d-mi3)*100000 ; d=imag(p4) fac3=trunc(d) ob3=(d-fac3)*100000 ; da=real(p5) t=da<0 if (t) da=-da endif start=2-t dd=trunc(da) da=round((da-dd)*100) if (dd<5) start=0 vb=(dd==3)+(dd==4) else d=trunc(dd/10000) vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) or1=d>5 d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) dd=dd-d*1000 d=trunc(dd/100) or2=d>5 d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) dd=dd-d*100 d=trunc(dd/10) inr1=d>5 d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) dd=dd-10*d d=trunc(dd) inr2=d>5 d=d-5*inr2 v3=(d==3) v4=(d==4) d2=(d==2)+(d==4) endif ; d=trunc(da/10) da=da-10*d ab=d>=5 d=d-5*ab bb1=(d==1) bb2=(d==2) ab1=(da==1) ab2=(da==2) ; d=imag(p5) dd=trunc(d) mm=round((d-dd)*100) da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=dd>=5 dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) if (ismand) if (vb) c=0.4*log(sqr(pixel^mm)) z=pixel else c=pixel z=0 endif else c=p1 z=pixel endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn4(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z2=z*z z=z2*z2+(p6+u)*z2+c else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif bo=|z| If (wo) t=t+1 if (bo>b1) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else z=pixel c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2&&bo<ob2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3&&bo<ob3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif bo<=ba } ------------------------------------end-------------------------------

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FOTD 23-05-03 (Isolated Minibrot [8])
by Jim Muth 24 May '03

24 May '03

FOTD -- May 23, 2003 (Rating 8) Fractal visionaries and enthusiasts: Today's fractal is different enough to rate an 8. It has a midget in it, which is the center of attention, but the midget is not at the center of the image. Most surprising, today's 'exceptional' image is merely a step on the way to the real image, which lies invisibly buried in today's scene, and will rate a 9, which equals 'one of the best of all time', when it appears tomorrow. Today's image is named "Isolated Minibrot" for obvious reasons. Most of today's scene consists of 'inside' material made visible by the < bof60 > fill. The areas of radiating bands of color are 'outside' areas that are normally flat, but have been given interest by the < atan > option. When rendered in the normal manner, the scene consists of large areas of black accented by scattered splotches that at one point in the frame appear to vaguely outline a Mandeloid 'atom'. As fractals go in this era of multi-layered and transformed images, today's image might not be considered worth its rating of an exceptional 8. But after trying those options, which are features of another program and draw images that may or may not be considered real fractals, I rejected them, and decided to stick with the more traditional methods of rendering my fractals. When today's image is compared with only my past FOTD images, I feel that it does indeed rate an 8. Whether I have become an old fractal fogy is up to the individual to decide. Today's FOTD image is fast, one of the fastest of all time. It renders in a zippy 38 seconds despite the fact that it consists mostly of trapped points. In today's case, the download will take somewhat longer than the time required to render the image from the parameter file. But as always, the download is available on the internet at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The clouds were plentiful here at Fractal Central on Thursday, but the rain held off, the temperature reached an acceptable 61F 16C, and the dynamically fractal cats managed a pleasant after- noon in the too-tall grass of the yard. When a robin swooped carelessly low, Tippy took a swipe at it, but I fear the duo's bird-catching days are pretty much behind them. Tippy missed the bird by a good meter. I guess the only birds they will eat from now on will be processed turkeys. Rain is in the picture again today, as is a bit of work for me. Hopefully, the fractal duo will resign themselves to a day by the window. Until next time and next FOTD, take care, and be at ease when surrounded by aggressive fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Isolated_Minibrot { ; time=0:00:38.74--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+0.09896836297685904/+0.030531986286429\ 95/284.6369/1/87.5/2.8e-012 params=-10/-1.1/-1/-11\ /0/525/0/0 float=y maxiter=410 inside=bof60 outside=atan periodicity=10 colors=000fRwhSwiTxjUxkWymXynYzoZzp_znZymZylZykZyj\ ZyiZxhZxfYxeYxdYxcYwbYwaYw`YwZXwYXvXXvWXvVXvUXvTXu\ RWuQWuPWuOWuNWtMWtLWtJVtIVtHVsGVsFVsEVsDVsCVsGYpJ_\ mMakPdhSffWhcZk`amZdoWgpUhmThjThgTheSicSiaSi_SiYRi\ WRjURjSQjPQiNQhLQgKOfKMeJKdJJcIHbIFaHD`HC_GAZG8YG6\ XH5WI3VJ1UK0TL2SM3RN5QO6PP7OQ9NRAMSBMTDMUEMVFNWHNX\ IOYKOZLO_MP`OPaPPjQQlSQnTQoURqWRsXRtYPq_Oo`MlaLjbK\ gcIedHbeG`fEYhDWiBTjARk9Ol7Mm6Jn5Ho7In8In9InAImBIm\ CImDImFIlGIlHIlIIlJIkKIkLIkMIkOIjPIjQIjRIjSIiTIiUI\ iVIiXJhYJhZJh_Jg`JgaJgbJgdJfeJffJfgJfhJeiJejJekJem\ JdnJdoJdpJdqJcrJcsJctJcoPXkURg_LcdE_j8Wo2Un4Sn6Rn7\ Pn9NnAMnCKnDImFHmHFmIDmKCmLAmN9mOBlPClQDkREkSGjSHj\ TIiUJiVKhVMhWNgXOgYPfYQfZSe_Te`Ud`VdaXcbYccZbc_bd`\ aebafc`fd`ge_hf_ihZiiZjjYkkYllYlmZmmZmmZmmZnmZnmZn\ m_om_on_on_pn_pn_pn`qn`qn`qn`rn`ro`roasoasoasoatoa\ toatobupbupbupbvpbvpbvpcw } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 24-05-03 (Return to the handle [9])
by Jim Muth 24 May '03

24 May '03

FOTD -- May 24, 2003 (Rating 9) Fractal visionaries and enthusiasts: Fractals rating a 9 are rare creatures indeed, but today, with perhaps a bit of stretching, we have one that I can rate at a 9. I have named it "Return to the Handle" because it is a huge blow-up of a tiny part of yesterday's image, which is located in the narrowest part of the neck of the fan element of the Mayparent fractal. In yesterday's 'isolated' image, notice the tiny dot just beyond the southeast edge of the large scalloped element below the midget. When blown up, this dot proves to be an entire universe, and today's image is a mere speck in that tiny universe. I now must make a confession. To create today's image I made a change in the formula of the Mayparent. I reduced to bailout radius to 30, which changed the original skeletal image into a fully-developed one marginally worth the 9 rating it was given. To have an image that rates a 9 is good, to have an image that rates a 9 and renders in a mere 40 seconds is great. Rarely have we seen such a combined value in the world of fractals. Those choosing to take advantage of the value will render the image from the attached parameter file. Those who choose to download the finished GIF image will do almost as well. The download is available at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Rain fell most all day Friday here at Fractal Central; the fractal cats sulked most of the day. With hopeful hearts, they checked the outdoors several times and from all doors, but regardless of which door they looked out from, the rain was there. They finally satisfied themselves with several treats of tuna, and settled grudgingly into their beds. This morning is once again wet; I suppose the duo will once again be sulky. As for me, it's the beginning of a supposed 3-day holiday, but from the amount of work to be done, one would never guess it. Until next FOTD, take care, and see you soon. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ ReturnToTheHandle { ; time=0:00:40.04--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+0.09658172776961572/+0.029025664502679\ 04/5.431823e+008/1/-178/2.40360522547888866e-007 params=-10/-1.1/-1/-11/0/-70/0/0 float=y maxiter=410 inside=bof60 outside=atan periodicity=9 colors=000GMUHNTIOSJPQKQPLROMSNNTLOUKPVJQWHRXGSYFT\ ZDU_CV`BVaAV`CU_EUZGTYHTXJSWLRVMRUOQTQQSRPRTOQVOPW\ NOYNN_MM`LLbLKdKJeKIgJHiJHjKIkKIkKJlKJlKKlKKmKLmKL\ mKLnKMnKMnKNoKNoKOoKOpKOpKPpKPqKQqKQqKRrKRrKSrKSsK\ SsKTsKTtKUtKUtKVuKVuKVuQXpVZl``gebcjd_pfVuhRziNveM\ sbLoZLlWKiSJePJbLI_IHWEHTBGO7GQ8GR9GS9GTAGVBGWBGXC\ GYDG_DG`EGaFGbFGdGGeHGfHGgIGiJGjJGkKGlLGnLGoMGpNGq\ NGsOGtPGuPGvQGwQGvRHvSIvTJuUKuULuVMtWNtXOtXPtYPsZQ\ s_Rs_Sr`TraUrbVqcWqcXqdYqeYpfZpf_pg`ohaoiboicnjdnk\ enlfnlfnmfmngmogmphlqhlrilrilriksjksjksjjsjjsjjsji\ tjitjitjhtjhtjhtjhujgujgujgujfujfujfvkevkevkevkdvk\ dvkdwkdwkcwkcwkcwkbwkbxkbxkaxkaxkaxkaxkbulbslbqmco\ mcmnckndiodfoddoebpe`peZqeXqfVrfTrfQrgOsgMsgKthIth\ GuhEuf9whCuiFtjHslKqmMpnPooSmqUlrXksZitahvdgwfexid\ yjcwidugesffqdgochmahk_iiZjgXkeWlcUmaTmbSkcSicSgdR\ edRdeRbdAacD`cE_cFYcHXcIW } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Missing a Detail (Multifractal)
by Martin Dove 23 May '03

23 May '03

Hello List! I downloaded 'lhs_mf01.par' from http://www.fractalus.com/sylvie/lsmultifrace.htm. When I run any of the entries from 'lhs_mf01.par' Fractint (version 20) returns the following error: Oops. I couldn't understand the argument: outside=tdis I'm either missing some bit of software, or have mis-configured something. Can anyone help with this? tia, Martin

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Re: [Fractint] Missing a Detail (Multifractal)
by Fr. Jim Lacasse 23 May '03

23 May '03

I also tried to run one of these and got the same error message. So I also need help. Jim >>> mjdove(a)visi.com 05/23/03 06:38AM >>> Hello List! I downloaded 'lhs_mf01.par' from http://www.fractalus.com/sylvie/lsmultifrace.htm. When I run any of the entries from 'lhs_mf01.par' Fractint (version 20) returns the following error: Oops. I couldn't understand the argument: outside=tdis I'm either missing some bit of software, or have mis-configured something. Can anyone help with this? tia, Martin _______________________________________________ Fractint mailing list Fractint(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint

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Multifractal_1
by Albrecht.Niekamp＠t-online.de 23 May '03

23 May '03

Hi, Iïm sorry, I included a wrong test version in my posting, only a small error, but the rendering is different. So please use this one. Thanks. Fractal Greetings, Al. -------------------------------------start-par---------------------------- The_basket { ; Albrecht Niekamp May, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult240.frm formulaname=multifractal_1 ismand=y function=exp/exp/exp/exp passes=t center-mag=-2.22045e-016/-0.31207/0.6666667/1/-90/3.88578058618804789e-0\ 16 params=-0.1738944669942329/-0.3000579851680044/384.00004/2048.1133/768.0\ 0008/768.00128/768.00256/1536.0205/18922.01/0.16 float=y maxiter=2048 inside=maxiter outside=tdis logmap=yes periodicity=0 rseed=-2436 colors=200999<3>222000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<22\ >keOmgPoiQqjRslSunT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C0\ 0A00800<3>000<23>eeegggiiijjjlllnnn<2>sss<25>BBB } Gallery { ; Time 1.50.48.79 ; Albrecht Niekamp May, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult240.frm formulaname=multifractal_1 ismand=y function=exp/exp/exp/exp passes=t center-mag=0.981945/-0.000647375/18.72659/1/-90/-1.23373533611470521e-01\ 4 params=-0.1738944669942329/-0.3000579851680044/384.00004/2048.1133/768.0\ 0008/768.00128/1024.00256/1536.01024/18922.01/0.32 float=y maxiter=2048 inside=maxiter outside=tdis logmap=yes periodicity=0 rseed=-2436 colors=200BBB<3>444222000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<22\ >keOmgPoiQqjRslSunT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C0\ 0A00800<3>000<23>eeegggiiijjjlllnnn<2>sss<24>DDD } The_cave2 { ; ; Albrecht Niekamp May, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult240.frm formulaname=multifractal_1 ismand=y function=exp/sin/exp/exp passes=t center-mag=-3.05311e-016/-2.01313/13.33333 params=-0.1738944669942329/-0.3000579851680044/384.00004/2048.1133/768.0\ 0008/768.00128/1024.00256/1536.01536/18922.01/10.32 float=y maxiter=2048 inside=maxiter outside=tdis logmap=yes periodicity=0 rseed=-2436 colors=200M00<5>A00<4>000<23>eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222\ 000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<22>keOmgPoiQqjRslSunT\ <2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<19>O00 } Ice_art { ; Albrecht Niekamp May, 03 ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult240.frm formulaname=multifractal_1 ismand=y function=exp/exp/exp/exp passes=t center-mag=+0.96493194144406380/-0.02344562282263514/209.9394/1/-90/-1.2\ 3373533611470521e-014 params=-0.1738944669942329/-0.3000579851680044/384.00004/2048.1133/768.0\ 0008/768.00128/1024.00256/1536.01024/18922.01/0.32 float=y maxiter=2048 inside=maxiter outside=tdis logmap=5 periodicity=0 rseed=-2436 colors=200BBB<3>444222000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<22\ >keOmgPoiQqjRslSunT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C0\ 0A00800<3>000<23>eeegggiiijjjlllnnn<2>sss<24>DDD } -----------------------------------------start-frm------------------------- FRM:Multifractal_1 { ; Albrecht Niekamp 220503 ;only integers as first input, second input 5 digits to the right ;real(p2) factor1, border1 ;imag(p2) (-)bailout,input bas.frm1_2digits input bas.frm2_2digits ;real(p3) maxiter2, border2-in ;imag(p3) factor2, border2-out ;real(p4) maxiter3, border3-in ;imag(p4) factor3, border3-out ;real(p5) 1digit_shape only 5digits: shape,out1,out2,in1,in2 ; 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset (not shape) <0_no in/out1 ; optional basic frm2 digit1: 1_out1 2_out2 3_both +5_shape ; digit2: 1_in1 2_in2 3_both ;imag(p5) digit1 : many_mods multipl.shutoff 1_in/out1 2_in/out2 3_both ; digit2 :1_iter1reset 2_iter2reset 3_both +5_shape effect ; input2: Number of sides 2 digits (many_mods L.Allison) ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=d<0 if (da) d=-d endif ba=trunc(d) d=round((d-ba)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) mi2=trunc(d) b2=(d-mi2)*100000 ; d=imag(p3) fac2=trunc(d) ob2=(d-fac2)*100000 ; d=real(p4) mi3=trunc(d) b3=(d-mi3)*100000 ; d=imag(p4) fac3=trunc(d) ob3=(d-fac3)*100000 ; da=real(p5) t=da<0 if (t) da=-da endif start=2-t dd=trunc(da) da=round((da-dd)*100) if (dd<5) start=0 vb=(dd==3)+(dd==4) else d=trunc(dd/10000) vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) or1=d>5 d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) dd=dd-d*1000 d=trunc(dd/100) or2=d>5 d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) dd=dd-d*100 d=trunc(dd/10) inr1=d>5 d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) dd=dd-10*d d=trunc(dd) inr2=d>5 d=d-5*inr2 v3=(d==3) v4=(d==4) d2=(d==2)+(d==4) endif ; d=trunc(da/10) da=da-10*d ab=d>=5 d=d-5*ab bb1=(d==1) bb2=(d==2) ab1=(da==1) ab2=(da==2) ; d=imag(p5) dd=trunc(d) mm=round((d-dd)*100) da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=dd>=5 dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) if (ismand) if (vb) c=0.4*log(sqr(pixel^mm)) z=z*le else c=pixel z=0 endif else c=p1 z=pixel endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn4(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z2=z*z z=z2*z2+(p6+u)*z2+c else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif bo=|z| If (wo) t=t+1 if (bo>b1) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else z=pixel c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2&&bo<ob2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3&&bo<ob3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif bo<=ba } ----------------------------------------------------end--------------------- ---------------------------

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FOTD 22-05-03 (Fractal Claws [8])
by Jim Muth 22 May '03

22 May '03

FOTD -- May 22, 2003 (Rating 8) Fractal visionaries and enthusiasts: Today's image is what yesterday's should have been. Looking at yesterday's image one day later, I see that I over-rated it. It now looks more like a 6 than a 7. But regardless of the true value of yesterday's image, today's image, which mirror's yesterday's, rates a true 8. In fact, if I had more time to color today's image, I might have been able to work it into a 9-rater. As it is, the colors are a bit gaudy, a flaw which costs one rating point. Today's image is located on the northwest edge of the fan, where the fan blends into the surrounding area. Like yesterday's image, today's lies in a vague spiral arrangement in a kind of pseudo-valley. I studied the image for several minutes before I noticed the claw-like features and named it "Fractal Claws". These claws are not to be confused with Santa Claus, whose reality lies somewhere in the range of today's image. In both cases, we can see the picture but not the object. The always-annoying render time of today's image is 15 minutes on my machine, but can be bypassed by letting Paul and Scott do the rendering and going to one of their web sites to view the image. The URL of Paul's site is: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's site is at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The all-day rain here at Fractal Central on Wednesday made the fractal cats very unhappy. The temperature of 55F 13C made them even more unhappy. They spent a few minutes under the cover of the porch roof, but soon realized that a pleasant afternoon in the yard was simply not going to happen. They consoled them- selves by sleeping. Today promises more of the same, and in addition, I have more work to do. So until next FOTD, take care, and is today's fractal as real as Santa? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Claws { ; time=0:15:34.54--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+4.19356285882042800/-1.852233346795663\ 00/4434460/1/-2.5/2.4608337104159439e-009 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=2400 inside=0 logmap=267 periodicity=10 colors=000j`hiaihbihbigcjfdjfdjeejdfkdfkcgkbhlbhla\ il`jl`jm_kmZlmZlnYmnXnnUpmXnn_lobjpehqgfrjdsmbtp`u\ sZvx_zuYwsWuqVroTpmSnkQkiPigNgeLdcKbaI__HYYFWWETUC\ RTAOSBPRBQQBRQBSPBTOBUNBVNBWMBXLBYKBZKB_JB`IBaHBbH\ BbGBcFBdEBeEBfDBgCBhBBiBBjABk9Bl8Bm8Bn7Bo6Bp6Bp9Fq\ CIqELqHOqJRqMUrPXrR_rUbrWerVfqUgqThqSiqRjqQjqPkqOl\ qNmqMnqLnqKoqKpqJqqIrqHrqGsqFtrEusDvtCvuBwvAxw9yx8\ zyAzz6tk5ne4h_2bU1XO0SIDZJQeKblLnsMmqNmoNmmOmlOmjO\ mhPlfPlePlcQlaQl_RlZRkXRkVSkTSkSSkQTkOTkMUjLUjJUjH\ VjFVjEVjCWiAWi8Xi7Xi5Xi3Yi1Yi0Yg1Xf2Wd2Wc3Vb3Va4U`\ 4U_5T_5TY6SX6SW7RV8QU8QT9PS9PRAOQAOPBNOBNNCMMCMLDL\ KDLKJJRPHYUFd_DhbCkdBn`BpWBsSAuNAxJAzFAxGGwGLuGQtG\ VrG_qHeoHjnHolHtkHyjIxiJxhJwgKwfKveLvdMueMugNuiNtk\ OtmPsoPsqQrsQruRqwSqxSqyTpzTpzUozVozVnzWnzWkzWnzFq\ zHpzIozJnzLnzMmzNlzOlzQkzRjzSjzUizVhzWhzXgzZfz_fz`\ ezbdzcdzdczebzgbzhazi`zj` } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] pixel bug
by Mark Christenson 22 May '03

22 May '03

At 10:24 PM 5/20/03 -0600, Lee wrote: >This behaves differently than periodicity checking. Once the bug occurs, >EVERY pixel is returned the same from that pixel on until the end of the >image. If you change passes mode or image resolution, every pixel in >the new image will be the same. If you do a save immediately upon >hitting the bad pixel (there may only be 1 or 2 such pixels in the whole >image!), exit fractint, and then restart with the saved image, the image >will continue normally. Hmmm. That *is* an odd one. Good luck. I wonder if a pointer is getting trashed. Are any (user-variable) parameters altered? - Bud

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FOTD 21-05-03 (Mandelbrot with Aura [7])
by Jim Muth 21 May '03

21 May '03

FOTD -- May 21, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today's curiously festive scene is located right at the top of the 'fan' feature of the May parent fractal. In this area there are many pseudo-valleys with randomly shaped pseudo-buds. These almost-valleys and buds are surrounded and filled not by featureless 'inside' areas, but by higher-iteration areas. Today's image is located in the interior of one of these almost-buds. I have named the image "Mandelbrot with Aura". The blue glow surrounding the central pink area inspired the name. The rating of 7 equals above-average, though I have long since forgotten exactly what an 'average' FOTD fractal should look like. The render time of 7 minutes is also average, and if the internet is running as it should, the download of the completed GIF image will take an average minute or so. The download can be found by visiting Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Perfect weather on Tuesday here at Fractal Central produced perfect cats. The temperature of 74F 23C gave them several happy hours in the yard. When the day was finished, they settled into their beds to sleep peacefully. This morning it is raining. The cats will not be happy. For me, it will be another day filled with work. Until the next FOTD appears in 24 hours, take care, and keep up with the big- time thinkers. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ MandelbrotWithAura { ; time=0:07:46.57--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip center-mag=+4.93017670069942400/-0.204074678607860\ 70/442925.4/1/102.5/3.95373518646824351e-009 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=800 inside=0 logmap=137 periodicity=10 colors=000rXUseUsnUstUqsSppRnoQmlPkkOjhMhgLgdKecJd\ aIb_Ha_Fb_EcaDdcCeeBfgCgiAhk8im6io5iq3is1is0iw3iu6\ js8kqBloDmmGnkJoiLqhOrfQsdTtbWu`YvZ`wXbxVezViyUgxT\ ewTcvSbuS`tRZsRYrQWqQUpPSoPRnOPmONlNMkNKjMIiMGhLFg\ LDfKBgJBfKAeKAdLAcLAbMAaMA`NA_N9ZO9YO9XP9WP9VQ9_M5\ XO7UQ9RRBOTCLUEIWGDYFFXHGWJHUKITMJRNLQPMPQNNSOMTPK\ VRJWSHYTGZUF`VDaXCcYAdZ9f_7g`6ib4ha5jY5lU6nQ6pM6qH\ 7sD7u98w58y18zD7xQ5zP7wO9uNBrMDpLFnKHkJJiILfHNdGPb\ FR_ETYEVWIXULYTOZRR_QU`PXaN_bMbdKeeJifIlgGphFsiDwj\ CzkByiEugHqfJndMkbPhaRe_UbZWZXZWVaUUcQSfNQiKPkHNnG\ JuFLrFMpEOmEPkDRhDSfCUcCVaBXZBYXA_UA`S9bP9cN8eK8fI\ 7hF7iD4lA7jBAhCCfDFdEIbFK`GNZHPXISVJVTKXRL_PMbNNdL\ OgJPiHQlFRoDSqBTt9Uy6Tv7Vt8Wq9Xo9YpBXpCXpDXpEWpFWp\ GWpIVpJVqKVqLUqMUqNUqPTqQTqRTqSSrTSrUSrWRrXRrYRrZQ\ r_Qr`QpaRnaSmbSmbTmcTmcUmdVmdVmeWmeWmfXmfYmgYmgZmh\ Zmh_mi`mi`mjamofmjamfYmbU } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] Multifractal
by Mark Christenson 21 May '03

21 May '03

At 10:55 PM 5/19/03 -0600, Lee H. Skinner wrote: >Ricardo M. Forno wrote: >>> Hi! >>I'm curious. How do you know that a pixel is "buggy"? > >After the showdot hits a buggy pixel, every pixel after that is colored >the same. And the showdot usually slows down as if every pixel had the >value maxiter. And it continues if you change passes or resolutions! >You have to exit fractint and then restart it. I've not seen it in >other than the multifractal formula. I'm told it only happens at >1600x1200. So far, no one knows the cause. Maybe I'm barking up the wrong tree, but when I have encountered this it is usually caused by periodicity checking and can be cured by turning it off. What the exact cause is I have no idea. It occurs under certain conditions (hitting a point inside the set, plus some unknown factor) with certain fractal formulas (my "gravijul" being one). Aloha, Bud

2 1

Multifractal
by Albrecht.Niekamp＠t-online.de 20 May '03

20 May '03

Hi, here are 3 more zooms with into the easter-eggs image with different settings. Fractal greetings, Al. --------------------------start-par---------------------------------------- Fractal-central { ; Time 0.39.19.50 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=cosxx/exp/exp passes=t center-mag=-1.57408/0.154265/15.99346/1/95/1.31075705844807544e-014 params=-0.8940855128635518/0.8105868709372235/384.00001/256.1133/4094.00\ 016/768.0003400000001/768.0076800000001/256.01024/18937.52/5 float=y maxiter=3072 inside=maxiter outside=tdis logmap=7 periodicity=0 rseed=-2436 colors=200444222000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<24>oiQqj\ RslS<3>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<2\ 5>iiijjjlll<3>sss<25>BBB999777555 } Wonderland2 { ; Time 0.41.12.14 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=sin/exp/exp passes=t center-mag=-1.59327/0.155944/14.26617/1/95/3.85524945301085609e-014 params=-0.8940855128635518/0.8105868709372235/384.00001/256.1133/4094.00\ 016/768.0003400000001/768.0076800000001/256.01024/18937.52/5 float=y maxiter=3072 inside=maxiter outside=tdis logmap=7 periodicity=0 rseed=-2436 colors=200444222000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<24>oiQqj\ RslS<3>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<2\ 5>iiijjjlll<3>sss<25>BBB999777555 } Warp-nine { ; Time 0.54.00.28 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/exp/exp passes=t center-mag=-1.18936/0.117529/13.33333/1/-85.0000000000000142/3.855249453\ 01085609e-014 params=-0.1738944669942329/-0.3000579851680044/768.00001/256.1133/4094.0\ 0016/768.0003400000001/768.0076800000001/64.01024/18937.52/5 float=y maxiter=3072 inside=maxiter outside=tdis logmap=7 periodicity=0 rseed=-2436 colors=200444222000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<24>oiQqj\ RslS<3>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<2\ 5>iiijjjlll<3>sss<25>BBB999777555 } -----------------------------------------start-frm------------------------- FRM:Multifractal { ; Albrecht Niekamp 13.3.03 ;only integers as first input, second input 5 digits to the right ;real(p2) factor1,border1 ;imag(p2) (-)maxiter1,input bas.frm1_2digits input bas.frm2_2digits ;real(p3) bailout,hyb.mandel: number of sides (Many_mods L.Allison) ;imag(p3) factor2,border2 ;real(p4) maxiter2,factor3 ;imag(p4) border3,maxiter3 ;real(p5) 1digit_shape only 5digits: shape,out1,out2,in1,in2 ; 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset (not shape) <0_no in/out1 ; optional basic frm2: out-nbr 1digit in-nbr 1digit 3_both +5_shape ;imag(p5) 1digit : 1_iter1reset 2_iter2reset 3_both +5_shape effect ; 2digits : many_mods multipl.shutoff +10_in/out1 +20_in/out2 +30_both ; optional input2: frequency_2digits level_2digits amplitude_2digits ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=d<0 if (da) d=-d endif mi1=trunc(d) d=round((d-mi1)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) ba=trunc(d) mm=round((d-ba)*100000) ; d=imag(p3) fac2=trunc(d) b2=(d-fac2)*100000 ; d=real(p4) mi2=trunc(d) fac3=round((d-mi2)*100000) ; d=imag(p4) b3=trunc(d) mi3=round((d-b3)*100000) ; da=real(p5) t=da<0 if (t) da=-da endif start=2-t dd=trunc(da) if (dd<5) start=0 endif vb=(dd==3)+(dd==4) da=round((da-dd)*100) d=trunc(dd/10000) vb=(d==3)+(d==4)+vb dd=dd-d*10000 d=trunc(dd/1000) or1=d>5 d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) dd=dd-d*1000 d=trunc(dd/100) or2=d>5 d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) dd=dd-d*100 d=trunc(dd/10) inr1=d>5 d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) dd=dd-10*d d=trunc(dd) inr2=d>5 d=d-5*inr2 v3=(d==3) v4=(d==4) d2=(d==2)+(d==4) d=trunc(da/10) da=da-10*d ab=d>=5 d=d-5*ab bb1=(d==1) bb2=(d==2) dd=da>=5 da=da-5*dd ab=ab+dd ab1=(da==1) ab2=(da==2) ; d=imag(p5) dd=trunc(d) d=round((d-dd)*1000000) le=d>10000 da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=dd>=5 dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) if (le) freq=round((trunc(d/10000))*10) ;frequency_lake effect by S.Gallet d=d-freq*1000 level=(trunc(d/100))/100 ;water level d=d-level*10000 ampl=d/100 ;amplitude of the wave u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) d3=2*q*t rs=2*bo*(dd+flip(1))*t z2=center+(-q-bo*dd-flip(bo))*t z=pixel-z2 d=imag(conj(d3)*z)/imag(conj(d3)*rs) if (d<=level) da=level-d z=z+2*da*(1+ampl*sin(freq*da^0.2))*rs endif z=z+z2 endif if (ismand) if (vb) c=0.4*log(sqr(pixel^mm)) z=z*le else c=z*le+pixel*(le==0) z=0 endif else c=p1 z=z*le+pixel*(le==0) endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn1(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z2=z*z z=z2*z2+(p6+u)*z2+c else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif bo=|z| If (wo) t=t+1 if ((t<mi1)+(bo>b1)) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=z*le+pixel*(le==0) endif else z=z*le+pixel*(le==0) c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif bo<=ba }

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Re: SSTOOLS.INI
by JackOTradez 20 May '03

20 May '03

Martin - SSTOOLS.INI is a parameter/initialization file used by Fractint and the Windoze version, Winfract. A skeleton version is installed by default, but you can edit/modify it in any text editor like notepad. It can be quite usefull. At the DOS prompt, type: FRACTINT MAKEDOC and hit ENTER key. You will create a 600K DOC file that can be read in any text editor or word program. It can be a bit overwhelming at first, but in it is everything, and I mean everything, you ever wanted to know about Fractint. It will also tell you all you need to know about sstools.ini. Here is one of mine: [Fractint] Passes=1 ;drawing method, slowest but most accurate Corners= ;forces corners definition instead of center-mag FillColor=0 ; Float=Yes ;forces floating point calculation - most accurate Inside=0 ;lake color algorithm - black Outside=Iter ;colors as function of iteration Maxiter=2110000000 ;maximum iterations. best image, but takes longer Video=F3 ;video mode from fractint.cfg file Map=MDMA ;color map used LogMap=2 ;coloring algorithm best for deep zooms Savename=x000.gif ;name of gif file if you save it Sound=Off ;no sound when picture finishes Have Fun JoTz

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FOTD 20-05-03 (Vision Obious [8])
by Jim Muth 20 May '03

20 May '03

FOTD -- May 20, 2003 (Rating 8) Fractal visionaries and enthusiasts: Today's image, with its infestation of tiny dot-like areas of chaos, rates an 8. In my opinion at least, it is an exceptional image, perhaps the best yet to come from the May parent fractal. The scene is located in a disconnected area of chaos in the left part of the parent fan, at a point in a vague spiral where two rings almost touch. The trip back out to the surface of the parent will reveal all these features and is quite amusing. But be sure to reset the logmap to 0 before starting the trip. The image's name "Vision Obious" is the name of an old computer animation from the 1980's. I forget who created the original animation, though an internet search will probably turn it up in some library somewhere. For some reason the image reminds me of this animation, though I can't say why. And no, the word 'obious' is not a mis-spelling of 'obvious'. Usually, the better images take the longest time to render, but today's image is an exception to that rule. Not only is it better, it is faster as well. It renders in less than 9 minutes on my Pentium-200 machine. On newer faster machines it will render in even less time. The fastest way of all to view the image is to download it from the internet. It is available on Paul's web site, which can be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather was absolutely perfect here at Fractal Central on Monday. Nothing but blue sky and sun was visible from morning until evening, and the temperature of 72F 22C was all a duo of fractal cats could ask for. Being fractal in nature, the duo took full advantage of the ideal conditions, spending almost six hours alternating between porch and yard. This morning, unfortunately, the clouds in advance of the next rain are already on the horizon. The duo might get in one more pleasant day, but after today, no more sun or dry weather is expected until next week sometime. Regardless of the weather, the work goes on however. And it's time to get busy. So until next FOTD, take care, and everything is ultimately chaotic in nature. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Vision_Obious { ; time=0:08:42.34--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+2.87750361369992900/+1.639815171435586\ 00/1.878522e+008/1/-12.5/-0.000239196080041567671 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=1200 inside=0 logmap=167 periodicity=10 colors=00030440550660771882993AA4BB5CC6DD7EE8FF9GG\ AHHBIKDJMELOFMRGNTHPVIQXJRZMT_OVaQXbSZdU`eWbgYdh_f\ jahkcjmelngnpipqkrsmtsmtomsjkqeio`gmWelRcjMahH_fDY\ eEVcFTaGQ_HAZGHYGNXFTXFZWEdWEjVEpVFrRGsNHuJIuFHtEG\ rDFpDFoCEmBDkBCiACh9Bf9Ad8Ac8f83bD4ZI5VN5SS6OX7Ka7\ Gf8Dj8Hg9LdAOaASZBVWCZTCaQDeNEhKE_woYtmXrlWpkVnjUk\ iSigRgfQeePbdO`cMZaLX`KU_JSZIQYHOXELYCIZ9F_7C`CBaH\ AbMAcR9dW9e`8fe8gj7ho7it6jy6ju8iq9hnAhjCggDgcEf_Gf\ XHeTIeQKdMLdIMcFOcBPb8QbVDNSIOQMPOQPLUQJYQHaRFeRCi\ SAmS8qT6uTKiRYYPkMNyALwCPuETsGWrI_pKbnMflOikQmiSpg\ UtfWweWvdXvdXvcXvbYvaYuaYu`Zu_Zu_ZuXXtVWsDLjTUrQTq\ ORpMQoJOnHNmFLlCKkAIj8Hi80772A73D74G75J76L77O78R6A\ U6BX6CZ6Da6Ed6Fg61h65i69i6DiqtEgkLYcRPeYFgcqimgklY\ mkPojFqiSs3Qt7OuANvDLwGKxJIyMHzPFzSDzVCzYAz`9zc7zf\ XzyJzqnz8izDdzH_zLVzPQzULzYGzaBzeDzFCzIBzKBzNAzPAz\ R9zU9zW8zZ8z`ezdazaYzZVzW } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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SSTOOLS_INI File
by Martin Dove 20 May '03

20 May '03

Hello Fractint List! I have a couple of questions about the sstools.ini file: What is it? How is it created? Can it be edited? Where can I get documentation about it's contents & structure? Where can I get a sample? tia, Martin

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FOTD 19-05-03 (Whirling Dervishly [6])
by JimMuth＠aol.com 19 May '03

19 May '03

FOTD -- May 19, 2003 (Rating 6) Fractal visionaries and enthusiasts: To my eyes, today's vision from the parent fractal appears to be whirling in a clockwise direction, so I named it "Whirling Dervishly". This name has no connection to the remote religious sect whose members work themselves into a religious ecstasy by a spinning dance. It is simply a spontaneous verbalization of my initial impression of the whirling spiral image. The scene is located in the May-parent, deep in the handle of the fan, on the fan side of the point where the handle is pinched off. This area holds numerous areas that are trying to shape themselves into Mandeloid features, though not all of them are making it. Today's scene, with its tiny midget, lies far out on a filament that leads from a proto-Mandeloid bud into a spiral basin. As for rating, today's image is a come-down from yesterday's, but it still rates a little above average 6, whatever average means. The render time of 19 minutes is trying. As always, the wait can be cut to a minute or so by downloading the finished product from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Rain Sunday morning here at Fractal Central left the grass too wet for the tender paws of the dynamic duo. A temperature of 55F 13C made it too chilly for the rest of their bodies. After a brief afternoon check of outdoor conditions, they passed the rest of the day sleeping on the couch. A treat of tuna in the evening brought only a bit of consolation to the otherwise disconsolate duo. Today is starting sunny, and after a very chilly start, promises to be warmer. For the fractal cats this is good news; for me it makes little difference. I will be quite busy most of the day. Until next FOTD in 24 hours, take care, and seek fractal salvation. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Whirling_Dervishly { ; time=0:19:11.24--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+0.34961797486433630/-0.004768779208217\ 24/5.021491e+007/1/180 params=-10/-1.1/-1/-11/0/52\ 5/0/0 float=y maxiter=1700 inside=0 logmap=403 periodicity=10 colors=000V10T33S46Q58P6BN8EM9GLAJJBMIDOGERFFUBEVE\ GWHIXKJYMLZPN_SO`UQ`XSa_TbaVcdWdgYei_el`fobgqdhtei\ wgjyhjvgksgkpfkmflkelheledmbdm_cmYcnVbnSbnPaoMaoI`\ rKaoMalNbiPbfQccSc`TcYVdVXdSYeP_eM`fJbfGfgEcfDafD_\ fDXfCVfCTfCQfBOfBMeBJeAHeAFeACe9Ae98e99cr6e9AdADdA\ GdBJcBMcBPcCSbCVbCZbDabDdaDgaEjaEm`Ep`Fs`FzaDv`Fr`\ Go`Hk`Ig`Jd`L``MX_NU_OQ_PM_RJ_SF_TB_U8_VAYTBXSCWRE\ UQFTOGSNIQMJPLKOJLNINLHOKGPJERHDSGCTFBRC9UEAXFB_GB\ aICdJDgKDjLElNFoOFrPGtQGrPHpPHnPHmPHkOHiOHhOHfOHdN\ HbNHaNI_NIYMIXMIVMITMIRLIQLIOLIMLIUT2LLICDY46l6Bj8\ GhAKgCPeETdGYbIaaKf_JkYLjZNi_Oh_Qh`Sg`TfaUfaUebUdb\ UdcUccUbdUadUaeU`eU_fU_fUZgZYgcYhhXhmWizWizXgwYftZ\ eq_dn_bl`aka`ib_hcZgcXfdWdeVcfUbgTagR_hQZiPYjOSnIX\ jNagSfdXkaapZeoc_nhUoqPnrOmsNltMkuMjvLiwKhxKeyLczM\ azM_zNXzNVzOTzPRzPOzQMzQKzRIzRLzQOzPQzOTzOVzNYzM`z\ MbzLezKgzKhzIhzGTz9Tz7Tz5 } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: MultiFractal
by JackOTradez 19 May '03

19 May '03

There is an excellent file (albiet a few years old) called PHCTUTOR.ZIP which contains a TXT tutorial and a FRM example file. It describes and demonstrates the multifractal concept quite well. I have been investigating it. It uses the IF/THEN/ELSE programing logic and uses an "alternating pixel" technique to superimpose different fractals. I am trying to animate these but it is not so easy so far. I am not sure where to get it - probably one of the Fractint support sites. If U R interested I can just email it to you or post in on my web site for download. JoTz

3 2

More Multifractal
by Chris Curnow 19 May '03

19 May '03

Three more Multifractal pars. I've used your colour map, Albrect, as it *does* seem to go well with this formula. 'Baroque' is odd. The pattern in the dark section is a moire, - it changes with resolution, never seen that before on a Fractint image. Best regards, Chris Curnow Heraldic { ; Version 2002 Patchlevel 2 reset=2002 type=formula formulafile=niekamp.frm formulaname=multifractal ismand=y function=tan/acosh/acos center-mag=0.856619/-0.0199012/2.255223/1/90/-1.23373533611470521e-014 params=0.1591998046815394/-0.2558214056825465/384.00004/256.1121/2048.00\ 016/768.000017/768.01536/512.01025/14289.27/0 float=y maxiter=20048 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200A84<18>keNmgOoiPqjQslRunS<2>zsW<25>CB6A95874653442220000400<23\ >o00q00s00<3>z00<25>C00A00800<3>000<2>554776998BBACCB<16>eedggfiihjjillk\ nnm<2>ssr<25>BBA998776<2>221000011<24>0bn0cp0er<3>0ky<25>09B089067<2>021\ 000210<2>863 } Baroque { ; Version 2002 Patchlevel 2 reset=2002 type=formula formulafile=niekamp.frm formulaname=multifractal ismand=y function=tan/acosh/acos center-mag=0.120964/0.137316/23.19454/1/90/3.88578058618804789e-016 params=0.1591998046815394/-0.2558214056825465/384.00004/256.1121/2048.00\ 016/768.000017/768.01536/512.01025/14289.27/0 float=y maxiter=20048 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200A84<18>keNmgOoiPqjQslRunS<2>zsW<25>CB6A95874653442220000400<23\ >o00q00s00<3>z00<25>C00A00800<3>000<2>554776998BBACCB<16>eedggfiihjjillk\ nnm<2>ssr<25>BBA998776<2>221000011<24>0bn0cp0er<3>0ky<25>09B089067<2>021\ 000210<2>863 } Trophy { ; Version 2002 Patchlevel 2 reset=2002 type=formula formulafile=niekamp.frm formulaname=multifractal ismand=y function=tan/acosh/acos center-mag=0.942923/0.000382602/14.77717/1/90/3.88578058618804789e-016 params=0.1591998046815394/-0.2558214056825465/384.00004/256.1121/2048.00\ 016/768.000017/768.01536/512.01025/14289.27/0 float=y maxiter=20048 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200A84<18>keNmgOoiPqjQslRunS<2>zsW<25>CB6A95874653442220000400<23\ >o00q00s00<3>z00<25>C00A00800<3>000<2>554776998BBACCB<16>eedggfiihjjillk\ nnm<2>ssr<25>BBA998776<2>221000011<24>0bn0cp0er<3>0ky<25>09B089067<2>021\ 000210<2>863 }

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Chaos Theory Explains Origin Of New Moons
by Mark Christenson 18 May '03

18 May '03

Hi folks. Here's a relevant link from another list I belong to. Enjoy! Aloha, Bud >Date: Fri, 16 May 2003 16:36:17 -0500 >From: Ron Baalke <info(a)jpl.nasa.gov> >To: mchris(a)value.net >Subject: Chaos Theory Explains Origin Of New Moons >Organization: NASA Jet Propulsion Laboratory >... >http://www.bris.ac.uk/news/2003/188 > >Chaos theory explains origin of new moons >University of Bristol (United Kingdom) >May 15, 2003 > >The ability to understand how small bodies such as moons switch from orbiting >the Sun to orbiting a planet has long remained one of the outstanding problems of >planetary science. A paper published in Nature on 15 May shows how this >problem has been resolved using chaos theory, enabling scientists to predict >where astronomers might search for new moons orbiting the giant planets. > >... (see link for full text)

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FOTD 18-05-03 (Fractals Forever [8])
by Jim M. 18 May '03

18 May '03

FOTD -- May 18, 2003 (Rating 8) Fractal visionaries and enthusiasts: Sometimes I surprise myself at the way I find midgets in the most unlikely places. I appear to have become a specialist in finding the little things. This does not mean that I consider images with midgets (sometimes called molecules or atoms) at the center to be better in any way than fractals without midgets. I simply have unintentionally become a specialist in one type of fractal. The midget in today's scene was a total surprise. The scene is located in the 'handle' of the fan-shaped element of the parent fractal, in an area that appears to be total non-critical chaos with no chance at all that midgets could lie there. I cannot say what led me to the scene. As is the case with many of my images, I simply got a feeling, and followed my instincts. If anyone were to ask me how I find these midgets, my only answer would be 'I don't know'. Today's image rates an 8. If I had given it more effort, it might have rated a 9, which equals one of the best FOTD images of all time. But an 8 equals an exceptionally good image, and that is nothing to shrug at. When I find an (IMO) exceptionally fine image, it renews my enthusiasm. If this trend continues, I'll be searching for fractals forever. Recognizing this trend, I named today's image "Fractals Forever". Luckily, today's image renders in somewhat less than forever. It renders in 15 minutes, in fact. And even that 15 minute wait can be avoided by visiting one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> and downloading the completed GIF image from there. Clouds and an unusually cool temperature of 50F 10C prevailed Saturday here at Fractal Central. The dynamic duo ventured briefly into the yard in the evening when we returned from the day's adventure and let them out, but the wet grass soon sent them back indoors, where they received their treat of tuna. Today is promising to be a repeat, with the exception that no more all-day antiquing trips are in the works. Until next FOTD, take care, and walk in peace. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractals_Forever { ; time=0:15:12.43--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=-0.33556966157394530/+0.031769085133724\ 92/1.169398e+009/1/172.5/1.49805316335127614e-006 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=2400 inside=0 logmap=229 periodicity=10 colors=000AK89J79I68I58H57G47F36E26D15C05C09E1DF2G\ G2KI3NJ3RK4VM5YN5aO6dQ6hR7lS8oU8sV9xV8vW9tWAsWAqXB\ oXCnXClYDjYEiYEgYFeZGdZGbZH`_I__IY_JW_KV`KT`LR`MQa\ MOaNMaOI_NLaONbOPcORdOTeOWfPYgP_hPaiPcjPfkQhlQjmQl\ nQnoQopQoqRpqRprSqsSqsSprUprWorYor_nranrcmremqglqi\ lqkkqmkqojqqjqsjqtiprioqinohmnhllhkkgjigihghffgefg\ cffbee`ed_ecYdbXdaVd`Uc_ScZRcZPbYObXMbWLaVJaUIaTG`\ SF`RD`QC`QBaRBaRBaRBaRBbSBbSBbSBbSBcSBcTBcTBcTBdTB\ dUBdUBdUBeUBeUBeVBeVBfVBfVBfWBfWBgWBgWBgWBgXBhXBhX\ BhXBhXBgYEfYHfYJeZMdZOdZRc_Tb_Wb_Ya_```c``e_`hZajZ\ amYaoXbrXbtWbwWbyU`vT_tSYrRXpQWnPUlOTjNShMQfLPcKOa\ JM_ILYHKWFIUEHSDGQCEOBDMACJ9AH89F78D66B55944732521\ 3101844F76MA8TEA_HCeKEfLFgLGhMHiMIiMJjNKkNKlOLmOMm\ ONnPOoPPpQQqQQqQRrRSsRTtSUuSVuSVvTUwUTxVSyWRzXQzYP\ zZOzZNzZMzZLzZKzZJzZIzZHzZGzZFzZEzZDzZCzZBzZAzZ9zZ\ 9zZCzZEzZGzZIzZKzZMzZAzZ9 } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 17-05-03 (Four Score and Seven [6])
by Jim M. 17 May '03

17 May '03

FOTD -- May 17, 2003 (Rating 6) Fractal visionaries and enthusiasts: I must be brief again today. The fractal lady is getting impatient for us to set out on the 'antiquing' trip that I somehow got myself roped into. I think the destination is New Oxford, PA. Today's FOTD image is named "Four-score and Seven". I chose this title because of the four prominent basins of chaos that surround the almost-invisible midget at the center, and because of the 7 minutes it takes to render. These coincidences reminded me of a famous speech that was delivered around 140 years ago and opens with the words 'Four score and seven...'. The scene is located on the left edge of the fan, in a disconnected area of chaos slightly inland from the actual edge. It is buried quite deeply, and located not too far from a larger midget. The magnitude of the scene is so large in fact that I added the <mathtolerance> entry to the parameter file to be certain that it renders at the correct magnitude. Since I lacked sufficient time to color the image properly, I could rate it no higher than a 6. But 7 minutes is not too long a time to wait for an image rated at a 6. And the completed GIF image is available as always at the FOTD web sites, which can be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> It rained heavily all day Friday here at F.C., producing flooding and unhappy cats. The temperature of 54F 12C did nothing to help. This morning is once again cloudy, but it is dry, and it is still wet. The cats' moods are yet to be determined. Somehow, I got myself into another day of studying the old worn- out things that others no longer want. It's time to hit the road, so until next time, take care, and see you in 24 hours. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Four-scoreAndSeven { ; time=0:07:24.40--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+1.42863500914334400/+0.523635926654827\ 70/2.351342e+012/1/92.5024661017474159/0.003654086\ 24294973061 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=1600 inside=0 periodicity=10 mathtolerance=/1 colors=000U7bJKAfFTiK_lPfoUmqZthSb`MMTG5UH6UH6UH7U\ H7UH8UH8UH9UH9UH9VODVVGWaJWhMWnPWnSWmVVlYVl_UkbUje\ UjgLYhDLi59i9AjCBjGBkJCkMDlQDlTElWFm_FmbGneHniHolI\ ooIonImnIkmIimIglIelIckIakI_jIYjIWiIUiIShIQhIO6YS7\ XT8WU8VU9UVATVASWBRWBQXCPXDOYDNYEMZEMZGL_HL_IL_JL`\ LK`MK`NKaOKaQJaRJbSJbTJbVIcWIcXIcYIcUJaRJ`NK_KKYGL\ XDLWALVBHQBELCBGC8BD56D21G28J2EL2LO2RQ2YT2cV2iS2gQ\ 2eN2cL2aI2_G2YI5_J7`LAbMCcNFdPHfQKgRMhTPjURkVTlSLY\ QEJO74QCASGFULKWY_YUVa`b`bdbfjdkofotgsyetucurauo_v\ kzzzWwezzuSxZzzmOyTzyQNvPmsPNqP`nOOlOOgOPfNPdNPaNQ\ _MQXMQUMRSLRPLRNLWKK`IJeGIWUXMgkDtzFltGeoHZjJSeKL`\ LEWM7Rbffedhgbjiakk_mnYopXprVrtUsgQpWNmKKkJRgJXcJc\ _JiWJpSJvOKoNKhNLbNLWMMQMMJMMDMKCRICWGC`FBeDBjBBoA\ BsJIuSPw`Wx7D9BG8FJ8JL8MO8QQ8UT8XV860ZIkLEnTBp`7sh\ 4up1wxOrvjmtdlr_lpUknPklKkjOfcSbYVYSZUMaPGeLAhH4kF\ LnDaTO_TM_UJ`UH`UEaUCaU9b } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Multifractal
by Albrecht.Niekamp＠t-online.de 16 May '03

16 May '03

Hi, I stuck my neck out too far and that bug is nastier then expected. As far as I know, it is apparent at 1600/1200 only and at very few images and deepzooms only. On my own pre-testings I never saw it. If it happens, only unicolored pixels are drawn, starting anywhere within the image. If it happens, type "D" (dosshell) and "exit". So far in every case the calculation was resumed. To avoid a possible stack overflow I have removed as many variables as possible, but I dont think thatïs the reason. Anyway this can also be useful if you run fractint with a "tight" dos configuration. A new feature is that border2 now has a fractional input, like border1. In order to avoid confusion, updates from now on will be marked with a date. Of course the update is compatible, I have tested about 20 images and could not detect a difference. Many good images have been posted, Lee`s are far better then mine, but I noticed that no one has tried to compose a new image from the scratch. Of course this takes some hours, but if the result is a new "spectacular" like the flying mandel it`s worth the effort, isnït it? If wanted Iïll try to write a more in depth instruction file or a better description of all inputs, although my English is not very good. Here is a new Basic Image, "Air Mandel" (It very much reminds me of a DC3), which uses my hybrid Julia as outside option. It can easily be modified and has many zooming spots. Micro_macro has many decorative micro structures, each one an image itself. About the last image I was not sure if I should post it. It is an overnight fractal, 2 hours 48min, and not even beautiful, but its what the name says. Tell me what you think of it. Please post your images. Fractal Greetings, Al. Air_mandel { ; Albrecht Niekamp 14.5.03 ; Time 0.14.21.23 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/exp/exp passes=t center-mag=-1.84684/-2.22045e-016/1.788803/1/90/-1.23373533611470521e-01\ 4 params=-0.2724234748374889/0.09260841700491348/384.00004/256.1121/2048.0\ 0016/768.000017/768.01536/512.01025/14289.27/0 float=y maxiter=2048 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200000<2>554776998BBACCB<18>iihjjillk<3>ssr<25>BBA998776<2>221000\ 011<24>0bn0cp0er<3>0ky<25>09B089067<2>021000210<24>oiPqjQslR<3>zsW<25>CB\ 6A95874653442220000400<23>o00q00s00<3>z00<30>200 } Micro_macro { ; Albrecht Niekamp 14.5.03 ; Time 1.15.30.97 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/exp/sin passes=t center-mag=-2.07100969925984700/-0.17947005902838390/35.77606/1/90/-1.23\ 373533611470521e-014 params=-0.2724234748374889/0.09260841700491348/384.00004/256.1121/2048.0\ 0016/768.000017/768.01536/512.01025/14289.27/0 float=y maxiter=2048 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200A84<20>oiPqjQslR<3>zsW<25>CB6A95874653442220000400<23>o00q00s0\ 0<3>z00<25>C00A00800<3>000<2>554776998BBACCB<18>iihjjillk<3>ssr<25>BBA99\ 8776<2>221000011<24>0bn0cp0er<3>0ky<25>09B089067<2>021000210<2>863 } War { ; Albrecht Niekamp 14.5.03 ; Time 2.48.36.29 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/exp/sin passes=t center-mag=-2.06392270811221700/-0.14949647118179270/559.0009/1/90/3.885\ 78058618804789e-016 params=-0.2724234748374889/0.09260841700491348/384.00004/256.1121/2048.0\ 0016/768.000017/768.01536/512.01025/14289.27/0 float=y maxiter=20048 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200A84<20>oiPqjQslR<3>zsW<25>CB6A95874653442220000400<23>o00q00s0\ 0<3>z00<25>C00A00800<3>000<2>554776998BBACCB<18>iihjjillk<3>ssr<25>BBA99\ 8776<2>221000011<24>0bn0cp0er<3>0ky<25>09B089067<2>021000210<2>863 } -----------------------------------start-frm------------------------------ FRM:Multifractal { ; Albrecht Niekamp 13.3.03 ;only integers as first input, second input 5 digits to the right ;real(p2) factor1,border1 ;imag(p2) (-)maxiter1,input bas.frm1_2digits input bas.frm2_2digits ;real(p3) bailout,hyb.mandel: number of sides (Many_mods L.Allison) ;imag(p3) factor2,border2 ;real(p4) maxiter2,factor3 ;imag(p4) border3,maxiter3 ;real(p5) 1digit_shape only 5digits: shape,out1,out2,in1,in2 ; 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset (not shape) <0_no in/out1 ; optional basic frm2: out-nbr 1digit in-nbr 1digit 3_both +5_shape ;imag(p5) 1digit : 1_iter1reset 2_iter2reset 3_both +5_shape effect ; 2digits : many_mods multipl.shutoff +10_in/out1 +20_in/out2 +30_both ; optional input2: frequency_2digits level_2digits amplitude_2digits ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=d<0 if (da) d=-d endif mi1=trunc(d) d=round((d-mi1)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) ba=trunc(d) mm=round((d-ba)*100000) ; d=imag(p3) fac2=trunc(d) b2=(d-fac2)*100000 ; d=real(p4) mi2=trunc(d) fac3=round((d-mi2)*100000) ; d=imag(p4) b3=trunc(d) mi3=round((d-b3)*100000) ; da=real(p5) t=da<0 if (t) da=-da endif start=2-t dd=trunc(da) if (dd<5) start=0 endif vb=(dd==3)+(dd==4) da=round((da-dd)*100) d=trunc(dd/10000) vb=(d==3)+(d==4)+vb dd=dd-d*10000 d=trunc(dd/1000) or1=d>5 d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) dd=dd-d*1000 d=trunc(dd/100) or2=d>5 d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) dd=dd-d*100 d=trunc(dd/10) inr1=d>5 d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) dd=dd-10*d d=trunc(dd) inr2=d>5 d=d-5*inr2 v3=(d==3) v4=(d==4) d2=(d==2)+(d==4) d=trunc(da/10) da=da-10*d ab=d>=5 d=d-5*ab bb1=(d==1) bb2=(d==2) dd=da>=5 da=da-5*dd ab=ab+dd ab1=(da==1) ab2=(da==2) ; d=imag(p5) dd=trunc(d) d=round((d-dd)*1000000) le=d>10000 da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=dd>=5 dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) if (le) freq=round((trunc(d/10000))*10) ;frequency_lake effect by S.Gallet d=d-freq*1000 level=(trunc(d/100))/100 ;water level d=d-level*10000 ampl=d/100 ;amplitude of the wave u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) d3=2*q*t rs=2*bo*(dd+flip(1))*t z2=center+(-q-bo*dd-flip(bo))*t z=pixel-z2 d=imag(conj(d3)*z)/imag(conj(d3)*rs) if (d<=level) da=level-d z=z+2*da*(1+ampl*sin(freq*da^0.2))*rs endif z=z+z2 endif if (ismand) if (vb) c=0.4*log(sqr(pixel^mm)) z=z*le else c=z*le+pixel*(le==0) z=0 endif else c=p1 z=z*le+pixel*(le==0) endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn1(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z2=z*z z=z2*z2+(p6+u)*z2+c else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif bo=|z| If (wo) t=t+1 if ((t<mi1)+(bo>b1)) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=z*le+pixel*(le==0) endif else z=z*le+pixel*(le==0) c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif bo<=ba } -------------------------------------end------------------------------

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FOTD 16-05-03 (Rosebuds [7])
by JimMuth＠aol.com 16 May '03

16 May '03

FOTD -- May 16, 2003 (Rating 7) Fractal visionaries and enthusiasts: On my machine, today's image from the May parent takes 52 minutes to render. But when I spent the 3/4 hour rendering it, the result was worth the effort, as the midget in the image is one of the most unusual I have yet encountered. The scene is located in the East Valley area of a distorted Mandeloid on the northeast edge of the prominent fan-shaped element of the parent fractal. I named the image "Rosebuds". A careful search will reveal the rosebuds in the chaotic region surrounding the midget. And that chaotic region is quite chaotic. Total chaos is sometimes seen around midgets; no chaos at all is sometimes seen. But the mixture of chaos and order that fills today's image is unusual indeed. The rating of 7 is earned honestly. The excessive render time can be avoided by downloading the image from the following internet addresses: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The clouds moved in on schedule here at Fractal Central on Thursday, but the rain held off. As a result, the cats had an unexpectedly pleasant day. This morning the rain is already falling, so their day will be far less pleasant. I've got about the usual amount of work to accomplish, so until next FOTD, take care, and walk with fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Rosebuds { ; time=0:52:42.12--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=mandelbrotmix2 function=recip passes=1 center-mag=+3.36125070444372700/-2.690969048142931\ 00/4.64483e+009/1/-30/-4.57683126884461666e-005 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=7200 inside=0 logmap=1100 periodicity=10 colors=000000pTZpSZpSZpRZpR_pQ_pQ_pP_qP_qO_qO_qN_q\ N_qM_qM_qL_qL_nNYlOWiQUgRTdTRbUP_WNYXMWYKT_IR`HObF\ McDJeBHfAEh8Ci66k28j4Aj5Bj7Dj8Ei9GiBIiCJiDLiFMhGOh\ HQhJRhKTgLUgNWgOYgPZgR`fSafTcfVefWfeXheZie_ke`mebn\ dcpddqdfsdgufitehtdhtcgtcgtbgsafsafs`es_es_esZdrYd\ rXcrXcrWcrVbqVbqUaqTaqTaqS`qR`pQ_pQ_pP_pOZpOZoNYsM\ YzMYzLXzKXzJWzJWzIWzHVzHVzGUzFUzFUzETzDTzCSzCSzBSz\ ARzARz9Qz8Qz8Qz9Qz9Qz9QzAQzAQzAQzAQzBQzBQzBQzBQzCQ\ xCQxCQxDQxDQwDQvDQvEQuEQuEQsEQsFQrFQrFQqGQoGQnGQmG\ QlHQkHQiHQhHQgIQfIPdIObJNaJM`JL_JLZKLXKGWKGVKGULGU\ LGTLGXML`MQ_MQZMQYNQXNQWNQVNQUOQTOQmXVRPQQPQPPQOPQ\ OQQJLLILLNQQMRQMRQMRQLSQLSQLSQMSQNTQOTQPTQQSPRTQST\ QTTQUUQVUQWUQXUQYVQZVQ_VQ`WQaWQbWQcWQdXQeXQfXQgYQh\ YQiYQjYQkZRlZRmZRm_Rm_Rm_Rm_Rm`Rm`Rm`Rn`RoaRpaRqaR\ rbRsbRtbRubRvcRwcRxcRydSzdSzdSzdSzeSzeSzeSzfSzfSzf\ SzfSzgSzgSzgSzhSzhSzhSzhS } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 15-05-03 (Christmas Trees [7])
by Jim M. 15 May '03

15 May '03

FOTD -- May 15, 2003 (Rating 7) Fractal visionaries and enthusiasts: When I saw the rows upon rows of Christmas trees, (seasonal or decorative trees in PC language), that fill today's image, I named it "Christmas Trees". But I almost named it something like "Square". The square around the small central midget is one of the best defined I have found. The entire scene is located near the tip of a decorative filament extending from a small bud on the left shoreline of the prominent Mandeloid feature of the parent. The filament terminates in a kind of lopsided spiral, though the word 'terminates' is not really correct, since these spiral filaments never really terminate. They wind inward, ever tighter and smaller, without limit. I rated the image at a 7. The rows of trees add just enough decoration to justify the rating. The unusually well-defined square also helps the rating. The render time of 11+ minutes is on the slow side, but that inconvenience can be eliminated by visiting one of the FOTD web sites and viewing the image there. Paul's site is: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's is: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> A near perfect day here at Fractal Central on Wednesday produced near perfect moods in the fractal cats. Lots of sun and a temperature of 72F 22C kept them in the yard most of the afternoon. When the cat from two doors down the hill walked by, Tippy threatened, but the other cat wisely kept going, and Tippy soon settled down. Today is a different story. The sun is now shining, but clouds are moving in and rain is supposedly on the way. If the worst happens, the duo will need a tuna treat to keep their moods bearable. My mood is always bearable, but it will be far better when I finish the day's work. The real joy will come however when, if ever, I finish the FOTD CD. For now, until tomorrow's adventure in the parent fractal, take care, and what does it all mean? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Christmas_Trees { ; time=0:11:42.17--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+2.62240247034622200/-2.976054286075551\ 00/2.636551e+009/1/-177.5/-0.000276830289356017056 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=1200 inside=0 logmap=195 periodicity=10 colors=000koKkoLjoMjoMjoNjoOjoPjoPioQioRioSioSioTh\ pUhpVhpVhpWhpXgpYgpYgpZgp_gp`gp`fpafpbfpcfpcfpdepe\ epfepfepghphephnoionjrmkxllumkumjsmirmipmhomgmmflm\ fjmeimdgmcfmcdmbcmaam``m`_jY_gWZeTZbRY`PYYMXWKXTIW\ RFWODVL9WMBWNDWOFWOGWPIXQKXRMXRNXSPXTRXTSYUUYVWYWY\ YWZYX`ZYbZZdZZeZ_gZ_f_Ye`WdaUcbSbcQadOaeMafKadKacM\ `bN``P`_Q`YR`XT_VU_UV_TX_RY_Q_ZO`ZNaZLcZKdZJfYHgYG\ hYEjYDkYClYFjWHhVKgUMeTPcSRbRU`QWZPZYO`WNcUMeTLhRK\ jPJmOIoMHrKGtJFwHEyGDvFEsEEqDEnDFlCFiBFgAGdAGb9G_8\ GX7HV7HS6HQ5IN4IL4II3JG2JD1JB1JD3IE5IF7IG9IHBIIDHJ\ FHKHHLJHMLHNMGOOGPQGQSGRUGSWFTYFU_FVaFWcFXdEYfEZhE\ _jE`lEanDbpDcrDdtDevDeyCfwDfuEfsFfqFfpGgnHglHgjIgi\ JggKgeKhcLhbMh`MhZNhXOhWOiVNiUMiTMiSLiSLiSKjTJjUJj\ VIjWIjXHjYGkZGk_Fk`FkaEkbDkcDldCleClfBlgAlhAli9mj9\ mk8ml7mm7mn6mo6lp8kq9jrAisC_tVasScrQerNgqLipIkoGmn\ DloEloFloGloGloHkoIkoJkoJ } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Corrected FOTD 14-05-03 (Silvered Mandeloid [7])
by Jim M. 14 May '03

14 May '03

FOTD -- May 14, 2003 (Rating 7) Fractal visionaries and enthusiasts: Once again I have departed from my promise of fractal purity. I have colored the outside parts of today's image with the < atan > option, which changes the normally flat areas to lively, colorful ones. I have also colored the normally black inside background a pale sky-blue, a color that, because it resembles earth's atmosphere, gives the psychological impression of infinite depth. To find today's image, we wander to the very edge of the 'fan' of the parent fractal for May, to an area that is falling apart even as we watch. In its original form, the scene was falling apart a bit too rapidly, so I solidified it by lowering the bailout radius from 625 to 223, which is very near the point where the scene goes totally blank. I colored the image a silvery-blue and named it "Silvered Mandeloid". The rating of a 7 is above average. If I had not departed from my plan to use only the equal-iteration-bands method of coloring, the image might have rated an 8. The 15-minute render time can be avoided by going to one of the FOTD web sites and viewing the image there. Paul's site is: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's is: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Mostly cloudy skies, a brisk wind, a few sprinkles of rain and a temperature of 63F 17C kept the dynamic duo ensconced safely indoors Tuesday. They were so busy sleeping that they hardly noticed the less-than-optimum outdoor conditions. Today is starting a little better. It is less cloudy and promises to be a bit warmer. Hopefully, the duo will notice the improvement. I will notice no improvement until the day's tasks are finished. Until next FOTD, take care, and be ready to help a fractal in need. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Silvered_Mandeloid { ; time=0:15:09.13--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+1.50347722580943400/-1.169078899042974\ 00/2.151038e+007/1/-132.5/2.56574306786716555e-006 params=-10/-1.1/-1/-11/0/123/0/0 float=y maxiter=1200 inside=253 outside=atan periodicity=10 colors=000INCJODKPDLPEMQFNRFPRGQSGRTHSUHTUIUVIVWJW\ WKXXKYYLZZL`ZMa_Mb`Nc`OdaOebPfcPgcQhdQieRigQjeRkdR\ kcRlbSl`Sm_SmZSnYTnWToVToUUpTUpRUqQUqPVrOVrMVsLWsK\ WtJWvHXtIWsIWqIVpJVoJUmJUlJTjKTiKShKSfLReLRdLQbLQa\ MP_MPZMOYNOWNNVNNSGKUNNWUQY`T_gWanZbq_bt``raYqaWob\ _ofXodUnbLmWBkP2jI4iK5hL7hM8gN9fPBfQCeRDeSFdTGcVHc\ WJbXKaYLa_N``O`aP_bRZcSZeTYfVXgWXhXWjZWk_Vl`UmbUnc\ TpdSqfSrgRsiQvhRtgSsgTqfUpeUneVmdWldXjcYibZgb_fa`d\ aac`bb_c`_d_ZeYZfXYgVXhUXiTWjRWkQVlOUmNUnLToKTpJYq\ Sbr_fshktplutosxmqvkoujmthkrgiqfgpeencdmacl_bjYaiX\ `hV_fTZeRYdPXbNWaMV`KUZITYGSXERVCRUBRTCSWDUZEVaFXd\ GYfH_iI`lJboKdrLetMgwNhzOjzQjzPkzPkzPkzPkzPkzPkzOk\ yOkxOkwOkvOkuOktNksNkrNkqNkpNkoNknMkmMklMkkMkjMkiM\ khLkgLkfLkeLkdLkcLkbLkbOfXRaQUXKUWLUVMUVNUUOUUPUTQ\ UTQUSRUSSURTURUUQVUQVUPWUOXUOYUNZUN_UM`UM`IS8GR9EN\ 9CJ9EKAFLBGMBHMCYjrS_8Sa8 } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Wrong palette
by Jim M. 14 May '03

14 May '03

At 11:53 AM 5/14/03 -0500, Paul Lee wrote: >Was the correct PAR sent with the 14-05-03 FOTD?? I goofed. Somehow, the wrong color palette was sent. These kind of mistakes only happen when I don't check. The correct version will follow in a minute. Jim M.

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FOTD 14-05-03 (Silvered Mandeloid [7])
by Jim M. 14 May '03

14 May '03

FOTD -- May 14, 2003 (Rating 7) Fractal visionaries and enthusiasts: Once again I have departed from my promise of fractal purity. I have colored the outside parts of today's image with the < atan > option, which changes the normally flat areas to lively, colorful ones. I have also colored the normally black inside background a pale sky-blue, a color that, because it resembles earth's atmosphere, gives the psychological impression of infinite depth. To find today's image, we wander to the very edge of the 'fan' of the parent fractal for May, to an area that is falling apart even as we watch. In its original form, the scene was falling apart a bit too rapidly, so I solidified it by lowering the bailout radius from 625 to 223, which is very near the point where the scene goes totally blank. I colored the image a silvery-blue and named it "Silvered Mandeloid". The rating of a 7 is above average. If I had not departed from my plan to use only the equal-iteration-bands method of coloring, the image might have rated an 8. The 15-minute render time can be avoided by going to one of the FOTD web sites and viewing the image there. Paul's site is: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's is: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Mostly cloudy skies, a brisk wind, a few sprinkles of rain and a temperature of 63F 17C kept the dynamic duo ensconced safely indoors Tuesday. They were so busy sleeping that they hardly noticed the less-than-optimum outdoor conditions. Today is starting a little better. It is less cloudy and promises to be a bit warmer. Hopefully, the duo will notice the improvement. I will notice no improvement until the day's tasks are finished. Until next FOTD, take care, and be ready to help a fractal in need. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Silvered_Mandeloid { ; time=0:15:09.13--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+1.50347722580943400/-1.169078899042974\ 00/2.151038e+007/1/-132.5/2.56574306786716555e-006 params=-10/-1.1/-1/-11/0/123/0/0 float=y maxiter=1200 inside=253 outside=atan periodicity=10 colors=000RFUSETTDTUCTVBTW9SX8SY7SZ6R_5R`4Ra3Rc2Td\ 2Uf2Vg2Wi2Xj2Yl2_m2`o2ap2br2cs2dt2eu3du4du5dv6cv7c\ v8cw9bwAbwAbwBbxCaxDaxEayF`yG`yH`yH`wJcuLftMhrOkqP\ noRpnSslUvkVxaSvSPuJNs9Kr0Iq3Ko5Lm7Ml9NjBPiDQgFRfH\ SdJUcLVaNW`QXZSYXU_WW`UYaT_bRadQceOefNggLihKfjMdkN\ blP`nQYoRWpTcqUmsVwtXzuYzwZzx`zyazzbzyczxdzwdzvezu\ eztfzsgwsgmrhcqhUpiKoj6nj5mk5mk7mf8mbAmZBmVDmREmMG\ mIHmEJmAKm6Lm2Oi4Rf5Ub6X_7_W8aT9dQAgMBjJCmFDpCEr9F\ uGJxMMwLLvKLuJLtILsHLrGLqFKpEKoEKnDKmCKlBKkAJj9Ji8\ Jh7Jg6Jg6JfCMeHPeMSdRVdXYca`cfcbkfbph`nf_mdZlbYkaX\ j_WhYVgXTfVSeTRdRQbQPaOO`MN_LLZJKXHJWFIVEHUEGTGFSI\ HUKJWMLYONZQP`SRbUTcWVeYXg_Zia`jcbledngfoihqkjsmkt\ oipqglsehucdwcawcYwcUwcQwcNwcJwcFwcBwc8wd7we7wf7wg\ 7wh7wk6wn6wq6wt6ww6wzEwzFwzFwzFwzFwzFwzGwzGwzGwzGw\ zGwzHwzHwzHwzHwzHwzNwzSwzXwzUwzUwzUwzPwz2wz6wzAwzE\ wzHwzLwzPwzTwzUwzUwzUwzUw } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

2 1

Multifractal
by Albrecht.Niekamp＠t-online.de 13 May '03

13 May '03

Hi, John, as I did not receive any messages for 5 days, I have downloaded the may-archive and found your message: "I can't render these. What is "formulafile=070503.par"? " The file name is just the name of the file I used for posting. It has no meaning as the formula is part of the par-file. You can change it if the formula is in your frm-folder. Did you get an error message or what happened when you tried to generate the image? Maybe the file was corrupted. If you start Fractint from a dos-commander it could be a ram problem pending your dos configuration. Regards, Al.

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FOTD 13-05-03 (Fractal Membrane [5])
by Jim M. 13 May '03

13 May '03

FOTD -- May 13, 2003 (Rating 5) Fractal visionaries and enthusiasts: There is a huge rush here at Fractal Central this morning, which once again means a truncated discussion. I don't know whether to cry or curse, so I'll probably do a bit of both. With more work than I could handle, I had almost no time to search the parent fractal for another scene. What I did was follow another filament that led into a kind of ring, and chose the first midget I found there. I named the image "Fractal Membrane" because that's what it reminds me of. I rated the scene at an average 5. What else could I do? The render time is a dragging 22 minutes, but this can be cut to a minute or so if the image is downloaded from one of the FOTD web sites. Paul's site is at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's site is at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Monday was cloudy, chilly and blustery here at Fractal Central, with light showers in the afternoon. The temperature of 68F 20C completed the miserable scene that kept the fractal duo confined indoors all day. Their moods reflected the weather, and treats were needed. Today could well be a repeat, so I had best have the treats ready. Until tomorrow's FOTD, take care, and watch your words. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Membrane { ; time=0:22:05.25--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=-1.08701862978801700/-6.408597513799762\ 00/5.748507e+008/1/145/-5.27237241383787802e-005 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=1800 inside=0 logmap=441 periodicity=10 colors=000M6EM6EM7FN7FN8FO8FO9GP9GPAGQAGQBHRBHRCHP\ AFRCHTDJVFLXGNYHO_JQaKScLUdNVfOXhPZjR`kSamTcoVeqWg\ rXhsZgs_ftadtccuebugavi`vj_wlYwnXxpWxrVytUyuTrlQkc\ NeVLZMIV7ITDGSIEROCQTAOZ8Nc6Mi4Ko1Ln3Mm5Nl7Ok8PjAQ\ iCRhDRgFSfHTeJUdKVcMWbOXaPY`RY_TZZV_YW`XYaW_bV`cUb\ dTd``jdTegLakDYl5Yn6Uo7Qp7Mq8Ir8FqAHqBJqCKqEMqFNqG\ PqIQqJSqKTqLVqNWqOYqPZqR`qSaqTcrVfqUdpUcpUboTanT_n\ TZmSYmSXlSWkRUkRTjRSjQRiQPhQOhPNgPMjNIgPLeROcTQaVT\ _XV`_WaaXadYbfZci_ck_dm`epaerbfucgwdgydhsfhnhihjic\ kjYmjTokNqkIriJohKmgLkfMhdNfcOdbPaaQ_aO_`RY`TX`VV`\ XU`_S`aR`cP`eO`gM`jL`lJ`nI`pGavC`rF_oH_lJZhMZeOYbQ\ XZTXWVWTXWQZVMaUJcUGeTChT9jS6lS3nR5kR7iQ9gQBdPDbPF\ `OHZOJWNLUNNSNPQMRNMTLLVJLXGKZEK`CJbAJd7If5Ih3Ii1P\ d0V`0`X0gY0m_0sa0pc1ne1lg1ji2hk2im2jm0km2lm3mm4nm5\ om6pm9qmCrmEsmHtmKumMvmPwmSxmUymXzm_zmazmDzmBzmCzm\ CzmCzmCzmDzmDzmDzmDzmEzmE } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Multifractal
by Albrecht.Niekamp＠t-online.de 13 May '03

13 May '03

Hi, here are two more zooms into "Siamese_twins". Hope you like them. As I have not received a digest since 5 days it is possible that some mails remain unanswered. Please, Tim, if you are listening check what happened. Thank you! Fractal Greetings, Al. -----------------------start-par------------------------------------------ Work_of_art { ; Time 0.09.55 ; Albrecht Niekamp May, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifrac_239 ismand=y function=exp/exp/exp passes=t center-mag=-1.15085452099411000/+1.01529571735795100/1205.83/1/132.50000\ 0000001307/2.82471962487207406e-012 params=-0.1738944669942329/-0.3000579851680044/384.00001/256.1113/3072.0\ 0016/768.0001600000001/768.01536/32.01025/34231/5 float=y maxiter=3072 inside=maxiter outside=tdis logmap=5 periodicity=0 rseed=-2436 colors=2000Ub<13>09B089067<2>021000210<22>keNmgOoiPqjQslRunS<2>zsW<25>CB\ 6A95874653442220000400<23>o00q00s00<3>z00<25>C00A00800<3>000<2>554776998\ BBACCB<16>eedggfiihjjillknnm<2>ssr<25>BBA998776<2>221000011<24>0bn0cp0er\ <3>0ky<10>0Wd } Come_in { ; Time 0.11.01 ; Albrecht Niekamp May, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/sin/exp passes=t center-mag=-0.00071948591619709/-0.46563800841117850/64.10257 params=-0.1740997192297128/-0.2996141087069308/384.00004/256.1106/4096.0\ 0016/768.00009/768.01536/128.01025/28984.5/0 float=y maxiter=2048 inside=maxiter outside=tdis logmap=10 periodicity=0 rseed=-2436 colors=0003A84DA5EB5HB<2>7NG8PI8RJ9TKAVNAXM<3>DdTDfVEhWFjYFlYGn_Gp`Prd<3\ >zzz<2>_ulRsgHqaHo`GmZFkXFiX<5>BYOAWMAUL9SK<4>6IC5GB5DA<3>25424312100000\ 1023025047049<5>0BL0DN0DP<2>0IV0JX0KZ0L`0Mb<3>0Rj0Sl0Tn0Up4Yr8atCgvGkxKq\ z<3>4_s0Vq0Uo<6>0Ma0L_0KY<3>0FQ0DO0DM<3>08E06C06A048046024012000100<12>R\ 0LT0NV0PX0P<3>d0Wf0Yh0Z<3>p0e<3>xOtzUxyOuwIquCns6iq0g<2>k0bi0`g0_e0Z<3>Y\ 0SW0RU0O<8>C0AA09807506304102010<11>0P30R30T40V40X3<3>0d40f50h5<3>0p6<3>\ WxZczeUyY<2>0s8<4>0i60g60e60c4<2>0Y40W30U4<5>0I20G20E20C20A1081<3>000010\ 122153265386 } ---------------------------start-frm-------------------------------- FRM:Multifractal { Albrecht Niekamp May, 03 ;only integers as first input, second input 5 digits to the right ;real(p2) factor1,border1 ;imag(p2) (-)maxiter1,input bas.frm1_2digits input bas.frm2_2digits ;real(p3) bailout,hyb.mandel: number of sides (Many_mods L.Allison) ;imag(p3) factor2,border2 ;real(p4) maxiter2,factor3 ;imag(p4) border3,maxiter3 ;real(p5) 1digit_shape only 5digits: shape,out1,out2,in1,in2 ; 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset (not shape) <0_no in/out1 ; optional basic frm2: out-nbr 1digit in-nbr 1digit 3_both +5_shape ;imag(p5) 1digit : 1_iter1reset 2_iter2reset 3_both +5_shape effect ; 2digits : many_mods multipl.shutoff +10_in/out1 +20_in/out2 +30_both ; optional input2: frequency_2digits level_2digits amplitude_2digits ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=d<0 if (da) d=-d endif mi1=trunc(d) d=round((d-mi1)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) ba=trunc(d) mm=round((d-ba)*100000) ; d=imag(p3) fac2=trunc(d) b2=round((d-fac2)*100000) ; d=real(p4) mi2=trunc(d) fac3=round((d-mi2)*100000) ; d=imag(p4) b3=trunc(d) mi3=round((d-b3)*100000) ; da=real(p5) t=da<0 if (t) da=-da endif start=2-t dd=trunc(da) if (dd<5) start=0 endif vb=(dd==3)+(dd==4) da=round((da-dd)*100) d=trunc(dd/10000) vb=(d==3)+(d==4)+vb dd=dd-d*10000 d=trunc(dd/1000) or1=d>5 d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) dd=dd-d*1000 d=trunc(dd/100) or2=d>5 d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) dd=dd-d*100 d=trunc(dd/10) inr1=d>5 d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) dd=dd-10*d d=trunc(dd) inr2=d>5 d=d-5*inr2 v3=(d==3) v4=(d==4) d2=(d==2)+(d==4) d=trunc(da/10) ab=d>=5 d=d-5*ab da=da-10*d bb1=(d==1) bb2=(d==2) d=da ab=d>=5 d=d-5*ab ab1=(d==1) ab2=(d==2) ; d=imag(p5) dd=trunc(d) d=round((d-dd)*1000000) le=d>10000 da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=dd>=5 dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) if (le) freq=round((trunc(d/10000))*10) ;frequency_lake effect by S.Gallet d=d-freq*1000 level=(trunc(d/100))/100 ;water level d=d-level*10000 ampl=d/100 ;amplitude of the wave u=real(rotskew*pi/180) t=exp(-flip(u)) h=1/real(magxmag) q=h/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) w=2*q*t v=2*h*(dd+flip(1))*t z2=center+(-q-h*dd-flip(h))*t z=pixel-z2 d=imag(conj(w)*z)/imag(conj(w)*v) if (d<=level) da=level-d z=z+2*da*(1+ampl*sin(freq*da^0.2))*v endif z=z+z2 endif if (ismand) if (vb) c=0.4*log(sqr(pixel^mm)) z=z*le else c=z*le+pixel*(le==0) z=0 endif else c=p1 z=z*le+pixel*(le==0) endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn1(z)+c ;Linda Allison sqz2=cos(z2) z=c*(1-sqz2)/(1+sqz2) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z2=z*z z=z2*z2+(p6+u)*z2+c else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif bo=|z| If (wo) t=t+1 if ((t<mi1)+(bo>b1)) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=z*le+pixel*(le==0) endif else z=z*le+pixel*(le==0) c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif bo<=ba }

3 3

FOTD 12-05-03 (Ghostbusters [7])
by JimMuth＠aol.com 12 May '03

12 May '03

FOTD -- May 12, 2003 (Rating 7) Fractal visionaries and enthusiasts: The rush continues here at F.C. The customer is due in three hours and there is two hours work yet to do. This means another short FOTD discussion. Today's image rates a 7, which is somewhat of an improvement over the recent days' efforts. I named the image "Ghostbusters" because it reminds me of those mischievous entities that filled the film of the same name some 20 odd years ago. The location of the scene is near the tip of the filament that extends from the southeast-pointing bud of the obvious Mandel area of the parent. Actually, the filament goes on forever until it is absorbed into the ring-like feature. The render time of 12 minutes can be bypassed by downloading the finished image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather was unexpectedly pleasant here at Fractal Central on Sunday. The forecasted severe weather never developed, and the sun actually appeared in the afternoon, raising the temperature to 81F 27C and giving the fractal duo the best romp in the yard they have had in nearly a week. Their resulting moods were beyond reproach. Today is starting in a far more pleasant manner, with no hint of foul weather. With things going their way, I expect the duo will have another pleasant day. My day will turn pleasant when the work is finished. Until next time, take care, and the search for truth will never end, because we invent truth by the act of searching. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Ghostbusters { ; time=0:12:13.70--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=-2.98713609027161200/-4.227785958369030\ 00/884250.2/1/25/1.99687892998151595e-006 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=1600 inside=0 logmap=247 periodicity=10 colors=000C8AD9AEAAFBAGCAHDAIEAKFAMGBOHCPIDRJESKFU\ LGVMHXNIYOJ_PK`QLbRMcRNeSOfTPhUQiVRkWSlXTnYUoZVq_W\ r`Xs`XrdVqgUpjTomSmpRlsQkoPjkJigDjc7l_2jW5iS8hOBfK\ EeMGdOJcQMaTP`VR_YUY_XXb_WdaVfdTigSkjRnlPpoOsrNuuM\ wwLuuKssJrqJppInnHmlGkkGiiFhgEfeDddDcbCa`B__AZYAXW\ 9VU8UT7SR7QP6PO5NM4LK4KJCOEKS9RV4QT6QR8QQ9QOBQMDQL\ EPJGPHIPGJPELPDMPBOO9QO8RO6TO4VO3WO1YO0ZP2bP4eP6hP\ 8kPAoPCrPEuPFxQHvRJtSLsTNqUPoVRnWTlXVjYXiZZgZ`f_bd\ `dbafabh_cjYdlXenVfpTgrShtQhuPfnNdhLbbJ`WHZQFXKDVD\ BT79S17V7AXCDZHG`MJbRLeXOgaRifUkkXmpZli_kb_jX_iQ_h\ J`gD`f6`f0``BdWLhRWkMeoHorLjlPfgTabWYYVZXUZWT_VS_U\ S`TR`TQaSPaRPbQObPNcPMcOMdNKdMUeLcWLmWKwUJzTIzSHzT\ HFbJFcKFdMFdNFePFeQEdSEdTEeVEfWEgYEhZDi_DjaDkbDldD\ meDogCqhCsjCukCwmCxnCyoGzjKzfNzbRzZVzUYzQazMezIhzD\ lz9pz5sz1qz4oz7mz9kzCizEhzHfzJdzMbzP`zR_zUYzWWzZUz\ `SzcRzeWzg`zidzkizmJzCJzC } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 11-05-03 (An Undecided Fractal [5])
by Jim M. 11 May '03

11 May '03

FOTD -- May 11, 2003 (Rating 5) Fractal visionaries and enthusiasts: Today's fractal appears undecided. It cannot make up its mind which way it wants to go, and as a result, its rating suffers. The scene is filled with fragments of themes, any one of which could be developed into a satisfying overall theme, but none of which actually are. It's no wonder that I named the image "An Undecided Fractal". This indecision is caused by the location of the scene in its parent -- exactly on the left edge of the 'fan', where it merges into the chaos surrounding a small irregular hole. At this particular point, all the forces are balanced. The situation is unstable, poised at the brink, but there is no trigger to flip the scene into a definite theme. As a result of all this indecision, I could rate the overall result no higher than a 5. The render time of 14 minutes is a bit slow for an image that tries hard but doesn't seem to know in which direction to go. And that 14-minute wait can be cut drastically by downloading the completed GIF image from either of the two FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> It rained and thundered in the morning of Saturday here at F.C. The rain was not too heavy, but the high humidity and light winds that followed left the grass soaked for the rest of the day, a situation that always keeps the cats' moods less than optimum. The temperature reached 72F 22C -- comfortable enough -- were it not for the wet grass. How long it seems since the dynamic duo were actually doing things other than being in moods -- such as climbing trees and catching birds. But this is what happens to cats when they reach the age of 12 years. Well, today is starting with more wet grass, and possible tornadoes are forecast for this afternoon. So it's time to say 'see you next time', and batten down the fractal hatches. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ AnUndecidedFractal { ; time=0:14:53.64--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+3.68764793983902500/+2.385906045025763\ 00/520464.8/1/-147.5/1.08806127205318681e-007 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=1600 inside=0 logmap=235 periodicity=10 colors=0007cF6dD6dC5dA5d94d74d66c87cA8cBAcDBbFCbGD\ bIFbKGaLHaNIaPKaQLaSM`UO`VP`XQ`ZR__T_aU_cV_dWZfYZh\ ZZi_Zk`Zl__jZ`iZahYbgXbeXcdWdcWebVfaUf_UgZThYTiXSi\ VRjURkTQlSQlRPlPOmOOnNNoMLpJNqLOrNPqPRpRUnTZlYcjYb\ hYahY`gY_fY_eYZdYYcYXcYWbYVaYU`YT_YSZYTYZSZYRZXQZW\ PZVO_UN_TM_SL_RK`QJ`PI`OH`NGaMFaMEaLDaKCbJBbIAbH9b\ G8cF7cE6cD5cC4dB3dA2d90f82d94b95`AZZA8YAcZBBUBWVBE\ QCGPCINCJLDLJDMHDOGEPEERCESAFU8FU5CV7FW9HXAJYCLZDN\ _FP`GRaITbJVcLXdMZeO`fQbgRdhTfiUhjWjkXllZom_rnauob\ zobxnYslTokOjjJfhEag9Ye2Vf5Ug7Th9ThCSiESjGRjIRkLQl\ NQlPPmRPnUOnWNoYNp`MpbMqdLrfLriKskKtmJsnHtoJviLwcM\ yYOzSPyTRyUTyVUxWWxXXxYZxZ_w_aw_bw`dvafvcgvfivijul\ luomuqouopsmlqkipifngblf_kfXifUgfQffNdfKbfMafO_fQY\ fSYgUXfWWfYVe_UeaTecTdeSdgRciQczPczPbzObzNbzMazLaz\ L`zK`yJ`wI_uH_sH_qG`oG`mF`kF`zE`zEazDazDazCazCazBb\ zBbzAbzAbz9bz9cz8cz8cz7cz } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

1 0

[Fractint] Re: [Fractint, Philofractal] FOTD 10-05-03 (The Edge [5])
by Jim M. 10 May '03

10 May '03

At 11:07 AM 5/10/03 -0600, you wrote: >On May 6, Jim Muth wrote: > >FOTD -- May 06, 2003 (Rating 7) > >>> As the month progresses, I shall use nothing but the conventional >equal-iteration-band method to render and color the images. There will >be no 'evaporated' or 'tdis' images. This limitation will not result in >boring images however. The parent fractal has nearly (and in fact, >actual) unlimited variety. << > >Just 4 days later on May 10, Jim Muth wrote: > >FOTD -- May 10, 2003 (Rating 5) > >>> Today's image is slow because most of it consists of inside material >made visible by the < bof61 > inside fill. But it is not an evaporated >image. A good part of it is real material rendered with the < tdis > >option. << > >Is this the result of: > (1) A promise made but not kept! :-) > (2) Just an exception to the proposed FOTD rule for May. > (3) Jim reserving the right to change his mind. > (4) Jim forgetting to focus on his announced mission. > (5) A test to see if his readers are paying attention to his comments. > (6) There was not unlimited variety in the parent and Jim was getting > bored. > > I suspect the answer is (5). ;-) :-) :-) ;-) ;-) ;-) Choice (1) is true by definition. But considering the unfulfilled promises I have made about the upcoming FOTD CD, it is not too serious a breach. Choice (2) is also true by definition. Choice (3) Ditto. Choice (4) is untrue. I knew all along that I was reneging on my word. This is why I mentioned 'evaporated' fractals in the short discussion. Choice (5) is partially true. I soon realized that my original plan was a hastily conceived and unnecessary limitation. When I intentionally departed from my announced plan, I did wonder how many, if any, would notice it. But the departure was not intended to be a test. I used the other options simply because they improved the image, which, in its original form, was in need of help, and I was rushed for time. Choice (6) is totally untrue. The parent fractal has more variety than I could find in a million lifetimes. Jim M. ;-)

1 0

Multifractal
by Albrecht.Niekamp＠t-online.de 10 May '03

10 May '03

Hi, good news. I found what caused that mysterious fractint-bug. It must be one as I have used the same bailout expression on some other formulas without problem. Lee, here is your bug-image running perfectly. I tested some pictures and I could not detect any difference to this version, so I have not renamed it. Suggest you just exchange it. I have a new zooming playing ground (siamese twins) and two zooms. Check it out. Fractal greetings, Al. ---------------------------start-par-------------------------------------- Alien_landscape { ; Time 0.35.37 ; Albrecht Niekamp May, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/sin/exp passes=t center-mag=-1.35882/-0.813178/13.33333/1/60.0000000000000711/-3.77822773\ 067748585e-014 params=-0.1740997192297128/-0.2996141087069308/384.00004/256.1106/4096.0\ 0016/768.00009/768.01536/128.01025/28984.5/0 float=y maxiter=2048 inside=maxiter outside=tdis logmap=10 periodicity=0 rseed=-2436 colors=00006D<3>0BL0DN0DP<2>0IV0JX0KZ0L`0Mb<3>0Rj0Sl0Tn0Up4Yr8atCgvGkxKq\ z<3>4_s0Vq0Uo<6>0Ma0L_0KY<3>0FQ0DO0DM<3>08E06C06A048046024012000100<12>R\ 0LT0NV0PX0P<3>d0Wf0Yh0Z<3>p0e<3>xOtzUxyOuwIquCns6iq0g<2>k0bi0`g0_e0Z<3>Y\ 0SW0RU0O<8>C0AA09807506304102010<11>0P30R30T40V40X3<3>0d40f50h5<3>0p6<3>\ WxZczeUyY<2>0s8<4>0i60g60e60c4<2>0Y40W30U4<5>0I20G20E20C20A1081<3>000010\ 1221532653863A84DA5EB5HB<2>7NG8PI8RJ9TKAVNAXM<3>DdTDfVEhWFjYFlYGn_Gp`Prd\ <3>zzz<2>_ulRsgHqaHo`GmZFkXFiX<5>BYOAWMAUL9SK<4>6IC5GB5DA<3>254243121000\ 00102302504704905B } Siamese_twins { ; Time 0.49.07 ; Albrecht Niekamp May, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/sin/exp passes=t center-mag=-0.500782/0/0.6666667 params=-0.1740997192297128/-0.2996141087069308/384.00004/256.1106/4096.0\ 0016/768.00009/768.01536/128.01025/28984.5/0 float=y maxiter=2048 inside=maxiter outside=tdis logmap=10 periodicity=0 rseed=-2436 colors=0003A84DA5EB5HB<2>7NG8PI8RJ9TKAVNAXM<3>DdTDfVEhWFjYFlYGn_Gp`Prd<3\ >zzz<2>_ulRsgHqaHo`GmZFkXFiX<5>BYOAWMAUL9SK<4>6IC5GB5DA<3>25424312100000\ 1023025047049<5>0BL0DN0DP<2>0IV0JX0KZ0L`0Mb<3>0Rj0Sl0Tn0Up4Yr8atCgvGkxKq\ z<3>4_s0Vq0Uo<6>0Ma0L_0KY<3>0FQ0DO0DM<3>08E06C06A048046024012000100<12>R\ 0LT0NV0PX0P<3>d0Wf0Yh0Z<3>p0e<3>xOtzUxyOuwIquCns6iq0g<2>k0bi0`g0_e0Z<3>Y\ 0SW0RU0O<8>C0AA09807506304102010<11>0P30R30T40V40X3<3>0d40f50h5<3>0p6<3>\ WxZczeUyY<2>0s8<4>0i60g60e60c4<2>0Y40W30U4<5>0I20G20E20C20A1081<3>000010\ 122153265386 } Bug_Test { ; Time 0.08.03 ; Image Lee Skinner ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=n function=exp/exp/exp passes=t center-mag=-6.52603785028786300/-0.01400828975779934/419.4063/1/77.50000\ 00000024869/-5.11394399049791559e-012 params=-0.1740997192297128/-0.2996141087069308/384.00004/256.1106/2048.0\ 0016/768.00009/768.01536/256.01025/28974.5/12 float=y maxiter=2048 inside=maxiter outside=tdis logmap=yes symmetry=none periodicity=0 rseed=-2436 cyclerange=2/255 colors=000000zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<2>I88H44G00<3>TA\ 5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5zP5zL\ 6zI6zE6wE6tD6<6>vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW4E<2>_4H<3>P3DN2CK2\ A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6\ X<2>F9LAAG7FO4KW0Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvlq\ votvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<4>XCAaB9fB7<3>zA0<13>S\ A1QA1NA1<3>D92<6>UXAW`BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi_5fc0ce\ 7_jFRoNIzb0zj0zr0 } Rainforrest { ; Time 0.14.27 ; Albrecht Niekamp May,03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/sin/exp passes=t center-mag=-1.40318296737838300/-0.78552661781075610/5333.334/1/60.00000\ 00000113332/-5.22844267880628877e-012 params=-0.1740997192297128/-0.2996141087069308/384.00004/256.1106/4096.0\ 0016/768.00009/768.01536/128.01025/28984.5/0 float=y maxiter=2048 inside=maxiter outside=tdis logmap=10 periodicity=0 rseed=-2436 colors=00006D<3>0BL0DN0DP<2>0IV0JX0KZ0L`0Mb<3>0Rj0Sl0Tn0Up4Yr8atCgvGkxKq\ z<3>4_s0Vq0Uo<6>0Ma0L_0KY<3>0FQ0DO0DM<3>08E06C06A048046024012000100<12>R\ 0LT0NV0PX0P<3>d0Wf0Yh0Z<3>p0e<3>xOtzUxyOuwIquCns6iq0g<2>k0bi0`g0_e0Z<3>Y\ 0SW0RU0O<8>C0AA09807506304102010<11>0P30R30T40V40X3<3>0d40f50h5<3>0p6<3>\ WxZczeUyY<2>0s8<4>0i60g60e60c4<2>0Y40W30U4<5>0I20G20E20C20A1081<3>000010\ 1221532653863A84DA5EB5HB<2>7NG8PI8RJ9TKAVNAXM<3>DdTDfVEhWFjYFlYGn_Gp`Prd\ <3>zzz<2>_ulRsgHqaHo`GmZFkXFiX<5>BYOAWMAUL9SK<4>6IC5GB5DA<3>254243121000\ 00102302504704905B } --------------------------start-frm---------------------------------------- FRM:Multifractal { Albrecht Niekamp May, 03 ;only integers as first input, second input 5 digits to the right ;real(p2) factor1,border1 ;imag(p2) (-)maxiter1,input bas.frm1_2digits input bas.frm2_2digits ;real(p3) bailout,hyb.mandel: number of sides (Many_mods L.Allison) ;imag(p3) factor2,border2 ;real(p4) maxiter2,factor3 ;imag(p4) border3,maxiter3 ;real(p5) 1digit_shape only 5digits: shape,out1,out2,in1,in2 ; 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset (not shape) <0_no in/out1 ; optional basic frm2: out-nbr 1digit in-nbr 1digit 3_both +5_shape ;imag(p5) 1digit : 1_iter1reset 2_iter2reset 3_both +5_shape effect ; 2digits : many_mods multipl.shutoff +10_in/out1 +20_in/out2 +30_both ; optional input2: frequency_2digits level_2digits amplitude_2digits ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=d<0 if (da) d=-d endif mi1=trunc(d) d=round((d-mi1)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) ba=trunc(d) mm=round((d-ba)*100000) ; d=imag(p3) fac2=trunc(d) b2=round((d-fac2)*100000) ; d=real(p4) mi2=trunc(d) fac3=round((d-mi2)*100000) ; d=imag(p4) b3=trunc(d) mi3=round((d-b3)*100000) ; da=real(p5) t=da<0 if (t) da=-da endif start=2-t dd=trunc(da) if (dd<5) start=0 endif vb=(dd==3)+(dd==4) da=round((da-dd)*100) d=trunc(dd/10000) vb=(d==3)+(d==4)+vb dd=dd-d*10000 d=trunc(dd/1000) or1=d>5 d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) dd=dd-d*1000 d=trunc(dd/100) or2=d>5 d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) dd=dd-d*100 d=trunc(dd/10) inr1=d>5 d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) dd=dd-10*d d=trunc(dd) inr2=d>5 d=d-5*inr2 v3=(d==3) v4=(d==4) d2=(d==2)+(d==4) d=trunc(da/10) ab=d>=5 d=d-5*ab da=da-10*d bb1=(d==1) bb2=(d==2) d=da ab=d>=5 d=d-5*ab ab1=(d==1) ab2=(d==2) ; d=imag(p5) dd=trunc(d) d=round((d-dd)*1000000) le=d>10000 da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=dd>=5 dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) if (le) freq=round((trunc(d/10000))*10) ;frequency_lake effect by S.Gallet d=d-freq*1000 level=(trunc(d/100))/100 ;water level d=d-level*10000 ampl=d/100 ;amplitude of the wave u=real(rotskew*pi/180) t=exp(-flip(u)) h=1/real(magxmag) q=h/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) w=2*q*t v=2*h*(dd+flip(1))*t z2=center+(-q-h*dd-flip(h))*t z=pixel-z2 d=imag(conj(w)*z)/imag(conj(w)*v) if (d<=level) da=level-d z=z+2*da*(1+ampl*sin(freq*da^0.2))*v endif z=z+z2 endif if (ismand) if (vb) c=0.4*log(sqr(pixel^mm)) z=z*le else c=z*le+pixel*(le==0) z=0 endif else c=p1 z=z*le+pixel*(le==0) endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn1(z)+c ;Linda Allison sqz2=cos(z2) z=c*(1-sqz2)/(1+sqz2) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z2=z*z z=z2*z2+(p6+u)*z2+c else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif bo=|z| If (wo) t=t+1 if ((t<mi1)+(bo>b1)) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=z*le+pixel*(le==0) endif else z=z*le+pixel*(le==0) c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif |z|<=ba } -------------------------------------end----------------------

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FOTD 10-05-03 (The Edge [5])
by Jim M. 10 May '03

10 May '03

FOTD -- May 10, 2003 (Rating 5) Fractal visionaries and enthusiasts: Still another unusually busy day subtracts from the time devoted to the FOTD. Today's image is titled "The Edge". What is it the edge of? It is a point on the right edge of the large irregular open area at the center of the parent fractal. At first glance, this edge appears to have nothing of interest to reveal, but upon magnification it proves to be rich in intricate detail and critical as well. Today's image is slow because most of it consists of inside material made visible by the < bof61 > inside fill. But it is not an evaporated image. A good part of it is real material rendered with the < tdis > option. I could see nothing in the image that would rate higher than a 5, and the relatively slow render time of 36 minutes sealed the image's fate. It is merely an average image, and average it will remain. The task of rendering can be avoided by downloading the completed image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> It rained a good part of the day here at Fractal Central on Thursday. The wet conditions and cool temperature of 60F 15.5C kept the fractal cats indoors and cranky. Tuna was needed to restore their spirits. Today is starting wet once again, so more bad moods are expected. As for me, I still have much work to do, so until next time in 24 hours, and next fractal, take care, and have a good day. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Edge { ; time=0:36:31.59--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=-0.36527211087213760/-2.458962463379425\ 00/3437243/1/135/-1.35280818422400806e-008 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=800 inside=bof61 outside=tdis periodicity=10 colors=000OPUOOTQMfQLfQKfQJfPIfPHfPGfPHhPGgPGfPGeP\ GdPGcPGbPGaPF`PF_PFZPFYPFXPFWPFVPEVPEUPETPESPERPEQ\ PEPPDOPDNPDMPDLPDKPDJPDIPCIPCHPCGPCFPCEPCDPCCPBBPB\ APB9PB8PB7PB6PB5O93PB5QC7QE8RFASHCSIDTKFULGUNIVOKW\ QLWRNXTPYUQYWSZXTZYV__X``Y`b_ac`bebbfdchedigdkielj\ fnlfomgqohrqhtriutivugstfqseordmrcjqbhpafp`doZanY_\ mXYmWWlVTkURkTPjSNiUDnRLiOTeKa`L`aL`aM_aM_bMZbNZbN\ YcNYcOYcOXdOXdPWdPWeQVeQVeQVeRUfRUfRTfSTgSSgSSgTRh\ TRhURhUQiUQiVPiVPiVOjWOjWOjWNkXNkXMkYMlYLlYLlZKmZK\ mZKm_Jm_Jn_In`In`HoaHoaHoaGpbGpbFpbFqcEqcEqcEqdEqe\ DrgCshBsiAtjAul9um8vn7wr5xp6wo7wn8wm9wlAwkBwjCwhDw\ gDwfEweFwdGwcHwbIw`Jw_KwZLwYLwXMwWNwVOwUPwSQvRRvQS\ vPTvOTvNUvMVvKWvJXvIYvHZvG_vF`vE`vCavBbvAcv9dv8ev7\ fv6gv5gv6fu7ft8et8es9dsAdrAcqBcqCbpCbpDboEanFanF`m\ G`mH_lH_kIZkJZjI_kJZjJYiJYhKXgKXfKWeKWdLVdLVcLUbLU\ aMT`MT_MSZMSZNRYNRXNQWNPV } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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