May 2008 - Fractint - mailman.xmission.com

FOTD 31-05-08 (Coronal Crisis [6])
by Jim Muth 31 May '08

31 May '08

FOTD -- May 31, 2008 (Rating 6) Fractal visionaries and enthusiasts: When I was in Catholic elementary school (I did survive it.) and the subject turned to religion, I had a way of asking questions that on several occasions caused me to be told in effect to sit down and shut up. I'm still not sure what I did wrong. Maybe I asked the wrong kind of questions. Or maybe I just had too much trouble believing in things that neither I nor apparently anyone else could see. (This was before I realized that the scientists known as physicists are even better at inventing theories about things that will never be directly seen.) Anyway, one sunny day in May, shortly after Sister Mary Thomas told the class that if we were good on earth, we would all have a seat at the right hand of our Savior when we went to heaven. So far, so good, but then I had a sudden insight. Not only did the thought of an eternal church service seem boring, but I remembered the baseball game I had attended a few days earlier. The crowd there had numbered about 45-thousand, a tiny fraction of the millions of Catholics who would go to heaven and sit next to the Savior, yet even that tiny fraction at the ball game took up so much space that those on the outer fringes were hundreds of feet from the field. If a hundred-million Catholics all had seats at the right hand of the Savior, the stands would stretch for miles. Those in the outer bleachers would be unable to even see Him. Feeling a surge of perhaps foolish bravery, I raised my hand and asked how millions of people could fit by one man's right hand. After a minute's thought, the sister said it's a mystery and told me to sit down and shut up. (Actually she said something like 'the question is silly, so sit down and pray for guidance.) Unfortunately, after all these years, guidance has yet to come. But in the meantime, fractals *have* arrived on the scene, and today's rates an acceptable 6. The parent fractal was created by iterating the formula Z^sqrt(3)+C at a level 123 levels up the logarithmic ladder when no function is applied. This parent is shaped roughly like a distorted Mandelbrot set rotated so that its main bud, which is actually only 0.732 of a bud, faces southwest. This bud is shaped quite like the main buds of the Z^3+C Mandeloid, with a small valley directly opposite its mouth. Today's scene is located in this valley. The colors are unusually brilliant. In fact, they are so brilliant that they actually detract from the worth of the image. But in this case, applying such extreme brilliancy was the only way to add life to the scene. Today's parameter file will reveal its secret in only 3-3/4 minutes running time on a 2000mhz machine, which is about the same time it will take to surf down to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the completed image there. Thursday was absolutely perfect here at Fractal Central, though Friday brought a few too many clouds for perfection. The temp- erature hovered around 79F 16C (13 Reaumur) on both days, while the fractal cats kept an eye on the yard, watching for intruding tomcats. My day on Friday was a lot less busy than Thursday, when I had no time for the FOTD. And speaking of the FOTD, the next one will be posted in 24 hours. Until then, take care, and if you don't know the answer to a question, humiliate the one who asked it by calling the question silly. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Coronal_Crisis { ; time=0:03:47.28-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-0.8004024479835327/-0.735937934452532/\ 348789/1/-12.5/0 params=1.732/0/123/0 float=y maxiter=5000 inside=0 logmap=174 periodicity=10 colors=000V1TX3VZ5X`7Zb9`dBbfDdhFfjHhlJjnLlpNnrPpt\ RruSsuTsuUsuVsuWsuXsuZsu`subsudsufsuhsujsulsunsups\ uqsursursursursursursurou0eu0Su1Iu69u60uB0uF0uK0uP\ 0qP0lU0gZ0cc0Zc0Ug0Pl0Kq0Fu0Bu06u01u01u00u00u00u00\ u00u00u00u40u90uI0uN0uX0ua0uj0uo0us0us0us0us0us0us\ 0us0ps0ks0ls0ms0nscoskpswzzzzzzzzswoluecuXZrIgl9lg\ 0u_0uU0uP0uM0uS0uZ0uc0ul0uu0uu0lu00u00u00qe0Bs0Ps0\ ca0q90u00u06u0Pu0gu0Uu0Fu01g00K000I00j00s00s00s0u0\ 0u40uD0lI0cS0PX0Fe06j00s00s00s00s00s00s00s00s00s00\ s00s00s00s00s00o00e00X00N00D0040000000000101606F0B\ K0FP0KU0Pc0Ug0Zl0cq0g00g00q00u00u00u00u00u00u00u00\ u00u00u00u04u09u09u0Du0Iu0Nu0Nu0Su0Xu0Xu0ju1su6su6\ suBslFsUFsBKs0Ps0Ps0Zs0gs0ls0us0us0us0us0us0us0us0\ us0us0usBusUusquNuu0uu0uu0uu0uu0uu00us0us0us0us0us\ 0us0uo0ua1uNFu9Uu0gu0uu0uu0uu0uu4uuDuuSuuauujuusuu\ suusuusuusuuscusBuj0uI0uX } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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 PARAMETER FILE=========================================

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No FOTD for May 30
by Jim Muth 30 May '08

30 May '08

Fractal fans: Due to a very busy day, there will be no FOTD for May 30. The FOTD for May 31 will be posted on schedule. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com

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FOTD 28-05-08 (A Stitch In Time [7.5])
by Jim Muth 28 May '08

28 May '08

FOTD -- May 29, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: I saw on the news this morning that the cameras on the latest Mars lander have picked up something in the distance that suspiciously resembles an intelligently designed artifact. I assume we'll soon be hearing that the artifact was left there by aliens from Vega-3, who have been spying on earth from this secret base on Mars, and neglected to clear all signs of their presence when they returned to their home world to report that the earth is ready to be invaded and conquered. I am sorely disappointed. I thought the space aliens were an alliance from the yet-to-be-discovered third star in the Sirius system and the fourth planet circling Procyon. Whatever, I will be watching the Pennsylvania skies very carefully in the days to come. And I can't help wondering whether fractals exist in the universe as perceived by the aliens. I often wonder whether fractals really do exist, or are mere inventions of the human fancy. Since aliens, by definition, must lack human minds, fractals might not exist in their world. One thing certain however is that something exists somewhere, for today's FOTD is a picture of it. The parent fractal was created when I mixed various negative portions of Z^(-1.732) and Z^(-7.32), then added (1/C). This parent fractal is little more than a chaotic mish-mash of fractal stuff, but even so it has at least some worth. Today's scene lies at the terminal of a filament extending from a small bud in the southernmost part of the parent. Most of the artistic effect is a result of my quasi-skilled coloring efforts. The extreme magnitude of 4.5*(10^12) requires the mathtolerance entry. The rating of 7-1/2 includes 1/2 point for my coloring. The name "A Stitch In Time" has nothing at all to do with the image, but then again I have no idea what "the tropic of Sir Galahad" has to do with "the tin man", yet it's in the song regardless. The calculation time of 2 minutes means immediate relief from fractal congestion. A trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the completed image, will bring even more relief. With a temperature of 66F 19C, Wednesday was just a bit too chilly for comfort here at Fractal Central, but the light winds and strong sun kept it from being uncomfortably cold. The fractal cats enjoyed the unbroken sun. I enjoyed a day that was not too busy. Tomorrow looks promising also. The next FOTD fractal will be posted in 24 hours. Until then, take care, and where will you be when the aliens arrive to carry off all of us as slaves? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Stitch_In_Time { ; time=0:02:06.01-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+0.6271399461988936/-1.226465429540339/\ 4.493818e+012/1/60/0 params=-5/-1.732/-1/-7.32/0/\ 0/0/0 float=y maxiter=1800 inside=0 logmap=226 periodicity=10 mathtolerance=0.05/1 colors=000LKzNNzPLzSJzTIzVJyWKyYLyZNy_PyZRxYTxYVxX\ XwXZwW`wVbwTdvSfvQhvShyPivNfsKepIbmF`jDZgAXd6Xe7Wc\ 8Ub9TaAR`AQ_BOZCNYDLXEKWEIVFHUGFTHESzzcptzA80AB0AE\ 0PHMTJKWMI_PGbREfUCiXAmZ8pa6td4wf2sa4p`5mZ7iW8fU9c\ RB_PCXMEUKFQHGNFIKCJGALD7MA5NA7PA8QA9RAASABTACUAEV\ AFWAGXAHYAIZAJ_8LY7MW6OU3NP4OR5PS6QT6RU7SV8SW8TX9U\ zAV_AWzBWaCXzCYcDZzE_eC`zE_fG_zHZmJZzLYtMYzPXjRXYR\ VWSTUSSSSQQTOOTNMTLKUJIUIGVGEVECVDAWB8W96X72z85W88\ z8BV8Ez8HU8Kz8NT8QT8TS8WS8ZS8aS8aR8`R8`RK`QKzQK_PK\ zPKZOKzOKZOKz000000000MKXMKXLKXLKWKKWKKWKLzJLVJMzI\ MUINUHNUHOUHOTGPTGPTFQSFQSERSERRESRDURDcQCcQzUQBmP\ zzPAmPzWOAmOzzO9mNzYN8mNzzM7mMz`M6aLzbL5cLzdK4eKzf\ KQgtzhjFiazjTFkSzlREmRznREoRzpRDqRzrQDsQztQCuQzvQC\ wQzxQCyPzzPBzPzzPBzPzzPAzPzzOAzOzzOAzOzzO9zOzzOWzT\ zzOYzKzzF_zBzz6`z2zzCSzLzzMQzMzzMPzNzzNOzNzzOMzOzz\ OLzPzzPCznzzlBzmzznGzozzp } frm:MandAutoCritInZ {; 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 PARAMETER FILE=========================================

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FOTD 28-05-08 (Fortune Always Calls [5.5])
by Jim Muth 27 May '08

27 May '08

FOTD -- May 28, 2008 (Rating 5.5) Fractal visionaries and enthusiasts: Today's image shows one of those generally disappointing mini- brots lying in the Mandeloids with exponents between 1 and 2. This one lies in the Z^(sqrt(3))+C as it appears 4 levels up the complex logarithmic ladder. Due to its modicum of organization, it squeaks by with a rating of 5-1/2, barely worth the honor of being declared a FOTD. At this not-very-lofty log level, the parent fractal resembles nothing more than a numeral 8 listing to starboard. Today's scene is located on the northern side of the west branch of the prominent valley dividing the main bay into the figure 8. Choosing the square-root of 3 as an exponent was done in jest. Significant numbers such as this apparently have no effect on the quality of the fractals they create. The name "Fortune Always Calls" has nothing whatever to do with the image, or with anything at all connected with fractals for that matter. It's simply a cute phrase, nothing more, nothing less. The calculation time of just over 1 minute is unexpectedly fast. But the trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> is equally fast, and going to the web site will avoid the minor hassle of copying this FOTD into your Fractint directory (or folder) in text format with a .par extension and running it as you would any other Fractint parameter file. A rather muggy day on Tuesday was interrupted by a shower of rain (what else?) in the afternoon, which knocked the tempera- ture down from 86F 30C to 73F 23C. The fractal cats watched the 15-minute shower with disinterest. My day was busy but under control. Tomorrow, when the next FOTD will be posted, should be the same. Until then, take care, and isn't the thought of the perfect fractal heavenly. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= FortuneAlwaysCalls { ; time=0:01:24.04-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-0.199082275456053/+0.1545238480953167/\ 39000/1/-75/0 params=1.732/0/4/0 float=y maxiter=2000 inside=0 logmap=83 periodicity=10 colors=0009KnBJjCIgDHdFHaGGZHFWJETKEQLDMNCJOBGPBDR\ AAS97T84U81SC3RF5PJ7OM9NQBLTDKXFJ_HHcJGfLFiNDkPCmR\ AoSFmVKkMPhOUeQZbSa_UcXWaVY`T_ZTaYWcXYeV`gUciUfkUi\ mUloUoqVqsXsuZtwauyctxesxhqxjpxlowonwqmwslwrkvrjvr\ ivrhurgurgurftretrdtrcsrcsrbsrarr`rr_rr_rq`nq`jp`f\ p`bo`_o`Wn`Sn`On`Ln`Ln`Km`Jm`Jm`Im`Il_Hl_Hl_Gk_Gk_\ Fk_FjZEjZDjZDiZCgY8iZCiZBhYBhYAhYAgY9gY9gY8zW5yX6y\ X6xX6xX6wX6wX6wX6vX6vX6uX6uX6uX6tX6tX6sX6sX7sX7rX7\ rX7qX7qX7qX7pX7pY7oY7oY7oY7nY7nY7mY7mY7mY8lY8lY8kY\ 8kY8kY8jY8jY8iY8iY8iY8hY8hY8gY8gY8WgRXfPYeOZeN_dL_\ cK`cJabIbaGcaFc`Ed_De_BfZAgY98bb9aaAaaAa`Ba`Ba_Ca_\ CaZDaZDaZEbYEcYFdXFeXGfWGgWHhWHiVIjVIkUJlUJmTKnTKo\ SLpSLqSMrRMsRNtQNuQOvPOwPPxPPyOzzOzzNzzNzzMzzMzzLz\ zLzzLzzKzzKzzJzzJzzIzzIzzIzzHYzHYzGZzGZzF_zFJzmKzh\ MzdNz`OzWQzSRzNSzJUzFVzAWz6Xz2Vz6Uz9SzCRzFPzIOzLMz\ OLzRJzUIzXGz_FzbDzeCzhAzk } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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 PARAMETER FILE=========================================

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FOTD 27-05-08 (Depths Without End [7.5])
by Jim Muth 27 May '08

27 May '08

FOTD -- May 27, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image returns to yesterday's scene in the Seahorse Valley complex of the Z^2+C Julibrot. I zoomed in on the lower right part of yesterday's image and turned the view upside down to produce an image that gives the impression of massive striped arms floating above an infinite depth. No wonder I named the image "Depths Without End". I created the banded effect by hand rather than using the banding feature included in the program. Though the view is double-rotated only two degrees or so (my estimate) from the Julia orientation, the ghostly remains of Mandelbrot buds are clearly visible along the top of the image. The fact that the circular bud outlines are undistorted shows that both parts of the double rotation are equal. (Mandel-bud remains are impossible in the exact Julia orientation because their outlines have enlarged to infinity.) I rated the image at a 7.5. Despite its several flaws, it still has something to offer. Just to the right of the center of today's image lies a cluster of tiny bright dots. These dots are actually holes in the surface stuff. Beneath the surface at this location lies a minibrot with its main bud facing left. When blown up, these holes prove to be julia sets of whatever part of the underlying minibrot they happen to be on top of. The minibrot itself is located somewhere in Seahorse Valley, though I have not the slightest idea of its actual Mandelbrot coordinates. The calculation time of the included parameter file is only 3/100 of a second in excess of 5 minutes, a bit slow but nothing that cannot be quickly accomplished. The finished GIF image is or soon will be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Monday was a repeat of Sunday here at Fractal Central, though with a few more clouds and a bit higher humidity. With all the sun, the temperature reached 84F 29C. Now, at post time, the wind is stirring and lightning is flashing in the distant west. Rain is threatening, but the day is finished, so let it rain. The fractal cats have their eyes on the sky however. The next FOTD will be posted in 24 hours. Until then, take care, and if you can't find the fourth dimension, try to be satisfied with the third. It's only a consolation prize, but it's still better than nothing. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Depths_Without_End { ; time=0:05:00.03-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=EvenMoreSlices passes=t center-mag=0.953034/-0.257883/17.1836/1/-167.8/0 params=2/0/0/0.15/-0.78/0/0/0 float=y maxiter=15000 inside=255 logmap=22 periodicity=10 colors=000088re8097re70A6rg60B6rh50C5rj40D4ql30E4p\ k50F5oj60G6ni70H7mh80I9lg90JAkfA1KBjeB2LCidD2MDhcE\ 3MEgbF4MFeaG5MHd`H5MIb_I6MJaZJ7MK`YK7ML_XM8MMZWN9M\ NZVO9MOZUPAMQZTQBMRZSRCMSZRSCMTZQUDMUZPVEMVZOWEMWY\ NXFMYXMYGMZWLZGL_VK_GK`UL_HK`TK`HKaSKaIKbRKbIJcQJc\ IJdPJdIJdOJeJIeNIfJIfMIgJIgLIhKIhKHiKHiKHiLHjLHjLH\ kLGkLGlLGlMGmMGmMGmMFnMFnMFoNFoNFpNFpNFqNEqOErOErO\ ErOEsOEsODtPDtPDuPDuPDvPDvOCwPDvPDvPDuQEuQEuQEtREt\ RFtRFsRFsSFrSGrSGrTGqTHqTHqTHpUHpUIpUIoVIoVInVJnVJ\ nWJmWJmWKmXKlXKlXLlXLkYLkYLjYMjZMjZMiZMwZNw_Nw_Nw_\ Ow`Ow`Ow`Ow`PwaPwaPwaPwbQwbQwbQwaRwbQwbQwbQwcQwcQw\ cQwdPwdPwdPwePweQweRwfSwfTwfUwgVwgWzgWzhWzhWzhWziW\ ziWziWziWzjWzjWzjWzkWzkWzkWzlWzlWzlWzmWzmWzmWznWzn\ WznWzoWzoWzoWzpWzpWzpWzrWzqWzpWzpWzoWzoWznWznWzmWz\ mWzlWzlWzkWzjWzjWziWziWzhWzhWzgWzgWzfWzfWzeWzeWzdW\ zcWzcWzbWzbWzaWzaWz`Wzmzz } frm:EvenMoreSlices {; Jim Muth ; P1--exponent, P2--angle, ; P3--M center, P4--J center, z=pixel+(p4), c=p3+(pixel*p2): z=(-z)^(p1)+c, |z| < 16 } END PARAMETER FILE=========================================

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FOTD 26-05-08 (The Fourth Dimension [Rating Arbitrary])
by Jim Muth 26 May '08

26 May '08

FOTD -- May 26, 2008 (Rating Arbitrary) Fractal visionaries and enthusiasts: The unknown fascinates me, and what could be more unknowable than space of four dimensions? The problem is, while our math has no difficulty dealing with 4-D, and computers can be programmed to deal with it as logically as they do 3-D, we pathetic humans can do nothing more than twist our faces into a look of astonished puzzlement when asked to visualize something as simple as a 4-D tesseract. Today's image is a scene in Seahorse Valley of the Mandelbrot set, an object every tyro fractalist becomes familiar with the day after he discovers fractals. But the image bears little resemblance to either Seahorse Valley or its Julia set, yet what we are seeing is all part of the great Seahorse Valley complex. What has changed in the image is the angle at which we are viewing the valley. We are seeing it sliced at an angle very close to but not exactly in the Julia orientation. The Seahorse Valley Julia set (actually the -0.78,0 set) may be seen by changing the (p2) parameter to 0,0. The Mandelbrot aspect, which is Seahorse Valley itself, may be seen by changing the (p2) parameter to 1,0 and the (p4) parameter to -0.78,0. I can logically deduce what is going on in all these changing views of the same 4-D object, but I am no closer to visualizing the entire 4-D Seahorse Valley complex than I was that day 20 years or so ago, when I realized that the Julia sets and the perturbed Mandelbrot sets are differently oriented slices of a single 4-D object, the Julibrot figure. Perhaps what we call dimensions are simply another way of describing levels of consciousness, and mankind is now at the three-dimensional level of consciousness. This would imply that space appears three-dimensional because that is the only way we can perceive the abstract reality. If this is so, it is only to be expected that we would naturally develop a mathematics that would be compatible with and would confirm our perception. Enough philosophical rambling already. I named today's image "The Fourth Dimension" for obvious reasons. I gave it no rating, or rather left it to the individual viewer to decide its worth. The calculation time is but a few seconds, so have no fear when running the included parameter file. But if fear strikes, rush to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the finished image there. BTW, tomorrow's image will be a zoom into today's. Absolute perfection wrapped in a package -- that describes the conditions here at Fractal Central on Sunday. How can cloudless skies, low humidity, light winds and a temperature of 77F 25C be improved upon? The fractal cats must have agreed, for they sat in their window for an hour, watching me finish the yard work, while FL supplied encouragement and occasional refreshment. And despite all this activity, I still found time for the FOTD. The next FOTD will appear in 24 hours or so. Until then, take care, and seek total fulfillment in your endeavor. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= TheFourthDimension { ; time=0:00:14.15-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=EvenMoreSlices passes=1 maxiter=1800 center-mag=0/-0.0486/0.86 params=2/0/0/0.15/-0.78\ /0/0/0 float=y inside=0 logmap=yes periodicity=10 colors=000IJJ97P7DU6IY5Nb4Sf3Yj2bo1gs0lw6muCnsHoqN\ ooSpmUmkWjiYgg_deaaccZaeW_gTYiQWkNUmKSoHQpEOpBMmCK\ kEIhGGeIEbKC`MAYOBVQCSSDQTEPUDPVDOWDOXDNYDNZDM_DM`\ DLaCLbCKcCKdCJeCJfCIgCIhCHiBHjBGkBGlBFmBFnBEoBEpBG\ qEHrHJsJKtMLuONrNPpNRmNTkMUiMWfMYdL_aL`_LbYKdVKfTK\ gRJiOJkMJmJInHIoFIpCHqAHr8HpAIpBJoCJoDKoEKnFLmHLlI\ MlJMmKNmLOnMOoNPpPPqQQqRQqSRqTRqUSqVSoWTmXUkYViZWg\ _Xe`YcaZab__c`YcaWcbUccScdQceOcfMcgKchIciHcjHckHcl\ HcmHcnHcoHcpHcqHcrHcsHctHcuHcvHcwHcxHcyHczHczHczHc\ zHczHczHczHczHczHczHczHczHczHczHczHczHczHczHczHczH\ czHczHczHczHczHczHdzHezHfzHgzHizHkzHzzHzzHzzHzzHzz\ HyzHxzHzzIvzJuzKtzPszUrzZqzcozhmzmzzrzzvzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:EvenMoreSlices {; Jim Muth ; P1--exponent, P2--angle, ; P3--M center, P4--J center, z=pixel+(p4), c=p3+(pixel*p2): z=(-z)^(p1)+c, |z| < 16 } END PARAMETER FILE=========================================

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FOTD 25-05-08 (Second Chance [No Rating])
by Jim Muth 25 May '08

25 May '08

FOTD -- May 25, 2008 (No Rating) Fractal visionaries and enthusiasts: Since I was busy on Saturday, out having fun for a change, I had no time for a FOTD search. But to avoid fractal disappointment I resurrected a fractal that I found several weeks ago, and gave it a second chance. I named the image "Second Chance". One glimpse will show why it failed its first chance. The mixed-up fractal has little going for it but a random scattering of randomly colored elements rendered with the outside set to 'tdis'. I did not dare rate the image. I hate to give a fractal a rating of a negative number. I think the image is located in a string of holes down the center of a valley of its parent, but I'm not sure. One thing I am sure of however is the 3-1/2 minute calculation time on my fractal-dedicated 2000mhx machine. The time is automatically written in the parameter file. As almost always, the finished image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> F.L. and I made the most of the perfect weather that prevailed here at Fractal Central on Saturday, while the fractal cats complained about being left alone most of the day. The next FOTD will very likely be posted in 24 hours. Until then, take care, then seek and find. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Second_Chance { ; time=0:03:31.53-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=+0.0089893132145013/+0.6702539704283154\ /3453.553/1/142.5/0 params=-5/-1.45/-1/-4.5/0/0/0/0 maxiter=5000 inside=0 outside=tdis periodicity=10 colors=000faFhaFjaFkaEmaEnaDpaDraDsaCuaCvaCtZDsXDr\ VDqTDpRDoPDnNDlLEkJEjHEiFEhDEgBEf9Ee7Ed9HcAKcBNbCQ\ bDTaFW`GZ`Ha_Id_JgZLjYMmYNpXOsXPuRVrL`oFflDehCeeBe\ bAe_9eX8eU7dQ6dN5dK4dH3dE2dB3cD4bF5bG6aI7aJ8`L8`M9\ _OA_PBZRCZSDYUDYVHUbLQjOMrHFEMPQRY`Wgl_pwbmtdjqfgn\ hdkkahmZeoWbqT_sRYUYj4dw5ev5fv5gv5hv5iv5jv6ju6ku6l\ u6mu6nu6ou6ouUerpWpoVnoUmnTlnSkmRjmQilPhlOfkNekMdj\ LcjKbiJaiI`iI_sYgkQhdIiXAjQ3kS6lT9lVCmWFmYHnZKn`No\ aQobSoYOpULqQIqMFrICrE9sA6s63t20t8BqELoKVmQdjWlhZn\ cYpbVn_SjXPdUM_RJVOGQLDLIAGF7BC4795AC6DE7GG8JIAESC\ 9`D5iEBfFHcFMaGSZHYXHbUIhSJnPJsNYvXkxfyzpxyqwyrwyr\ vysuytuyttyutyusxvrxwrxwqxxpxypxyoxzoxzjfgfQPb96`C\ B_EFYGJXJNVLRUNVSPZRSbPUfOWjMZnL`rJbvIdzRixZmvfrtn\ vrvzpryqoxqlxqiwqfvrcvr`urYtrVtrSssPrsMrsJqsGqsHnr\ IlqJiqKgpLdpLboM_oNYnOWmPTmPRlQOlRMkSJkTHjTFjWHhZI\ faJddKbgM`jNZmOXpPVcaGeaG } frm:MandAutoCritInZ {; 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 PARAMETER FILE=========================================

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FOTD 24-05-08 (Lilacs in Blueoom [7])
by Jim Muth 24 May '08

24 May '08

FOTD -- May 24, 2008 (Rating 7) Fractal visionaries and enthusiasts: A very heavy work load means a short FOTD discussion, which is what we have today. The day's image resulted when I subtracted Z^(0.35) from Z^(2.7) and added straight (C). The parent fractal is a slight variation on yesterday's parent. The image is actually surprisingly attractive, considering that almost no effort went into it. The rating of a 7 is due almost totally to serendipity. The name "Lilacs in Blueoom" came to mind when I glanced out the window and noticed a lilac bush that had just finished blooming. The calculation time of 3-1/2 minutes on a 2000mhz fireball is about average. Combined with an average image, everything should be under control. But to assure control, the finished image is or soon will be posted for instant viewing and total enjoyment on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Friday turned out to be a really nice late spring day here at Fractal Central. The blue sky was decorated with puffy cumulus clouds, the wind was gentle, and the temperature reached 68F 20C. The fractal cats as well as the ducks on the nearby Susquehanna River agreed. The cats purred and stretched in the sun, while the ducks quacked and swam on the water. Swamped in work, I had little time to do the obligatory FOTD, much less enjoy the quacking ducks. But the worst of the work is finished -- at least for the present -- so the next FOTD has an 80-percent chance of appearing on schedule in 24 hours. Until the next time, take care, and beneath every mountain lies a hidden fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Lilacs_in_Blueoom { ; time=0:03:29.71-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+0.9436889113880975/+0.646306059851099/\ 5.986522e+010/1/-40/0 params=1/2.7/-1/0.35/0/0/0/0 float=y maxiter=2400 inside=0 outside=tdis periodicity=10 colors=000rEwrDwrBxr9xs8xs6ys5ys3ys2ym4sh5nc6iZ7dT\ 9ZOAUJBPECK9DF9LE9SE8QI7OM6MQ6KU5IY4Ga4Ee3Ci2Am29q\ 5Ao8AnBBmDBkGCjJCiMDgODfRDeUEcXEbZFaaF_dGZgGYiGXjH\ WjIWjIVjJVjJVjKUjKUkLUkMTkMTkNTkNSkOSkOSOYb0gm4ej8\ dhCbfGadK_aOZ_SXYWWW_UTcTRgRPkQNnPLlRJkTIjUHiWGhYF\ gZDf`CdbBccAbe9ag7`h6_j5Zl4Ym3Xl5Wl7Wl9VlAVlCUlETl\ GTkHSkJSkLRkNQkOQkQPkSPkTQlQQmOQnMQoKQpHQqFQrDQsBQ\ t8Qu6Qv4Qv2Or5Mn8KjBIfEGbHE_KCWNASQ8OT6KW4GZ3Da2Hd\ 2Lf2Ph2Tk2Xm1`o1dr1ht1lv1ox5ms9knDiiGhdjNHZIMODQNC\ OLCLKBJIAGH9EF8BE89LJ7RT5Yc4cm2iw1hp9gjGfcOfYVgZUg\ _Ug`UgaUgbThbThcThdTheShfSifSigSihRiiRijRijRhhQhgP\ gfOgeOgdNfbMfaLf`Le_KeZJeYJfXLgWMhWNiVPiVQjURkTTlT\ UmSVmSWgW_bicXjgSkkMloHmsBnw6pzPnyblofjocip`jlchn`\ ijbjf`lcYi_WjXWcVWYTSRSNLQIEOE8NxPZtO`pObmNdXXHiNf\ fMhbMjt9bmEefIhZfd__g_TiwnN`VOylyuhwqdum`sjXqfTobP\ mifagccf`ddYfcVgaSiqHwrGw } frm:MandAutoCritInZ {; 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 PARAMETER FILE=========================================

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Re: [Fractint] Fractal question
by Paul N. Lee 23 May '08

23 May '08

On Mon, 19 May 2008 at 22:35:00, Tony Fisher <tfisher(a)hccs.hunter.cuny.edu> wrote: > > Greetings! I am a high school math teacher working > with some exceptional students. While my field is > originally group theory, I have been trying to work > with my students on fractals. I have used Fractint > for many years and am impressed... I have what I > think should be a simple question, but I have had > trouble finding the right program for what I want to > do. Fractint's "Newtonbasin" identifies points in > the complex plane by their ultimate destination, > through Newton's method, to solutions to the equation > z^3 - 1 = 0. I would like to do the same but with > the equation z^3 - z = 0. The movement of z changes > from: > z'=(2z^3 - 1)/(3z^2) > to: > z'=(2z^3)/(3z^2 - 1) > > However, one should still get a tricolored fractal as > long as one identifies points by destination rather > than speed. Is Fractint the way to go to create this > fractal? Or [other fractal generator]? Any assistance > you could give, either directly or in the form of > pointing me toward the best person to ask, would be > much appreciated. > The above was sent to me about 26 hours ago, but I have been way to busy to give it my full attention (as seen by the way the FOTD's are running late on the website). Would somebody care to assist this individual, please ?? Sincerely, P.N.L. ------------------------------------------------- http://home.att.net/~Paul.N.Lee/PNL_Fractals.html http://www.Nahee.com/Fractals/

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FOTD 23-05-08 (Dark Kisses [5])
by Jim Muth 23 May '08

23 May '08

FOTD -- May 23, 2008 (Rating 5) Fractal visionaries and enthusiasts: The recipie for today's 5-rated image subtracts Z^(0.4) from Z^(2.5) and adds (C). The parent fractal is a strange thing, a main unit divided into several large bays, the whole thing surrounded on the west by a horde of minibrots of varying sizes. Today's scene lies in scattered debris just off the negative X-axis just west of the main fractal unit. I named the image "Dark Kisses" because that's the first thing I thought of when I saw the scene. Much of the pizazz is due to the image being rendered with the outside set to 'tdis'. The rest of the pizazz is due to luck. The calculation time of almost exactly 2 minutes is just what the doctor ordered as a cure for fractal fatigue. Another good prescription is to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the completely calculated image posted there. But if the image is not yet available, be patient. Paul has been busy lately. Brilliant sunshine alternated with showers of rain through the day on Thursday here at Fractal Central, while the temperature of 55F 13C and a brisk northwest breeze made it quite a bit too cool to enjoy the spectacular clouds and rainbows. The fractal cats enjoyed the sunny intervals and searched for their catnip rat while the rains fell. My day was very busy, and I would not be surprised if tomorrow is the same. Unless the unexpected happens, the next FOTD will be posted in 24 hours. Until that semi-glorious moment, take care, and is there any such thing as a totally new fractal? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Dark_Kisses { ; time=0:02:00.01-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+0.416383005818/+0.002891533387/2599786\ /1/22.5/0 params=1/2.5/-1/0.4/0/0/0/0 float=y maxiter=1800 inside=0 outside=tdis logmap=76 periodicity=10 colors=000GHaGIdGIgIOiKTjMZkNclPhnRnoTspUxqXGDUFBR\ EAOD9LC7IB6FA5D94HD6LG8OKASNCVRDZUFaXHe`JicLlgMpjO\ snQwqSztTvrVspXpnYll_ijafibbgd_efXcgTaiQ_kNZlRXiUV\ gXTe`RccP`fNZjLXmJVpIT3LH5KI6JJ7JK8IL9HMBHNCGODFPE\ FQFERHDSIDTJCUKBVLBVMAVMAVM9WN9WN8WN8WMAXLCYKEZKG_\ JI`IKaCciIMbHObGQcGSdFUeEWfEYgD_hCaivxI2S53T84UB4V\ E5WG6WJ6XM7YP8ZR8_U9_XA`_AaaBbdCcgUd1Tc3Sc4Sc5Rc7R\ c8Qc9QcAPcCPcDOcEOcGNcHNcIMcJMcLLcMLcNKcPKcQJcRJcS\ IcUIcVHcWHcYGcZGc_Fc`FcbEccEcdDcfDcgCch_1tY5sW8rUB\ qSEpQIoOLnMOmKRlIVkGYjE`iOjeIfg4TS5UT5UT5UT5UU5UU5\ VU5VV6VV6VV6VV6VW6WW6WW6WX6WX7WX7XY7XY7XY7XY7XZ7XZ\ 8YZ8Y_8Y_8Y_8Y_8Z`8Z`8Z`9Za9Za9Za9_b9_b9_b9_b9_cA`\ cA`cA`dA`dA`dA`dAaeBaeBaeBafBafBbfBbgBbgBbgCbgCbhC\ chCchCciCciCcisI2pK5nL7lM9iNCgOEePGbRJ`SLZTNWUQUVS\ SWUPYXNZZL_`I`cGaeEbgfvgeuhduhdthcthbthbshasharh`r\ h_rh_qhZqhYqhYphXphFFWGGZ } frm:MandAutoCritInZ {; 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 PARAMETER FILE=========================================

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