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Re: [Fractint] AOTD
by JackOfTradeZ＠comcast.net 22 Dec '08

22 Dec '08

. error in link. sorry. try: http://www.fractal-animation.net/vid/tohuvavohu.zip .

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R: Re: AOTD
by jakovll＠libero.it 22 Dec '08

22 Dec '08

thanks for the link. I have got one question, please: I love fractals but I know just a bit about them. Maybe my question is silly, maybe not: do you happen to know places in Italy, particularly in rome, where one can go and fidn someone who takes oyu by the hand to better undesrtand and study them? apart form University... maybe someone of this e-list does! thank you Jacopo ----Messaggio originale----Da: JackOfTradeZ(a)comcast.netData: 22/12/2008 14.55A: <fractint(a)mailman.xmission.com>Ogg: Re: [Fractint] AOTD.error in link. sorry. try:http://www.fractal-animation.net/vid/tohuvavohu.zip.

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FOTD 22-12-08 (Long Time No See [No Rating])
by Jim Muth 21 Dec '08

21 Dec '08

FOTD -- December 22, 2008 (No Rating) Fractal visionaries and enthusiasts: Things were very busy here at Fractal Central on Sunday, as we finished the decorations and FL started planning the dreaded holiday feast. All this frenzied activity left almost no time for a proper fractal, but I did manage to find one slow image, which I let calculate while I tried to get the treetop ornament properly straightened. I named the image "Long Time No See" because it takes 15 minutes to run, and when it is finished, there is little to look at. Since the image was given almost no effort, I gave it no rating. Though the image may be seen by runnung the included parameter file, by far the best way to view it is to surf out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view it there, wondering what all the excitement is about. Overnight snow Saturday added up to about 2cm here at Fractal Central. The snow ended on Sunday morning, and by noon the sun appeared. The fractal cats fully appreciated the brilliant afternoon sun and temperature of 37F 3C. But late in the day a high wind arose, quickly dropping the temperature to freezing and sending the cats scurrying for the heat. My day was spent in holiday preparations and discussing the idea of a business web site with FL, who thinks such a site would be profitable. (IMO we have enough work as it is.) The next FOTD will be posted in 24 hours. Until then, take care, and search for the true meaning of the season. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Long_Time_No_See { ; time=0:14:51.53-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 passes=1 float=y center-mag=-2.095431790464875/+1.101841460808186/\ 6.811102e+007/1/-137.5/0 params=-5/9/0.001/52 maxiter=10000 inside=0 logmap=536 periodicity=10 colors=000z`bzcbzednzzUszsdzzuZwpzyszz0tzzmzzmzzkz\ zkzzkypkyphynhwkhwihwghugfuefucfs`fs_fs_dpYdpWdpTd\ nRdnRbnQbkObkMbkMbeQX`TTYWNT_JQcEMe9Hi5Ek0Ap05u02w\ 00z00z00z00z00z00z00z00z00z00w00p00i00`00W00O40Q50\ Q70R70R90T90TB0TB0WD0WD0YE0YE0YH0_H0_J0`J0`L0`L0cN\ 0cN0eO0eO0eQ0gT0gT0iV0iV0kX0kX0kY0nY0n`0p`0pb0pb0s\ d0sd0uf0uf0uh0wh0wk0yk0ym0zk0zm0ym0wm0um0sm0pm0km0\ im0gm0em0cm0`m0Ym0Wm0Tm0Rm0Qm0Om0Km0Hm0Gm0Ep0Cp0Ap\ 07p05p03p02p00p00p00p00p00p00p00p00p00p00p00p00p00\ p00p00p00p00p00k00f00Z00Z00Z00Z00Z00Z00p00p00p00p0\ 0p00p00p00p00p00p00p00p00p00p00p00p20X20p20p30p30p\ 50p50p52p72p73p73p50S50h30f30b30`20Y20X20T00Q00O00\ L00N50OA0OH0QO0QT0T`0Tg0Vu0`n0Vi0Qc0L_0HT0BQ07K02M\ 00H00G00E00C20A308727825A43E42z50_50G70_70R90T90WB\ 0_B0`D0eD0gE0iE0nH0pH0sJ0wJ0zL0zO0GN0zL0zJ0GHOzTQG\ TRzVTzVWzXYzX_zY`zYcz`ez` } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 21-12-08 (Groundhog Haven [7])
by Jim Muth 20 Dec '08

20 Dec '08

FOTD -- December 21, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's curious image lies in the parent fractal that results when 4 negative parts of Z^(-1.3) are mixed with 0.8 negative part of Z^(-7.6) and (1/C) is added. This parent fractal is the usual multi-bayed thing with the usual prominent 'fan' extending east from the origin. There is a very large minibrot near the eastern edge of this fan, though today's scene lies in a bit of debris inside the fan rather than in the minibrot. I named the image "Groundhog Haven". There is no logical reason for such a name. I apparently have no control over the phrases that come into my head when I am searching for a name. The rating of a seven seems about right for the image, which is only mildly great. The calculation time is downright great however. The 44 seconds is almost as fast as Nicholas finishes tuna and cheddar treats. An equally great way to see the image is to surf out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and study it there, gasping in awe and wonder. Despite ample afternoon sun, the outside temperature of 23F -5C kept the windows too drafty for the comfort of the fractal cats here at Fractal Central on Saturday. They decided to spend the day near the heat. My day was moderately busy doing last minute things of the season with FL. The next FOTD will be ready in 24 hours. Until then, take care, and make your fractals elegant, not elephant. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Groundhog_Haven { ; time=0:00:43.95-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip center-mag=+3.784861302774139/+0.780907901216123/\ 1401218/1/-112.5/0 params=-4/-1.3/-0.8/-7.6/0/0/0/0 float=y maxiter=1500 inside=0 periodicity=10 colors=00000t90qH0oR2mYBkfJhvZZmRfvYdHjvShqafmkfjt\ dfz0zfozjmzmkzqjzthtxfozdhzzzzyzzvzzqyzmrzhj0dc7dc\ HdcSdcadckdctdcHztPzqUzoazmfvkkqhrmfxhd0z07z0arLo0\ 0o00o70oFBoPLzYUW00mDBjztmyqqvorrkvojxkfzhd0YW4ZYJ\ aZUaZfcardc0Uzty0vv0xr0yo4ymFzjNzfW0azLczhdrzazzct\ zdkzzozzkzzjzyhzrfzkd0Dtzz0zzmzzkzzjzzhzxfzqdzjcy2\ dP0Fhj0N0FzzcL0FtxNK0FPwJ40FapRfvSmfWrmYqUSo9BoSHo\ JLoTPoSSoYWoaZmdzvdyFFSSNWdSYqZa0zz0zxD4FJzqDFKavk\ JHMtjdPHOSN2UJQcSDYKSkWNdMUtaWjRRz0mzzozzmzzkzyjzt\ hzofzjdqzztxxxqqzjjzY2zZBzaHzaNzcSzdYzzzzzWyzZzzaz\ zazzazzazjczhczfc000FB0RFL0oW0ztHjZYhamfcJhzfxxB07\ L0DS0HZ7NhHRoPWvYZzWxzYtzZrzZozamzcjzchzdd0kj9jhLh\ fWhfhfdrdcz0zz0zz0zz2zzBzzJtzRozYh00o00kH9jYLfmWdz\ x0zt7zrBzoHzmLzkRzhUzfZy0y0zY7zZHzZPzaYyaftamocvjc\ J0afJc0rz0ovNkohhhN4zS4zYBzcFxfLtkPqqSmtYjyaftzzzv\ PzmW0vx0rt9qqLmmYkkhhhrfd } 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 20-12-08 (Fair-Weather Fiend [6])
by Jim Muth 19 Dec '08

19 Dec '08

FOTD -- December 20, 2008 (Rating 6) Fractal visionaries and enthusiasts: Today's image lies in the parent fractal that results when a Mandelbrot set begins turning into a Z^(-33)+C Mandeloid. This parent fractal catches the Z^(-33)+C Mandeloid just starting to emerge. In this case the change is created by the tiny value of -(9*10^0000000000000000001), which is entered as the real(p2) parameter. Far lesser values may be entered when the parent fractal is on the screen, but they result in a blank screen when today's image is displayed. Today's scene is located along the positive X-axis, in one of the triangular points of the just-emerging Z^(-33) Mandeloid. The parent fractal has X-axis symmetry, though this has been lost by rendering the image with the outside set to 'summ', which disguises such symmetry. I renamed the image "Fair-Weather Fiend" when I glanced out the window at the sloppy scene outside. The original name was "Fair- Weather Friend". I had to cut short the coloring when FL hinted that the sidewalk needed to be cleared. As a result, I could give the image a rating no higher than a 6. This is still a bit above average, but nothing to e-mail home about. The calculation time of around 2 minutes is about what the image is worth. Those who think the image is not worth this much time may save a minute by viewing the image in finished form on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy snow Friday morning here at Fractal central gave way to ice pellets by midday and light rain in the afternoon, while the temperature hovered at exactly freezing. About 4-in 10-cm of slushy stuff covered the ground at day's end. The fractal cats looked upon the scene with disgust. My day was occupied with graphics work and shoveling the slush, but I still found time to find a kind of fractal. The next fractal will be posted in 24 hours. Until then, take care, and experience the truth. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fair-Weather_Fiend { ; time=0:01:58.66-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 passes=1 center-mag=+3.876991316377663/0/1.712864e+007 params=-33/37/-9e-019/0 float=y maxiter=1500 inside=0 outside=summ symmetry=none periodicity=10 colors=000az_eoeLjjJlmHmpFosDpuJnuPluVju`huffukeug\ dvdcvabvZavW`vT`vP_vMZvJYvGXvDWvAWvCSwEPwGMxIJxKGx\ MDyOAyP7yN9tMBpLDlKFgJGcII_HKVGMRFONEPJIOMLOOONRSN\ TVMWYMYaL`dLbgKekKgnJjqJloMgmPbkSYiVTgYOe`JccEbe9a\ YB`RD`KF_DH_6IY5LW5OV5QT5TS5VQ4YP4_N4bM4dK4gJ4iH4l\ G4nE4qD4sJ4nO5iU6eZ7`c8Wi9SnANsBJpELmHNkKOhNQeQScT\ T`WVYZXWaYTd_QgaOjbLmdJoeMlbOi_QfXTcUV`SXYP_VMaSJc\ PIeQKgRMhSOjTQkUSlVUnWVoXWpYXrZYs_YrYXoWWlUVhRTdPP\ aNOYMNUKNRHNPFMPGPRIQTKTVMWXOZZQa`SdbUgdWjfYmg_oja\ pmcpodqrfqtgqrhrphroirmirljsjjsiksgksfkshmqjoolpnn\ rlpsjruitvgvxewydooegff_XfSOgLFgHGaDHX9IS5JN2JI5MK\ 7OL9QMBTNDVOFXPI_QKaRMcSOfTQhUSjVUlWPaPLRIHGBD55UC\ 4iI4gG6eF8cEAaDC_CEYBGWAIU9JS8LQ7NO6PM5RK4TI4VH4Wa\ eQbdPbcPccOcbOcaNdaNd`Md`Me_LeZLfZKfYKfXJgXJgWIgWI\ eXHcXHaYH_YHYZHWZHU_HS_GQ`GO`GMaGKaGIbGGbGEbGCfFBj\ F9nF8rFEoDKlCPjBVgA`d9eb8 } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 19-12-08 (Olive Oil [6.5])
by Jim Muth 18 Dec '08

18 Dec '08

FOTD -- December 19, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: With today's image we return to the good old MandelbrotMix4 series of formulas, still the most often used of all the FOTD series of formulas (formulae). The parent fractal is a Mandelbrot set rotated 180 degrees, with a huge extra bay beyond its East Valley, which in this case is on the west side of the main bay. This new bay is enclosed by East Valley, which now appears in two branches, exactly like Seahorse Valley. Today's scene is located on the shore line of this East Valley that faces the new bay. I named the image "Olive Oil", not after Popeye's girl friend, but after the olive green colors of the bubbles. I could rate the image only at a 6.5, and this includes a 1/2 point reward for my coloring effort. The bubbly effect was achieved by rendering the image with the inside set to 'bof60'. The olive bubbles are actually open holes. The calculation time of a speedy 1-1/2 minutes may be avoided entirely by surfing out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoying to the maximum the finished image posted there. Partly cloudy skies and a temperature of 37F 3C made Thursday a rather pleasant start-of-winter day here at Fractal Central. The fractal cats continued to keep their eyes on the local squirrels, who were still unusually active. My day was average. The next FOTD will be posted in 24 hours. Until then, take care, and it's obvious that nothing could exist but the natural world. Therefore all the so-called supernatural things skeptics dislike must be parts of the natural world that have yet to be accepted by conventional science. Skeptics and believers appear to be disagreeing on little more than where the natural world ends. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Olive_Oil { ; time=0:01:31.05-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident center-mag=+0.276483351592095/+0.1559172895409065/\ 1.143798e+008/1/76.5/0 params=-0.5/3.5/1/2/0/0/0/0 float=y maxiter=1500 inside=bof60 periodicity=10 colors=000zzzyyzxxzwwvuvrsumqthoscmrZkpUinQgmNekLc\ hKaeI_bHY_GXXEWUDVTETSCRPBPMAMJ8KG7HD6FA5DK4QU4Wc4\ `m4WhBRdIM_PHWW5mMCSbD0uJ6rPBoUGmgFYtEIkORbXZUefLn\ nRllXjkbhihfhndfsce000tbduacvabv`bw`aw`asbaocakeag\ facga_iaWjaSka46`57a58a69a69a7Aa7Ba7Ca8Ca8Da9Ea9Ea\ 9FaAGaAHaBHaBFaCGaCHaCIaDJaDKaELaEMaENaFOaFPaGQaGR\ aGRaHSaHTaIUaIUaJVaJWaJXaKXaKYaLZaLZbL_cM`dMaeNafN\ bgOchOdiOdjPekPflQgnQipQkrRmtRnvSpxSrz0UG4WI5YJ6_K\ 7aK8cL8eM9fMAgNBhOChOChPFhQKiQPiRUiSZiScoChlFmiJrf\ MvcPzYOzTOzOOzINzDNz8NzFQzLSzRzzXzwbzxhzmlzjgzgczd\ ZzbVz_QzXMzUHzYCzSDzMDzGDzCAzADzB2z9Fz7Rz5bz8_zBYz\ EWzHTzKRzNPzTJzPNzMRzIVzFZzBbz3jz8fzDbzI_zMWzRSzWP\ z`LzhBzdIziGz`OzSVzKazJ_zIZzIYzHXzGWzGVzKYzO`zYWzg\ SzuRzqOzmMzjKzfHzbFzO5z_DzjLzuSzkTzbUzTVzKWzAXz1Yz\ 5_z9`zDbzHczGXzFRzEKzDEzC7zB1zG8zLEzQKzUQzZWzcazhg\ zlmzn_zoMzw0zp9ziIzbRzW_z } 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 18-12-08 (The Mandelbrot Set [6])
by Jim Muth 17 Dec '08

17 Dec '08

FOTD -- December 18, 2008 (Rating 6) Fractal visionaries and enthusiasts: Today's image shows a Mandelbrot set. The name "The Mandelbrot Set" is a little confusing. To begin, there is not one Mandelbrot set, but an infinity of them. The Mandelbrot shape is kind of a universal shape, much like the parabolic shapes that appear so often when the graphs of functions are plotted. Actually, the scene shows a tiny minibrot just east of the large Minibrot on the main negative spike of the Mandeloid that results when the familiar M-set just starts changing into the Z^(-2) Mandeloid. At this early stage of the changeover, only a few extra rings around the original M-set are obvious. Most of the effect of the image is a result of rendering it with the outside set to 'summ'. The apparent X-axis symmetry is an illusion. A close look will reveal that no symmetry exists. If I had more time to work on the colors, the image might have rated a 7. As it is, the predominant theme of orange and green is rather unattractive, holding the rating to a 6. The calculation time of a fireball 50 seconds makes up for the less-than-great colors. And the finished image is posted for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Two centimeters of snow overnight Tuesday changed to rain at daybreak Wednesday here at Fractal Central. By midday, the temperature had reached 37F 3C, and the snow was gone, making the fractal cats happier. But the cats' main interest was watching the squirrels, which were unusually active gathering nuts all day. Maybe the squirrels know something about the coming weather that the weather people don't. We'll keep our eye on things for the next several days. My day was very busy, making for another hasty FOTD. The next in the apparently endless series of FOTD fractals will be posted in 24 hours. Until then, take care, and check for reason. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Mandelbrot_Set { ; time=0:00:50.66-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 passes=1 center-mag=-1.745\ 9134924/0/13838 params=-2/6/0.001/100 float=y maxiter=750 inside=0 outside=summ logmap=yes colors=000zZ0zZ0zZ0zZ0zZ0zZ0zZ0zZ0zZ0zZ0zZ0zZ0zY0z\ X0zW0zV0zU0zS0zQ0zO0zM0zK0tF0gA0W50L20BD06N02W09P0\ GL0NDBU9Rz2zz0zz0zz0zz0zbgzYgzzgzzgzzgzGgzBgz6IR2J\ N0KI0MD0O90Q40S00U00U00V00W00X00Y00Z00_20aD0cR0db0\ cm0cm0cm4bjD``NWRWRIeP9eRDeWIg`NgeRgjYglbjqgjvljzq\ jzvjzzlzvozqozoqxjqvettbtqYvoUxlRxjNzjIzgGzeBzb6z`\ 4zY0zW0zU0zR0zP0zP0zR0zR0zR0zR0zU0zU0zU2zU4zW6xWBx\ WDvWGtYItYLqYPqYRo`Uo`Wl`Yl`bjbejbggbjgblWe`LeR9eG\ 0e60e00e00b00b00b00b00b04`09`0G`0L`0P`0U`0YY0bY0gY\ 0oY0tY0xW0zW0zW0zW0zW0zW0zl0zz0zz0zz00000B00b00Y00\ W00U02R0BP0LN0UL0bI0lG0vD0zB0z90zG0zL0zP0xU0vY0tb0\ og2ll4jq9exzbzz`zzWzzUzzRzzNzzLzzIzzLzzLzzLzzLzzLz\ zLzzLzzLzzLzzLzzLzzLzzLzzLzzLzzLzzLzzLzzLzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 17-12-08 (Going Too Far [No Rating])
by Jim Muth 16 Dec '08

16 Dec '08

FOTD -- December 17, 2008 (No Rating) Fractal visionaries and enthusiasts: The rush continued here at FC on Tuesday, though things were not as hectic as on Monday, when we had two customers crying for their jobs immediately. This allowed me a bit more time to find a fractal, but the result still falls short of FOTD standards. Today's image is absolutely saturated with fractal detail, so much in fact that it suffers from the excess. With so much detail, I'm not even sure the image can be called good. I gave the image no rating. The name "Going Too Far" refers to the detail in the image, which is so excessive that it spoils the fractal effect. The scene lies in the East Valley area of a Mandelbrot set just starting to morph into a Z^(-12) Mandeloid. The tiny real(p2) parameter of 0.0000001 is what makes the M-set go crazy. The moderate calculation time of 4 minutes is still a bit too slow for such a mediocre image, but fractal salvation is to be found on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is or soon will be posted for instant gratification. Heavy clouds prevailed here at Fractal central on Tuesday, while the temperature hung around 34F +1C. The few light flurries of snow melted as fast as they fell. The fractal cats checked the weather, then decided to spend the day exploring the bookshelves in the long hallway. My day was very busy, but nothing like Monday. The next FOTD will probably but not certainly appear in 24 hours. Until then, take care, and hope for the best. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Going_Too_far { ; time=0:04:06.42-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 passes=1 float=y center-mag=+0.2681664100822315/+0.00007660809397/\ 6.490822e+007/1/97.5/0 params=-12/16/1e-007/17 maxiter=2500 inside=0 logmap=214 periodicity=10 colors=0008K77L46M07M27M37M47M67M77M87MA7MB7MC7ME7\ MF7MG7MI7MJ7MK7MM7MN7MO7MQ7MR7MS7MU7MV7MW7MY7MZ7M_\ 7Ma7Mb8La7Mc7Nd7Nf7Og7Pi7Pj7Ql6Rm6Ro6Sp6Tr6Ts6Uu5V\ x6Uv7Tu8Ts8Sr9SpARoBQnBQlCPkDPiDOhENgFNeGMdGMbHLaI\ K`IKZJJYKJWLIVLHUMHSNGRNGPOFOPENQELQDKRDISCHN8ISCG\ WFE_IDcLBhO9lR8pU6tX4x_3vc4ug5tk5so6rs7qw7no6kh5ia\ 4fV3cO2aH1`G2_G2_F2ZF2YE2YE2XD2WD2WC2VC2VC2UB3TB3T\ A3SA3R93R93Q83P83P73O73O73NA4ND4MF4MI4LK4LNzLQzKSz\ KVzJXzJ_zIazIdzIgzHizHlzGnzGqzFtzGszHszIszJszKszLs\ zMszMszNszOszPszQsFRsGSsHTsITrJUrKVrLWrMXrNYrOZrP_\ rQ_rR`rSarTbrUcmVdcWecXecXbcZ`m_Zt`zzzzzzzzzzzzzzz\ zzzzzzzzzzzzJvzLuzMtzNshPrhQqhRphTohUnhVmhXlhYkhZj\ h`ihahhcghdfheehgdhhchibhkahl`hm`hoahpbhrciqfhpiho\ mhoqhnthmwhlzglzgkzgjzgizgizghzggzffzffzfezfdzfczf\ czfbzeaze`ze`ze_zeZzeZze_zd`zdazdbzdczcdzcezcfzcgz\ chzbizbjzbkzblzaAzF9zC9z9 } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 16-12-08 (Microscopic Outlook [No Rating])
by Jim Muth 16 Dec '08

16 Dec '08

FOTD -- December 16, 2008 (No Rating) Fractal visionaries and enthusiasts: An unusual rush on Monday means the FOTD for December 16 is not only quite late, it is also quite abbreviated. The image is simply a deeper scene in the same type of image as yesterday's FOTD. I named it "Microscopic Outlook" because of its magnitude; I gave it no rating because of its hastiness. The cauculation time of 5-2/3 minutes is a bit longer than the image is actually worth, so I recommend viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> But before surfing out there, give Paul a chance to calculate and post the image. Heavy clouds and occasional light rain spoiled the spring-like temperature of 61F 16C here at Fractal Central on Monday. The fractal cats sulked through most of the day, while my day was frantically busy. Hopefully, tomorrow will be a bit less fran- tic, though the actual appearance of a FOTD is problematic. Until next time, whenever that might be, take care, and when we finally see the truth, will it be the theists or atheists who we find out were right? (Atheists already tell me I'll never find out that they are right!) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= MicroscopicOutlook { ; time=0:05:38.70-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 center-mag=+2.550756942047\ 727/+0.351679539861654/1.721177e+011/1/-80/0 params=-2/6/0.005/70 float=y maxiter=6200 inside=0 periodicity=10 mathtolerance=0.05/1 colors=000GjTKfROcOS_MWXJ_THnJBkOAcQFWRJOSOD_JHTSQ\ tzOhbNYaLM`Q8YO9ZMA_KB`JBaHCbFDcDEd3GM6FT9EZCEdFDj\ ICpFk6KCvLFzMIzMKzNNtNPsOSsQVuOUsNTqMSoLRnKQlJPjJO\ kIPjIPiIQhIQgIQfIReIRdKaxJWnIRdHMVGHLFCBE72FE8GKDH\ QIIXNJbSo5bMg_KhXJiVHjSGkQElNDmLBnIAnG5_80L02KA3KJ\ 4KT5Ja6Jk7JtJOeUTSTTSSTRRSRRSQQSPPRPOROORNNQNMQMLQ\ MLQLKPKJPKIPJIOIHOIGOH9_w1ax4Zr6Xl8VfAT`DRVFPPHNJJ\ LDIQEIUEHZFHbFGgGGkGZdKuSTsWQqZNoaKmdHkgEijBzsLzuG\ uzCgm8ak4TkBVj5Wj0bmPmvpjrnholflkciiafh_cfeZXb____\ bY`eVzhSakQznNbqUWyRZwO`uLbtIdrFfpCho9jmWxJ_lR4qm7\ llAhlDdlG_kJWkMSkOLmONlOOkOPjOQiOShOTgOUfGXRK_ZOVe\ SQmSExUIvWLtYOr_RpaUncXlqFmmMliTke_jbhkbgjbfjbej`d\ dZc_YcVzKcGemaEtYRbVbLXQzVPvTOsRNpPMmNLiLKfJJcnQLb\ NRSLWHJ`JLaLMbMOcOPcQRdRSeTUfUVfVZgWahXeiXhiVhfUhc\ Th`RhYQhVPhSLjOOhQQfSSeUUcVWVXY`ZZUp__g_R_TLSKKKPC\ Ce54RIFIbk2mz9f_laUWfTBnW } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 15-12-08 (Emergency Valley [No Rating])
by Jim Muth 14 Dec '08

14 Dec '08

FOTD -- December 15, 2008 (No Rating) Fractal visionaries and enthusiasts: Today's fractal is another one found so hastily that I could give it no rating. It's actually a scene in the fractal that results when the Z^2+C Mandelbrot set is starting to change into the Z^(-15)+C Mandeloid. In this case the minute real(p2) parameter of 0.000000001 makes a world of difference. I'll not try to describe the parent fractal, which is very easy to calculate. But I will say that today's image is found in some new detail that has appeared some distance east of East Valley of the M-set. The name "Emergency Valley" was supposed to be "Emergent Valley", but when I typed 'emergency' by mistake, I thought it a serendipitous error, and kept the mistake. I had little time to work with the colors, which obviously could be improved quite a bit. The calculation time of a blessedly brief 48 seconds is just what the doctor ordered. As always, the finished image may be accessed on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Lots of sun and a temperature of 45F 7C kept the fractal cats happy while FL and I decorated the tree here at Fractal Central on Sunday. Except for a minor disagreement about what ornament should be at the top of the tree, (star or angel), things went better than usual. The next FOTD will be along in 24 hours. Until then, take care, and stand by your fractal when it is in distress. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Emergency_Valley { ; time=0:00:48.69-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 passes=1 periodicity=10 center-mag=+0.6657136196201/+0.00194141904577634/\ 2.561881e+007/1/-135/0 params=-15/19/1e-009/17 float=y maxiter=1500 inside=0 logmap=42 colors=000hAOTYjWTQZWZaXVdXbggMMipmUq0cne`uWguVaQ0\ 00000000RUMZZSfcYnhcvmiswfzzUnz0kJ`zcZfIXcIVaITzLV\ eNWgQYiSZkV`lXagcXbiSYoNTuJUhCVX5ZT7aP9dLBhHDkDFn9\ Hq5IhJG_XFaZGb_GdaGebHgdHheHifHV`TGWd2RoSSWpTCrODs\ JDtEDu9Dv4DtAJsFPrKVqP`pVfo_lndrmixPXe0KO2NP4PQ6SR\ 7US9WTBZUD`VEbVLcNRdFXe7UZ5ST4QN3OG2MA1K40I82HB3GE\ 5FH6DK7CN9BQAATB9SC8RD8QE7QF7PG6OH6OH4aX3nl9P4NIJ_\ CXm6kz0yq4vh7t`AqSDoKGmOMiRRfVXcYa_agXdlUcnzbpzaqz\ `sz_tzZvzZwzYxzXyzXzzWzzWzzVzzVzzczzlzzuzzdzzPzz9z\ zIzzQzzYzzezz`zzXzzSzzOzzQzzSzzTzzVzzWzS`zLtz_szUr\ zPqzKpzEoz9nz4lz8jzBhzFfzIdzMbzPazS_zPZzMXzJWzGUzD\ TzBQzCNzCKzDHzDEzDOzYLz_Iz`FzbCzc9ze6zf3zh0zi2zd4z\ _6zV8zRAzMCzHDzDIzEMzERzEVzE_zEczEdzDezCfzBgzAhz9i\ z8iz8Ez9Hz8Jz7Lz7Nz6Qz5Sz5Uz4Wz4Vz5Vz5Uz6Uz6Tz7Tz7\ Tz7SzCSzGSzKSzOSzSSzWSz_bzmmzzkzhizRgz9jz7lz5nz4jz\ 9fzEbzJZzOVzTSzXszMvzFuzK } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 14-12-08 (Superspiral [No Rating])
by Jim Muth 14 Dec '08

14 Dec '08

FOTD -- December 14, 2005 (No Rating) Fractal visionaries and enthusiasts: Sorry for the lateness fractal folks, but with all the shopping and graphics work, Saturday was just a bit too busy to produce an acceptable FOTD by the usual post time. For some reason, spirals are quite popular among those who aspire to turn fractals into fine art. Since I would like nothing better than being a world renowned and fabulously wealthy 'fractal artist', I decided to post a spiral that I found in a couple minutes late Saturday evening. The parent fractal pictures a Mandelbrot set well along the way to becoming something else. I'm not sure what 'something else' is, but the result resembles a swiss cheese filled with bits and pieces of stuff with Mandelbrot buds. Today's scene is located in some of this cheesy stuff in the northwest part of the parent. I named the image "Superspiral" perhaps a bit too enthusiastic- ally. Considering the way the spiral rotates when the colors are cycled, I could just as easily have named it something like 'Pinwheel". I could not take the image seriously enough to give it a rating however. Adding to the difficulties is the fact that the calculation time of over 11 minutes is simply too slow for a commonplace fractal spiral. But this little difficulty may be overcome by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it is or soon will be posted for instant viewing pleasure. Partly cloudy skies and a temperature of 32F 0C were just enough to keep the fractal cats happy here at Fractal Central on Saturday. The 1cm of snow that fell overnight Friday did not worry the feline duo. My day was busy with work and shopping. Tomorrow should be less busy. The next FOTD is due in 24 hours. Wait for it with bated but not abated breath. Until then, take much care, and I have nothing against fine art, but I think fractals should be consid- ered wonders of nature rather than products of human artistic aspiration. I'll show the world a great piece of 'fractal fine-art' the day after someone shows me a great 'paint by numbers' fine-art oil painting. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Superspiral { ; time=0:11:33.98-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 passes=1 center-mag=-6.789971557495536/+1.764777547153925/\ 3474.939 params=0/4/0.09/60 float=y maxiter=15000 inside=0 outside=summ periodicity=10 colors=000QI8QG8QE8QF8RG8RD8RB8R98Q66R78S79S7AT7BU\ 8CU8DV8EV8FW8GX9HX9JY9KY9LZ9M_AN_AO`AP`AQaARbBSbBT\ cBVcBWdCXeCYeCZfC_fC`gDahDbhDciDdiDfjEgkEhkEilEjlE\ kmFlnFmnFnoFopAqoDpoFpoHpoJpoLpoNpoPpoRpoUpoWpoYpo\ _pnapncpnepngpnjpnlpnnpnppnrpntpnvppxqoxpnwpmwplvp\ kupjtpisphrphqpgppfppeopdnpcmpblpakp`jp`ip_hpZgpYf\ pXfpWepVdpUcpUbpTapS`pR_pQZpPYpOXpNXpMWpMVpLUpKTpJ\ SpIRpHQpGPpFOpDMuENsEOqFOpFPnFQlGQkGRiGSgHSfHTdHTb\ IUaIV_IVYJWXJXVJXTKYSKYQKZOL_NL_LL`JMaIMaGMbENbDNc\ BNd9Od8Oe6Of4Pf3Pg1Pg0Re6TcCVaIX_NZYT`WZbUdcTiaUj`\ Uj_VkZVkYWkXWlWWlVXlUXmSYmRYmQYnPZnOZnN_oM_oL`oK`p\ J`pHapGaqFbqEbqDbrCcrBcrAds9ds7cu8dt8dt8ds9es9er9e\ r9fqAfqAfpAgpBgoBgoBhnBhnChmCimCilCilDjkDjkDjjEkjE\ kiEkiElhFlhFlgFmgGmfGmfGneGneHndHodHocEsgFqeGpdHoc\ HmbIlaJk_JiZKhYLgXRj8Rk8Rk8Rl8Rl8Rm8Rr9Ro8Rm8Rk8Rh\ 8Rc8RZ8RU8RS8RQ8RO8RM8RK8 } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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R: Re: R: FOTD 13-12-08 (Two Into Fifteen [6])
by jakovll＠libero.it 13 Dec '08

13 Dec '08

now it gets me there with no problem, don't know what happened! thanks anyway Jacopo >----Messaggio originale---- >Da: Paul.N.Lee(a)Worldnet.att.net >Data: 13/12/2008 1.40 >A: <fractint(a)mailman.xmission.com> >Ogg: Re: [Fractint] R: FOTD 13-12-08 (Two Into Fifteen [6]) > >Jacopo L. wrote: >> >> sorry when I try to get to that page it >> says Page URL Not Found!! why? >> >>> ----Messaggio originale---- >>> >>> FOTD -- December 13, 2008 (Rating 6) >>> The already finished image is posted to the FOTD web site at: >>> http://home.att.net/~Paul.N.Lee/FotD/FotD.html >>> > >This particular link, which is listed above, has been working since 1997. > >Or did you get an error when trying to view a specific FOTD web page >within the site ?? > > >Sincerely, >P.N.L. >------------------------------------------------- >http://home.att.net/~Paul.N.Lee/PNL_Fractals.html >http://www.Nahee.com/Fractals/ > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

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R: FOTD 13-12-08 (Two Into Fifteen [6])
by jakovll＠libero.it 12 Dec '08

12 Dec '08

sorry when I try to get to that page it says Page URL Not Found!! why? Jacopo L., Rome >----Messaggio originale---- >Da: jamth(a)mindspring.com >Data: 12/12/2008 20.53 >A: <fractint(a)mailman.xmission.com> >Ogg: [Fractint] FOTD 13-12-08 (Two Into Fifteen [6]) > > >FOTD -- December 13, 2008 (Rating 6) > >Fractal visionaries and enthusiasts: > >Today's image shows what happens when a fractal with a positive >exponent of Z (in this case 2) starts to change into a fractal >with a negative exponent of Z (in this case minus 15). As the >real(p2) parameter of 0.0000001 shows, a very small departure >from zero makes a great change in the appearance of the result- >ing fractal. Curiously, the image is also quite sensitive to >the bailout radius. > >The original Mandelbrot set is still present at the center of >the image, but the 16 points of the minus 15 Mandeloid are >already fully formed, symmetrically surrounding the Z^2 figure. > >I named the image "Two Into Fifteen" because it shows a Mandel- >brot set already well on the way to being a Z^(-15) Mandeloid. >There are almost certainly many interesting minibrots deep in >today's image, which is actually its own parent fractal. I >might search out a few of them in upcoming FOTD's. > >As for a rating, I decided on a 6. I really put too little >effort into the coloring to rate the image higher. > >Even with the passes set to 1, the image is extremely fast, >finishing in a mere 15 seconds. > >The already finished image is posted to the FOTD web site at: > > <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> > >Friday dawned with wet snow falling here at Fractal Central, but >with the temperature around 34F +1C, it melted almost as fast as >it fell. A little sun peeked through the breaking clouds in the >afternoon, too little too late to make the fractal cats happy. > >My day was rather busy, though not as hectic as it would have >been if problems had come up. The next FOTD is due to be posted >in 24 hours. A lot of graphics work remains to be finished >however, so there is no guarantee that the FOTD will appear as >scheduled. Until next time, take care, and shun disappointment. > > >Jim Muth >jamth(a)mindspring.com >jimmuth(a)aol.com > > >START PARAMETER FILE======================================= > >Two_Into_Fifteen { ; time=0:00:15.42-SF5 on P4-2000 > reset=2004 type=formula formulafile=basic.frm > formulaname=DivideBrot6 passes=1 > center-mag=-0.03296/0/0.295 params=-15/19/1e-007/17 > float=y maxiter=1000 inside=0 logmap=yes > symmetry=xaxis periodicity=10 > colors=000FoctThhKzmx0hzzHcdHUYHKSJMPKONLQLNSIOUGP\ > WEQYCMUKIQREMYAIdFKZKMUPOPUPKZRFcTAgU5hTMhTahTqiOs\ > jJukEzl9zl4zk7zj9ziBzhDzgFzfHzeJzeLziWzmezqoztyzrQ\ > z6YzJJzW4z`IzeVzdUzdTzdSzdRzdQzdPzdOzbTzaYzcUzdRzf\ > NzgKzhHzdIzaJzZKzWLzSMzPNzMOzJPzIQzIRzHSzHTzHUzHXz\ > p2z2Rz8SzETzKTzQUzWVzaVzgWzlWzAdzEezHezKezNezQezOX\ > zNOzK_zIkzGwzSpzcizoczHUzKOzNJzQDzT8zNizRhzzhfzhhz\ > hjzhkzdez``zXWzVOzTGzUUzTSzTQzTOzTNzTLzTJzSIzSGzSE\ > zSDzSBzS9zbNzXFzXgzUQzSezSbzS_zSYzSVzSSzSQzSNzSLzS\ > IzSFzSDzSAzUdzkgzfazaWzXQzSKzNEzI8zE2zF3zG4zH5zI6z\ > J7zK8zK9zIAzGAzEAzCBzABz8Bz6BzCQzHczMqzQjzKazETz8K\ > zTebmzYntUonPqhLscNudOweQxfRygSzgzzezzdzzczzbzzazz\ > `zzazzbzzczzczzdzzezzfzzfzzgzzizzjzzkzzkzzkzzkzzkz\ > zkzzkzzkzzkzzkzzkzzkzzkzzkzzkizkkzjlzjmziozipzhqzh\ > rqhozdmzakzZizWjzXjzXjzXkzYkzYkzYkzYlzZlzZlzZlzZmz\ > _mz_mz_mz_izTfzNczHczGbz7 } > >frm:DivideBrot6 { ; Jim Muth >z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, >d=real(p2)+0.00000000000000000001, f=imag(p2)+16: >z=z^(a)/(z^(-b)+d)+c >|z| < f } > >END PARAMETER FILE========================================= > > > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

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FOTD 13-12-08 (Two Into Fifteen [6])
by Jim Muth 12 Dec '08

12 Dec '08

FOTD -- December 13, 2008 (Rating 6) Fractal visionaries and enthusiasts: Today's image shows what happens when a fractal with a positive exponent of Z (in this case 2) starts to change into a fractal with a negative exponent of Z (in this case minus 15). As the real(p2) parameter of 0.0000001 shows, a very small departure from zero makes a great change in the appearance of the result- ing fractal. Curiously, the image is also quite sensitive to the bailout radius. The original Mandelbrot set is still present at the center of the image, but the 16 points of the minus 15 Mandeloid are already fully formed, symmetrically surrounding the Z^2 figure. I named the image "Two Into Fifteen" because it shows a Mandel- brot set already well on the way to being a Z^(-15) Mandeloid. There are almost certainly many interesting minibrots deep in today's image, which is actually its own parent fractal. I might search out a few of them in upcoming FOTD's. As for a rating, I decided on a 6. I really put too little effort into the coloring to rate the image higher. Even with the passes set to 1, the image is extremely fast, finishing in a mere 15 seconds. The already finished image is posted to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Friday dawned with wet snow falling here at Fractal Central, but with the temperature around 34F +1C, it melted almost as fast as it fell. A little sun peeked through the breaking clouds in the afternoon, too little too late to make the fractal cats happy. My day was rather busy, though not as hectic as it would have been if problems had come up. The next FOTD is due to be posted in 24 hours. A lot of graphics work remains to be finished however, so there is no guarantee that the FOTD will appear as scheduled. Until next time, take care, and shun disappointment. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Two_Into_Fifteen { ; time=0:00:15.42-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 passes=1 center-mag=-0.03296/0/0.295 params=-15/19/1e-007/17 float=y maxiter=1000 inside=0 logmap=yes symmetry=xaxis periodicity=10 colors=000FoctThhKzmx0hzzHcdHUYHKSJMPKONLQLNSIOUGP\ WEQYCMUKIQREMYAIdFKZKMUPOPUPKZRFcTAgU5hTMhTahTqiOs\ jJukEzl9zl4zk7zj9ziBzhDzgFzfHzeJzeLziWzmezqoztyzrQ\ z6YzJJzW4z`IzeVzdUzdTzdSzdRzdQzdPzdOzbTzaYzcUzdRzf\ NzgKzhHzdIzaJzZKzWLzSMzPNzMOzJPzIQzIRzHSzHTzHUzHXz\ p2z2Rz8SzETzKTzQUzWVzaVzgWzlWzAdzEezHezKezNezQezOX\ zNOzK_zIkzGwzSpzcizoczHUzKOzNJzQDzT8zNizRhzzhfzhhz\ hjzhkzdez``zXWzVOzTGzUUzTSzTQzTOzTNzTLzTJzSIzSGzSE\ zSDzSBzS9zbNzXFzXgzUQzSezSbzS_zSYzSVzSSzSQzSNzSLzS\ IzSFzSDzSAzUdzkgzfazaWzXQzSKzNEzI8zE2zF3zG4zH5zI6z\ J7zK8zK9zIAzGAzEAzCBzABz8Bz6BzCQzHczMqzQjzKazETz8K\ zTebmzYntUonPqhLscNudOweQxfRygSzgzzezzdzzczzbzzazz\ `zzazzbzzczzczzdzzezzfzzfzzgzzizzjzzkzzkzzkzzkzzkz\ zkzzkzzkzzkzzkzzkzzkzzkzzkzzkizkkzjlzjmziozipzhqzh\ rqhozdmzakzZizWjzXjzXjzXkzYkzYkzYkzYlzZlzZlzZlzZmz\ _mz_mz_mz_izTfzNczHczGbz7 } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 12-12-08 (Positively Negative [5])
by Jim Muth 11 Dec '08

11 Dec '08

FOTD -- December 12, 2008 (Rating 5) Fractal visionaries and enthusiasts: A very busy day on Thursday means a short discussion. Today's image exists in a fractal that is starting to change from a Z^2+C Mandelbrot set to a Z^(-12)+C Mandeloid. There is quite a bit of interesting stuff that happens when a fractal with a positive exponent starts to change into one with a negative exponent, but that story will have to wait for a less busy day. The chief feature of today's image is the incredibly sandy texture of the East-Valley-type elements surrounding the central minibrot. The name "Positively Negative" refers to the change from a positive to a negative exponent of Z. The rating of a 5 is all I could give the image, which is merely a fancy-decorated scene in an East Valley elephant trunk. The calculation time of 8-1/2 minutes is somewhat slow. For those who do not run parameter files, the finished image is or soon will be posted on the FOTD web site for instant viewing. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A steady all-day rain and temperature of 34F +1C kept a damper on things here at Fractal Central on Thursday. The fractal cats gave up hope early, and spent the day in the coziest places they could find. In my department, the day was far too busy for me to pay much attention to the weather. The next FOTD is due to be posted in 24 hours, though with another very busy day or two expected, don't be surprised if I miss a couple days. Until next time, take care, and be at peace. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= PositivelyNegative { ; time=0:08:27.85-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 passes=1 float=y center-mag=-2.265184766427815/-0.0000038148153571/\ 2.576178e+009/1/-145/0 params=-12/16/1e-007/17 maxiter=5000 inside=0 logmap=574 periodicity=10 colors=000LU_NVYPWXQXVSYTUZSW_QY`OZaN`bLbbJdcHedGg\ eEifCkgBmh9ni7pj6rk4tl2ul1epLQtcBwvGrsKmqOhnSdlX_j\ `VgdQemPhhMccJ__GWVDSO5KQ8MRBOSEPTHRUKTVNUWPWXSYYV\ ZZY`_`b`ccafebhgckhdnjeqlftmgwohypiwnjvlktjlsimqgn\ peoodpmbql`qj_riYsgWtfVueTvcRwbQx`Oy_MzdByaGyZLyWQ\ xUUxRZxOcxLhwJlwGqwDvwBzlClaCZRCL722C75HC8MHAQMDVR\ F_WIe_Lc`KbaK`bJ_cJZdIXeIWfHUgHThGSiGQjFPkFOkFNiIM\ hKLgNKfPKdSJcUIbXHaZH``DiW9qR5yM8uOBrPEoRGlSJiUMfV\ PcXR`YUY_XV`RZjZSafLTnEKu7Cq6En5Gj4Ig3Kc2M`2N_4O_6\ OZ8OZAOYBPYDPXFPXHPWIQWKQWMQVOQVQQURRUTRTVRTXRSYSS\ _SRaSRcSTiPSfRRdSQbTP_UOYVNWWNTYMRZLP_KM`JKaIIbG7Z\ IGcBNgGOhKPhOQhSRhWSh_ShdThhUhlVhpWhtXhnsTzckxXhvQ\ etKbrD_t3Tr5Vq7Xp9YoB_nD`mEblGckIejKfiMhhNigTZgZOf\ dDeh1fi2fj3fj4gk5gk5gl6gl7hm8hn9hn9hoAioBipCipCiqD\ jrEjrFjsGjsGktHktIkuJkuJ`zEOz8QzASzBTzDVzEWzFYzHZz\ I`zJazLczMdzOfzPgzQizSjzT } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 11-12-08 (Practical Split [6.5])
by Jim Muth 10 Dec '08

10 Dec '08

FOTD -- December 11, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image is a Julia set of a point in the West Valley of the main bay of the parent fractal, which is a Mandelbrot set about half way morphed into a Z^3.5+C Mandeloid. The main bay of this parent is filled with debris and has a valley on the west side as prominent as the valley on the east side. I named the image "Practical Split" for no rational reason. The lack of a reason is no shortcoming, since I need no reason when I choose FOTD names. The rating of a 6.5 honestly reflects what I consider the image to be worth. The calculation time of 2-4/5 minutes borders on slowness, but is nothing that a SOTA machine cannot handle. (Unless that machine turns panicky when it is fed an old-fashioned 16-bit program.) Those with panicky units can still see the image in completed form on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds and occasional rain here at Fractal Central on Wednesday spoiled the fractal cats' day. The temperature reached a mild 52F 11C, but totally failed to make up for the lack of sun. Despite the rainy weather, my day was fair enough. The work, though heavy, is pretty much caught up, while the day's fractal is at least acceptable. The next Fractal of the Day is due to be posted in 24 hours. Until then, take care, and debate what might be wrong with our modern culture. (Or on the other hand, what might be right!) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Practical_Split { ; time=0:02:49.53-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5Julia center-mag=0.132873/0\ /0.5 params=3.5/2/-0.5993/1e-007 float=y maxiter=7200 inside=0 symmetry=none periodicity=10 colors=000fvxS`_v2vN0LO0MP0NQ0PR0RS0ST0VU0ZV4cW8hX\ AmL0zIezFTz6CzUnzV0XM8MLCvJDjHEZFFNJLvGIZfZOSPHmfI\ VTEXfyi65tNKGo9EYAolbecWWWPMOIkF9UGACPjDMZDJN7ps8q\ u9rxAszDWiF8T1g7AcFI`NQXVZUbfQjnNrvKyuOouSeuWXt_Nt\ cDtg4rGtlFngFibEdYE_SEVNDQIDLDDGIBJN9MR8PW6R_5Ud3X\ h2Za4aV6dO8gHAjBBm96X71GK2CX29i25v22nLUlHVkDVjAVi6\ Vh3Vj5Sl6Pn7Mp9JrAGsBElDIeEMZFQSHTLIXEJ`7Kc9QaBW_C\ `ZG_UKZQOYLSYHWXD_W8cV4gV0i`2kf3ml5or6qw7ihCaVGUHL\ N3Pc4es4vF74xsDM5HLTLKpPVlYeifgjWikLjlB`oASrAIuA9x\ ARlVhaolWipRdtMZxHUhGNFEOTGHfTQSMIijITVER`UNVPKQKG\ LF4f8blQQWI9waBhTCUKORQLOMILIFIEMlfJcZHWRFOJ7NB9LB\ AJBCHB7O6N2vK6jI9ZFDNu5vf9fSDRobYWRMG4GF8EECCVUlxm\ ssUaYNOT2NVngFZzEShDMSGO2EK7OJvIHZC0gD6XDBMLPbJMWH\ KPFII95_A8TBBNCEHgd3_Y5SS7KM9krVUZL7bR9VLBNGMZEHPC\ WYkMPTBmn4agarmPZUk1Q_fnOTVeihW_XMQM239`_6zF8K0hzc\ XzzzQ_KJQFlHBcGBVGBMGBTwg } frm:DivideBrot5Julia { ; Jim Muth z=pixel, c=(p2), a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 10-12-08 (Julia in the Abstract [8])
by Jim Muth 09 Dec '08

09 Dec '08

FOTD -- December 10, 2008 (Rating 8) Fractal visionaries and enthusiasts: With little time to write a long discussion, I'll have to be brief. Today's image, another super-fast one, is the Julia set of a point in the East Valley of the large minibrot on the main negative spike of the parent fractal. This minibrot is a distorted order-8 one, while the entire parent fractal is about halfway between a Mandelbrot set and an order-8 Mandeloid. The image is basically a study in blues. I named it "Julia in the Abstract" because this name makes it appear I had deep thoughts in mind when I chose it, which of course is utter nonsense. Since the name means nothing, it can mean anything the individual chooses. The rating of an 8 indicates little more than the fact that I enjoy the color blue and think the image is rather pleasing. The calculation time of 8 seconds indicates that those who choose to run the included parameter file will no time to even think of impatience. And as always, the finished GIF product is posted for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The temperature of 43F 6C was notably milder here at Fractal Central on Tuesday, but there were so many clouds that the fractal cats turned sulky in the afternoon because their sun failed to appear. My day was fair enough, though rather busy. The next FOTD will likely be posted in 24 hours. Until then, take care, and when 'layers' became all the rage in fractal art, the magic part of fractals took flight to regions unknown. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= JuliaInTheAbstract { ; time=0:00:08.16-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5Julia passes=1 center-mag=0/0/1.253 params=8/2/-3.419/0 float=y maxiter=750 inside=0 symmetry=xyaxis periodicity=10 colors=000AFKAFKAFKAFKAFKAFKAFKAFKAFKAFKAFKAFKAFKA\ FKAGNBFMBFMAEMAEMADMADMACMADM9EL9EK9FJ9FI9FH9EH8EG\ 8DF8DE8CD8CC8CCAEFCFHEHJGILHJNJLPLMRNNTPPVQQXSRZUT\ aWUcXVeZXg`YibZkd`meaogbqidskeulfwhcreana_jZYfWWbQ\ E_SF`VFbSFcSFcRFfQFgPFeOFcNFaMFYLFWKFUJFSIFQHFOFFF\ 000zzqyunvplskjpfhmbfjZdgYbdX`aVZZUXWSVTRTQPRNNPKM\ NHLLbxT`uSZrRXoQWlQUiPSfORdOPaNNZMLWLKTLIQKGNJzHlw\ IjuIirIgpIfnIdkJciJafJ`QQYNQYKQYHQYEQYBQY8QY5QY7P_\ 8Oa9mzAhzBczDZzEUzFPzGKzHHzIFmKEcLDZMCXNBVMATLARKC\ UKEUKFUQHUXJYdKYlMYoOYrUYzcZzmWzmUzcYzWazRdzQhzPlz\ OozNszMvmVrXcoGklIljKliMmgNmfPrdRwcTzaUz`WzZYzYzzW\ zzVzzTzzSzzQzzPzzNvzMqzKqzJqwHqvGptLpsQprUpqZppcpn\ grmltlqvkuxjzzizzgzzfzyezxdzwbzuays`xq_xnZwkXvhWve\ VubUt_SsXRsUQrRPqPOq`RhlU`wWTvVRuUQtTPsSOrRNqQMpPL\ oOKnNJmMIlLGkKFjJEiIDhHCgGBfFAeE9dD8dD7bE9aEA`FBZF\ CYGDXGEWHFUHGTHHSIIRIJPJL } frm:DivideBrot5Julia { ; Jim Muth z=pixel, c=(p2), a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 09-12-08 (Study in Magnitude [6])
by Jim Muth 09 Dec '08

09 Dec '08

FOTD -- December 09, 2008 (Rating 6) Fractal visionaries and enthusiasts: Are your FOTD's for December 7 and 8 missing? I think the Fractint list has been having problems, so I'll post the FOTD to both the Fractint and Philofractal lists until I'm sure the Fractint list is up and running again. Meanwhile, the FOTD images and discussions for December 7 and 8 are posted on the FOTD web site. Today's image is named "Study in Magnitude". I gave it this name because its magnitude of over 1.7*(10^13) is one of the greatest in FOTD history. The mathtolerance entry is absolutely necessary to reach this magnitude, and even then, the signs of resolution breakdown are apparent along the sharp edges. The rating of a slightly-above-average 6 is all I could give the image, which has little but its magnitude going for it. The tiny order-7 minibrot at the center is immersed in a field of near total chaos. Do not try to zoom into the image with the type=formula DivideBrot5 formula. The breakdown gets very bad very fast beyond this point. Deeper zooms are reachable however with the type=dividebrot5 formula available in the latest release of Fractint. Arbitrary- precision math can be used with this version of the formula, albeit at the cost of a great slowdown in calculation speed. The scene of today's image is in a tiny bit of debris near the center of the main bay of its parent fractal, which is a Mandelbrot set starting to morph into a Z^7+C Mandeloid. The calculation time of a fleeting 31 seconds seems about fair for an image only a bit above average. And if even this is too slow or requires too much effort, the finished image may be seen on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> along with the missing FOTD's for December 7 and 8. Thick clouds here at Fractal Central on Monday kept the fractal cats away from their favorite window; the temperature of 21F -6C kept them near the heat. My day was about average. The next FOTD will be posted in 24 hours. If it doesn't appear on the Fractint list, check the philofractal list. Until then, take care, and let's get that old controversial fractal-related philosophy rolling again. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Study_in_Magnitude { ; time=0:00:31.09-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 center-mag=-1.126254785676\ 128/+0.00979922650540156/1.766964e+013/1/15.2/0 params=7/4 float=y maxiter=500 inside=0 logmap=57 periodicity=10 mathtolerance=0.05/1 colors=000H2HK5GN8GQAFTDFWGFZIIaLMeNQiQUmTZqVcuYcy\ _crWEmUFhSGcQF`PAeUFdUFmcFUcTMcfOct8xQArTBmWDgZEb`\ GXcHSfINhMReQVbUY_YaXadUdhRhkOloLprItvFwyCmfzcPzV7\ zW9zXAzXBzYCzYDzZFzZGz_Hz`Iz`JzaLzaMzbNzbOzcPzcQz`\ NjYKnVIrSFvQDzRCzRCzSBzSBzSBzTAzTAzTAzU9zU9zU9zUAz\ UAzUBzUBzUBzUCzUCzUDzUDzUDzXGzZIz`KzbMzeOzgQziSXkU\ YnWYpYZr_Zta_vc_nbcgam_`zT`zUXzVTzWPzXLzYHzZDz_9z`\ 5za1zW2zQ3zK4zE5z95zCEzFNzIWzLdzNlmRkzVkzYcMacMecL\ hcLlcKpcKscKpcJncJlcJjcIgcIecIccHacH_cHVizRXzUEzWG\ zYHz_IzaJzcKzeMzgNzhOzjPzlQznSzpUzrUztVzuWzjTz`Qzl\ nzahzRbzOZzMWzKSzHPzFMzDIzBFz8Dz6Gz4Iz2Lz3Oz4Rz4Uz\ 5Xz5_z6bz7ez7hz8kz8nzAqzCtzDwzFzzHzaIzbKzdMzfNzgPz\ iRzkSzlUznWzpXzqWzpVzpUzoUzoTznSznRzmRzmQzlPzlOzkO\ zkNzeMz`MzWLzRKzLKzGJzBJz6LzOMzeNzvLzmKzdIzWHzOLzQ\ OzSSzTVzVZzWazYezZhz`lzaozcrzdjznhzjgzgezddzabzZaz\ W_zTZzQuzpuztkzlazdTzXJzP } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 08-12-08 (Rhapsodic Interval [8])
by Paul N. Lee 08 Dec '08

08 Dec '08

On Sun, 07 Dec 2008 at 17:30:29, Jim Muth wrote: > > I try to keep my ambitions out of the FOTD > fractals as much as possible, making them > look like clear photographs of fractal > scenery rather than "look-Ma-I'm-an-artist" > abstract paintings. On Mon, 08 Dec 2008 at 14:12:25, Jim Muth wrote: > > ....and let's get that old controversial > fractal-related philosophy rolling again. > Speaking of controversy, fractals, and artists (especially the online variety).... Here are some definitions for 85 percent of them: _ART GALLERY_ n. -- A site for the merchandising of reputations, of which art is the incidental by-product. _ARTIST_ n. -- 1. Anyone talented enough to win foundation grants and critics' kudos by making an impression at the right parties. 2. Anyone who tweaks middle-class properties with the intention of generating free career publicity (such as those hosting and controlling fractal art contests). _ART_ n. -- This word has no definition. Its origin is related as follows by the ingenious Father Gassalasca Jape, S.J. One day a wag--what would the wretch be at?-- Shifted a letter of the cipher RAT, And said it was a god's name! Straight arose Fantastic priests and postulants (with shows, And mysteries, and mummeries, and hymns, And disputations dire that lamed their limbs) To serve his temple and maintain the fires, Expound the law, manipulate the wires. Amazed, the populace that rites attend, Believe whate'er they cannot comprehend, And, inly edified to learn that two Half-hairs joined so and so (as Art can do) Have sweeter values and a grace more fit Than Nature's hairs that never have been split, Bring cates and wines for sacrificial feasts, And sell their garments to support the priests. Sincerely, P.N.L.

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FOTD 08-12-08 (Rhapsodic Interval [8])
by Jim Muth 07 Dec '08

07 Dec '08

FOTD -- December 08, 2008 (Rating 8) Fractal visionaries and enthusiasts: I try to keep my ambitions out of the FOTD fractals as much as possible, making them look like clear photographs of fractal scenery rather than "look-Ma-I'm-an-artist" abstract paintings. But today's image is really little more than a result of the color manipulation I did on the original image. It is a scene in left-over debris in the 'Seahorse Valley' (if that's what it is) area of the parent fractal, which is a Mandelbrot set caught in the act of morphing into a Z^7+C Mandeloid. The image consists of half normal 'outside' stuff and half flat 'inside' stuff brought to life by the 'bof61' inside fill. I named it "Rhapsodic Interval" for no rational reason. I rated it at an 8 because I think it's worth the rating, which includes one full point for my coloring efforts. The calculation time of just under 3 minutes may be cut in half by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Long intervals of sun here at Fractal Central on Sunday kept the fractal cats happy, but the blustery winds and temperature of 25F -4C, combined with a few flurries of snow, kept the people on the streets well wrapped. My day was spent in recovery from yesterday's shopping expedi- tion. The next FOTD will be posted in 24 hours. Until then, take care, and everything that exists must be a part of the natural world, but as the known limits of the natural world keep receding ever farther beyond our understanding, they may soon include some things now considered supernatural. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Rhapsodic_Interval { ; time=0:02:55.00-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 passes=1 center-mag=-2.972161206163067/0/2809.658 params=7/4 float=y maxiter=3600 inside=bof60 logmap=yes symmetry=xaxis periodicity=10 colors=000zUQwTOtSMpQKlOJhMHdKF`IDXGCTEAPD8L90GA0G\ B3HC5HD5JEALFFSLXUM_WN_YO_ZP__Q_`R_aS_cT_eU_gV_iW`\ kXamYboZcq_cq`cq_cpZcoYcnXcmWclVckVcjUciTchScgRcfQ\ cePcdOccNcbMcaLc`Kc_JcZIcYHcXGchZJj_Ik`IlaHmbGncFp\ dFqeErfDsgCulBthCteDtaEtZFsVGsSHsOIsLJsIKlaQetVjp`\ nlfrhlvdrtfpsgorimqjlpljominogmpfkqejscitbhv`gw_fy\ YezXdzWbxY`u_Zs`XpbVndTkeRhgQfiOcjMalKZnIWoGUqERsB\ QvDPtEPsFPrHOqIOpJOoKNnMNmNNlOMjPMiRMhSLgTLfULeWKd\ XKcYKbZKaYJ`YI`YH`YG`XF`XE`XD`XC`U6ZXB`ZFaaJccNdfR\ fhVgk_imcjpglrkmuoowspywquunrtkorilqfipcfnacmZ`kWY\ jUViRSgOPfMMdJJcGGbED`BA_87Z6BYAEYDIXHLXKPWOSWRWWV\ ZVYbVaeUdiUhlTkpTosTrqUspVsoWsnXtmYtkYtjZui_uh`uga\ veavdbvccwbdwaew`ewbhndjfflZhnRikTjiUkgVleXlcYmaZn\ __oYaoWbpTcqRerPfsNgsLhtJjuHkvFlvDmwCjwCgwCdwCawCZ\ wCXmvhjochhZfbUdWQbQL`JGZDC`FEaGFcIHdJIfKKgMLiNNjP\ OkQQmRRnTTpUUqWWsXXtYZv__ } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 07-12-08 (Skeletal Remains [7.5])
by Jim Muth 07 Dec '08

07 Dec '08

FOTD -- December 07, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: Today's FOTD fractal image is late because I somehow let myself get dragged into a shopping trip on Saturday. IMO, wandering aimlessly through one store after another is one of the most boring activities ever devised by the mind of man. Luckily, I managed to find an electronics store and a book store in which to pass the time, while FL spent several hours browsing through totally useless places such as clothing outlets and trendy gift stores -- (the kind with scented candles and teddy bears). If the snow had not started, we might still be there. By the time the snow set in, I had wasted so much time that there was little time available for fractals. But I still found one that rates good enough to be honored as FOTD for December 7. The parent fractal combines various negative portions of Z^(-1.44) and Z^(-7.75). This parent consists of the usual string of circular bays with a prominent 'fan' extending east from the origin. (There is also a very large disconnected 'circle' some distance to the northeast, but this circle does not figure in the main part of the parent fractal.) Today's scene is located in a tiny disconnected dot of activity near the edge of the 'fan'. I named the image "Skeletal Remains" because when I finished the coloring, little of the original scene was left but its skeletal outline. The basic fractal itself rates about a 6. The rating of 7-1/2 includes a 1-1/2 point reward for the coloring, which is what makes the entire image. Without the skeletal effect, the image would be just another throw-away. The calculation time of 49 seconds is lightning fast, as fast as a trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the finished image there. The morning sun disappeared by midday here at Fractal Central on Saturday. The cloudy afternoon that followed turned into light snow by 4pm, much to the annoyance of the fractal cats, who were left alone all afternoon. And the temperature of 16F -9C didn't help at all. My day was, well, how good can a day of boredom be? The next hopefully glorious FOTD will be posted in about 24 hours. Until then, take care, and be patient. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Skeletal_Remains { ; time=0:00:48.90-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+2.1548914235/+0.3044777136/83465.38/1/\ 35/0 params=-5/-1.44/-0.8/-7.75/0/0/0/0 float=y maxiter=1500 inside=0 logmap=68 periodicity=10 colors=000000tlMznKcZItVGUQEPMhzzAzD8A9zP_zPtfkaR`\ TLQLGFDAeDijCwaCg_BdYB`WBXUAUTARR9OP9NN9LL8JJ8IH7G\ G7E00000000000000000000000000000000000000000000000\ 0B00A00900800700Q_bV`bZ`bcabhbbmbbrcbvcbtc`scZrcXq\ cWpcUocSncQmcPlcNkcLjcJicIhcGgcEfcDedHeeLefPegTehX\ ei`ejcekgelkemoenseowepzfesfWmfMgfCacE`aG`ZI`XK`VM\ `SO_QQ_OR_LT_JV_GXZEZZC`Z9bZ7dZ5eZUZVqSSnUVlVYiW`g\ XcdYfb_i_`lYaoVbrTcuY_saWreSqjOonKnrGmwCkz8jz5iz7f\ z8cx9`uBZsCWqDTnFRlGOjHLhIJiLNjORkQUlTYzVazYdz_hzb\ kzdozgszivzlzznzzSvz5ozEszMwzUzzfczsImuUmwemyqmxpm\ xomxnmwnmwmmwlmvlmvkmvjmvjmpemkameYm`UmWQmQLm77mLH\ mFDmA9mcEm`DmYCmVBmSBmPAmM9mJ8mG8mD7mA6m75mvMmzJmz\ GmzDmzAmz7mzpmzlmzimzfmzcmz`mzXmzUmzRmzOmzLmzHmzEm\ zBmz8mz8mz7mz7mz7mz7mz7mz7mz6Cz6Cz6Bz6Az6Az69z68z5\ 8z57z56z56z55z5IzY6z75z65z65z65z65z65z65z65z65z65z\ 65z55z55z55z55z55z55z55z5 } 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 04-12-08 (Sacred of Demonic? [7.5])
by Jim Muth 06 Dec '08

06 Dec '08

FOTD -- December 04, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: NEW FORMULA ALERT! Today's image was created with a new form- ula, posted today for the first time -- the DivideBrot6. The new formula is a generalization of the DivideBrot5 formula, with the added ability to change the bailout radius to any value and also change the hard-coded Z^2 of the Dividebrot5 formula to any exponent of Z. But the new formula runs about 1/3 slower. Today's image is named "Sacred or Demonic?". This name refers to the orientation of the 5-pointed star surrounding the quintic minibrot at the center. When such a five-pointed-star figure is oriented with a point directed straight up, it forms the star of Christmas, which symbolizes the sacred coming of salvation. But when this figure is rotated a mere 36 degrees so that a point is directed straight down, it forms the satanic pentagram, represen- ting a goat's head, with horns, ears and goatee, symbolic of the evil one himself. Since the star in today's image is oriented halfway between the sacred and profane positions, its meaning is ambiguous, open to any interpretation one wishes to give it. The image is located on the main spike of the parent fractal, which is a confusing cross between a Mandelbrot set and the order-5 Mandeloid. This spike holds both order-5 Mandeloids and Julia-like figure-8 shaped holes, with today's image being located in a valley of a figure-8 hole. I rated the image at 7.5. The coloring might have been improved if I had worked at it a bit longer, but it is good enough as it stands. The magnitude of over 2*10^12 requires the mathtolerance entry to assure that the image is calculated at the correct magnitude. The fast calculation time of 2 minutes makes the job of running the included parameter file almost a pleasure. But the trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the already-calculated image is a lot more fun. Total sun and a temperature of 43F 6C here at Fractal central on Wednesday equals contented fractal cats. If we forget the non- fractal work, my day was acceptable. The next FOTD will be posted in 24 hours. Until then, take care, and search for the perfect fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Sacred_or_Demonic? { ; time=0:02:01.89-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 center-mag=-2.957528927728\ 518/-0.000045568741728/2.02e+012/1/43.5/0 params=2/5/1.5/0 float=y maxiter=1800 inside=0 periodicity=10 mathtolerance=0.05/1 colors=000zoUzlSyiQwfPwcOu`NtYMsWKrTJrQIqNHpKGpIEo\ FDnCCn9Bm6Am49k3Aj3Bh3Bg3Ce3Dd3Db3Ea3F_3FZ3GX3Hz3H\ IXE5yC6xD6wD7vD7vD8uD8tD9tD9sD9rEArEAqEBpEBpECoECn\ ECnEFkFIiGLfHNdIQbJT_KVYKYVL`TMbRNeOOhMPjKPfJXbIcz\ IjzKhzMfzNdzPbzRazS_zUYzWWzXVzUTzRSzPQzMPzJNzHMzEK\ zBJz9Hz6Gz3Ez1Dz4Fz6GzzHQzIRzJzFKzILzKMzMNzPOzRPzT\ QzWRzYSz_Uz_TzPczU_zYXzZGz_Iz_Jz_Kz_Lz`Mz`NVzOWzPY\ zQ_zR`zSbzT1z64z86z98zAAcCCcDEcEHcGJcHLcINzKPzLRzM\ UzOWzPgiTgiThjUhjUhkUikVilVilVjmWjmWjnWknXkoXlp`ko\ XjoUioRhnNgnKoqAgnH_lOSiVKgaCdh3at4bo5zk6zg7zc8z_7\ zV9zWAzXBzXCzYDzYEzZFzZGz_Hz`Iz`JzaKzaLzbOzeMzbLz_\ KzYJzVIzTHzQGzOFzLELJDMGCMEENFGOFHPGJQGLRGMSHOUHPV\ IRWITYIU_JW`JWbGXaJXaLX`NX`PX_RX_TXZVXZXYY_YZaY_cY\ `hYamYbrXcvWezVgvUirTkmSmhRocNjZRlUUnQYpZcph`qfZqd\ XqbVq`Tr_RrYPrWNrULsTJsRHsPFsNDsMGoLIkLKhLNdLPaKRY\ KUVKXRKaOJfLJiKKmKKqKKUAA } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 06-12-08 (Three-Four-Five [6.5])
by Jim Muth 05 Dec '08

05 Dec '08

FOTD -- December 06, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Sorry about the lack of a fractal for December 5, but I had no time to find one. Today's image is named "Three-Four-Five". The name refers to the five arms in the image that converge on the minibrot. Only three of these arms come from outside the frame. The other two seemingly originate from nowhere within the image. This explains the three and five in the name. The four refers to the number of broad spiral loops around the minibrot. True, there is a fifth spiral, but it is so small as to be easily overlooked. The rating of a 6-1/2 seems about right. It includes a half- point reward for the 10 minutes or so I put into smoothing the colors. The calculation time of 3-1/2 minutes could be faster; it also could be slower. The way to totally avoid the hassle of calcula- tion is to view the completed image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunless skies here at Fractal Central on Friday made for cheerless fractal cats, while the temperature of freezing kept the unhappy duo close by the radiator. A small spat developed when Nicholas tried to dislodge Cassie from the warmest spot, but when Cassie uttered some un-lady-like cat words and refused to yield, Nicholas went off to sulk in the laundry basket. My day was unusually busy, but nothing to cause a sweat. The next FOTD is due to be posted in 24 hours. Until then, take care, and it's all a plot of the aliens from Sirius 3. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Three-Four-Five { ; time=0:03:28.70-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 center-mag=-0.2223987583448442/+2.429375020581819/\ 1.627062e+008/1/-147.5/0 params=3/4/10/1000 float=y maxiter=2500 inside=0 logmap=288 periodicity=10 colors=000GHjGGiGGhGFgGEfGEeGDeGCdGCcGBbGAaGA`G9_G\ 9_F8ZF7YF7XF6WF5VF5UF4UF3TF3SF2RF1QF1PF0OF0OG1OH2O\ I3OJ5OK6OK7OL8OM9ONAOOBOPCOPDOQEORFOSGOTHOUIOUJOVK\ OWLMXMKYNIZOG_PE`QCaRAaSA`SA`SA`SA_SA_RAZQAYPAXOAW\ NAVMAULATKASJARIAQHAPGAOFANE9MD8LC7KB8JA9I9AI8BJ7C\ K6DL6DM7EO7FP7GQ8HR8IS8IUAJWBKXDLZEM_FNaHObIPdJQeL\ RgMRhOSjPTkQUmSVnTWpUXqWYsXZtYZs_Yr`XqaWpbVocUpdTq\ eSsfRugQwhPziOzjNzkMvlLrmKmnJhoIepHaqG`rF_sEZtDYuC\ XvBWwAVx9Uy5Ty0Tx0Tw0Uv0Uu0Ut0Us3Wq8YpD_nH`mMbkRdj\ Vfh_ggdiehkdmlcqf`paZoXXoSVnMTmHRmCPl7Nk2Lk5Nj7Pj9\ RjBTjDUjFWiHYiJ_iLaiN`iP_hRZhTYhVXhXWhWVhWUiVWkVZn\ WcqWhtWjwWmzWmzWmzWnzWnzWnyWoxWowWnvWmuXltWksWjsWi\ sWhsWgsWfrWerWdrWcrWbrWarW`qW_qWZqW_qW`qWaqXapYbpZ\ cp_dp`epafpbfocgodhoeiofjogkohknilnjmnknnlonmplnqm\ ormpsmqtmrumqvmpwmpxmoymozmnzmmzmmzmlzmlzmkzmjzmjz\ mizmizmhzmhzmgznfznfznezn } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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No FOTD for December 5
by Jim Muth 05 Dec '08

05 Dec '08

Fractal people: The subject line says it all. The reason is too much work and not enough time. Jim M.

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Re: [Fractint] artistic question
by JackOfTradeZ＠comcast.net 05 Dec '08

05 Dec '08

. Any good fractint MAP creators here? Is it possible to design a map file that would make the fractal look metallic, like gold silver and copper? (all 3 would be nice together in one map) I have tried and tried - can't do it! I just get 'greys" and "tans" but they don't shine. Is it even possible? I seem to recall fractint images way in the past that looked like that .... Thanx for any help JoTz .

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FOTD 03-12-08 (Golden Nonabrot [8.5])
by Jim Muth 02 Dec '08

02 Dec '08

FOTD -- December 03, 2008 (Rating 8.5) Fractal visionaries and enthusiasts: Today's fractal impressed me as having a golden undertone, so I named it "Golden Nonabrot". The word 'nonabrot' is one I invented to describe a minibrot of order 9, which has (9-1) or 8 lobes. Normally, order-9 minibrots have a very compressed pattern sur- rounding them, but when combined with quadratic elements through the DivideBrot5 formula, the surrounding patterns become far more expansive and attractive. Today's scene is found in the northern branch of the Seahorse Valley of the large minibrot on the main spike of its immense parent fractal, which on its surface resembles a giant Mandelbrot set. I rated today's image at an 8.5, including the usual reward of 1/2 point for the 20 minutes I spent on the coloring, which is rather good, (IMO). The calculation time of 4-2/3 minutes is slow by some standards, but not so slow by others. All thoughts of calculation may be banished however by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Morning clouds gave way to afternoon sun on Tuesday here at Fractal Central, just in time for the fractal cats to enjoy their much-anticipated two hours in the sun. My day was pleas- antly busy, if that is not an oxymoron. The next FOTD will be posted in 24 hours. Until then, take care, and watch the fractals pass around you as you walk. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Golden_Nonabrot { ; time=0:04:40.84-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 float=y center-mag=-442.1377733748792/+0.1697133339657901/\ 7.386856e+009/1/-37.5/0 params=9/250 maxiter=5000 inside=0 periodicity=10 mathtolerance=0.05/1 colors=000ogQneSlbUk`WiZZgX`fVbdTddQkcRfcRbcRZcRVb\ SRbSNbSJbSF`OAbSBdVBfZBhaCjdClhCnkDpoDrrDsuDpsCnrC\ lqCjoBhnBfmBdkAbjA`iAZg9Xf9Ve9Xl0Vh5Td9S`DQXHOTLNP\ QLLUJHYIDaG9eF5iQNZYeP_dO`cNacMcbLdbLeaKgaJh`Ixb0i\ `IVZZ8VzHYoP_dXaUdcJpb2nd5le8jfAhhDfiFdjIblK`mNZnP\ XpSVqUTrXTuZRsZPrZNpZLoZJmZCpcIlZOhVUeQ_aMeYHkVDqR\ 8Lkuc_VvO4rP6oQ7lR8iSAfTBcUC_VEXWFUXGRYIOZJL_KWObh\ 8ueCtcFs`IrZLrXOqURpSUoQXoN_nLbmIelGhlEkkBnj9qi7ti\ ArlCqnEpqGosInvKmxSamZzbfzSmzIdzHWzGNzFzzEzzDzzBzz\ Azz5zqhzzMzwRzgKJzDBz6zQECoY9YM6zBMefzzSzzEzzBzz8z\ z5zz2ztENeAGS79z3RsK5rG4dC4z83z4GzV`C6zz3zzCzz9zz6\ zz3zz4zz3zz9zz1PFeO`CZSHhKLrBPz3TbcEWPdXL`WNWVPRUR\ MUTIRahiShyUJWE9ORkHHWA8GWKNOEHa9BA05s3Re2KT0DG06U\ 0dN0UG0K94Alnz`ajQPVECFMkECN7knHXXBm_YjYVhWSeUPcSM\ YOJ_QGaSKcVNfYRi`UlbYoe`rhdukfwmezodzncyocxpcwqcwr\ czscztczuczvhzwmzxrzyvzzz } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 02-12-08 (Tooth of the Tiger [7.5])
by Jim Muth 01 Dec '08

01 Dec '08

FOTD -- December 02, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: Today we have another fractal from nowhere to pause and stare at in awe and wonder. It's another Julia set of nothing. It is not an 'evaporated' fractal because nothing was ever there to be evaporated. It's simply a blank screen made manifest to the senses by the 'bof60' inside fill, the inside fill that works best with this particular nothing. (All 'nothings' are not the same.) I named the image "Tooth of the Tiger" to give it a Kung-Fu martial arts feeling. With too little time to do adequate work on the coloring, I rated it at a mediocre 7.5. More coloring work on the 64 or so colors that actually appear in the image might have raised the rating to an 8. The calculation time of XX seconds is faster than light, which means the calculation finishes 8 seconds before it is started. Another very fast to view the image is to surf out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted for instant satisfaction. Overcast skies, occasional rain showers and a temperature of 43F 6C made the Monday weather less than ideal here at Fractal Central. With one lamp knocked over and a cup of coffee spilled, the fractal cats' behavior was also less than ideal, so I guess things were pretty much the same everywhere. My day was ordinary; I expect a repeat tomorrow. The next FOTD, glorious or not, will be posted in 24 hours. Until then, take care, and keep track of all things fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Tooth_of_the_Tiger { ; time=0:00:04.08-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5Julia center-mag=0/0/0.73647 params=-32/4/-0.8186/-0.7005 float=y periodicity=10 inside=bof60 logmap=yes symmetry=origin maxiter=1500 colors=0003Q_IVXX_UjdRlbSm`So_SpYTrWTsVTfbSUjRHqRI\ iWJb_KWdLPhMIlcZVVfcNnkZpgiqctr_rVOq7CgEIYLOOSU__d\ kgowoy2SSVU94NP6IM8DJoMr`FjUDbNBVG9Nop6lIxP4bQvgIX\ UL7BF8E`mKUbJNTIGIHxVn0nuX1BL5ERrHIVGiJM`GKSDJJAHG\ 87D8Cwh0zsQ8VE9NFAFG6vf7i_8XT9KMOPhwBcFJgWczXXZjXB\ YODMGFSZVIAMB9GE8FG8EJ8DL8CO8BQ8AT89V88X77_76a75d7\ 4f73i72k71m70iA3eD6aG8YJBUMDQPGNRIRPNUNSYLX`K`cIeg\ GjjEomDsjCqgCpdBobBn_AmXAkU9jS9iP8hM8gJ7eH7dE6cB6b\ 96aFDKGHJGKJHNJHRJHUJIXJI`JJcIJfIJjIKmIKpILtILwILz\ IFhC9R63A15LF7WT9fe7d_6cU5aO4`J3ZD2Y71X2wVXuXYsZYq\ `ZpbZnd_lf_kh`ij`glafnadpbbrbasbQucEwc3xc6ua9s_CpY\ FnXIkVLiTOfSRdQUaOX_N_XLbVJeSIhQGkNEmLDlJDlHDlGDlE\ DlCDlBDk9Dk8Dk6Dk4Dk3Dk1Dk0Dh2Fe4Hc6I`7KY9MWBNTCPQ\ ERSqnRppPnrOltNkvLLvJNoHPiFQbDSXBUQ9VK7XD5Y7JJFX5M\ x7csFbnMbiTbd_a_faVmaXg`Yb__Y_`TZbNYcIYeDXf8XWGbMN\ hBUn1`t2Zq2Xn2Wk3Uh3Te3Rb } frm:DivideBrot5Julia { ; Jim Muth z=pixel, c=(p2), a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 01-12-08 (Julia Surprise [9.5])
by Jim Muth 30 Nov '08

30 Nov '08

FOTD -- December 01, 2008 (Rating 9.5) Fractal visionaries and enthusiasts: I sometimes receive e-mails asking how I find the fractals I post in the FOTD. I wish the question were not so difficult to answer. In a recent posting to the Fractint List, Mike actually had it right when he said I must have developed an intuition for fractals, and the ease with which I find them causes me to under- rate them. When searching for fractals, I simply get a feeling that a particular set of parameters or a particular spot in a certain parent fractal will yield something worth the effort. And as often as not I am right. Even more surprising, at least to me, is the fact that I some- times have little idea of the connection of the math to the shape of the fractal. This is quite the case in the images I make with formulas like the HyperMandelbrot2, where I can see no connection at all between the infinitesimal parameters I enter and the images that appear on the screen. When I was considering today's image, I had an instinctive feeling that the Julia aspect of yesterday's image might hold something interesting. As today's FOTD shows, I was right. The unexpected result, which is due entirely to the coloring, is quite striking, even though it hardly looks like a fractal. I named the image "Julia Surprise". After all, that's what it was to me. The rating of a 9-1/2 is exceptionally high. It includes 1/2 point for my serendipitous coloring, but still leaves room for improvement. The coloring took less effort than one would expect. Actually, I colored the image with a single strike of the <enter> key and one ot two register tweaks. The image is a ghostly one. It is not evaporated, since it started with nothing to be evaporated. Regardless, the 'bof60' inside fill once again worked its magic on a blank screen, and today's image is the result. The other inside fills work with much less success, with the 'bof61' being the best of the lot. I think the 'bof60' fill colors the bands according to how close the trapped points come to the origin in their limited wanderings, while the 'bof61' fill colors the bands according to which iteration brings the points closest to the origin. Perhaps the best feature of today's image is its faster-than- light calculation time of 8 swift seconds. This speed will give no one reason for impatience. But those with over-qualified machines that panic and freeze when booted with a DOS program will still need to view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunday began with sleet here at Fractal Central, but by noon the sleet had changed to a cold rain that, together with a temperature of 34F +1C, made the day quite unpleasant. The fractal cats divided their time between searching for the warmest places they could find, chasing each other up and down the 40-foot (12-meter)-long hallway, and asking for food. My day was spent doing little of value. (Except for the fractal fun.) The next FOTD will be posted in 24 hours. Until then, take care, and when things go wrong, shift the aspect of your attitude from the Mandelbrot to the Julia. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Julia_Surprise { ; time=0:00:08.09-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5Julia float=y symmetry=xaxis center-mag=0/0/0.1435945 params=-3/1.5/-0.987/0 maxiter=1500 inside=bof60 logmap=yes periodicity=10 colors=000zzzvvvrrrmmmhhhcccZZZUUUKKK000znUvlTrjTm\ hShfSeeR`dR_cQZbQXaQW`PV_PUZOTYOSWNRVNQVNOUMNSMMRL\ LQLKOKJNKIMJHLJFKJEJIDIICHHBGHAF0000L3gJ5dH7`F8WDA\ RBBN9DJx5zw6vv6ru7mt7hs7cr8Zq8Up8Uo9Un9Um9UlAUkAUj\ AUiBUhBUOASNCQLCPJCOHDMFDLDDKBEI9EH8th8rg8qf8oe8nd\ 8lc8kb8ia8h`8g_8eZ8dY8bX8aW8_V8ZU8YT8WS8VR8TQ8SP8Q\ O8PN8OM8ML8LK8JJ8II8GH8FG9GR8FQ8FQ8FP8FP8FO8FO8FN8\ FN8FM8FMW4fX4fZ4e_4e`4da5db5cc5ce5cf5bg6bh6ai6aj6`\ l6`m7_n7_o7Zp7Zq7ZpCYoGYoKYnPXnTXmXXlaWleWkiWknVjr\ VjvVmoaohgrantVtvPzsQwqQuoQsmRqkRoiRmgSkeSicSgaTe_\ TcYTaVU_TUYRUWPVUNVSLVQJWOHWMFWKDXIBXG9XE7XCCVFHTI\ MRLRPOWOQ`MTeKWjIZoGatFcuHcuJcuLcuNcvOcvQcvScvUcwV\ cwXcwZcw`cxacxccxecxgcxhcuiasj`qjZnkYllXjlVhmUenTc\ nRaoQ_oPXpNVqMTqKQrJOsIMsGKtFHuEFuCDvBBvAEuCGtEItF\ LsHNsIPrKRrLUqNWqOYpQ`oSboTdnVfnWimYkmZml`olalj_jh\ ZhfYfeXdcWaaV__UYZTWXS9EH } frm:DivideBrot5Julia { ; Jim Muth z=pixel, c=(p2), a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 30-11-08 (Something From Nothing [7.5])
by Jim Muth 29 Nov '08

29 Nov '08

FOTD -- November 30, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is named "Something From Nothing". The name came about when I began with a blank screen of trapped inside stuff -- nothing -- and applied the 'bof60' inside fill to change the nothing into something -- today's image. As for a theme -- forget it. Anything and everything appears in the image. I see quadratic elements, cubic elements, as well as some things that defy classification. Actually, the 'nothing' in today's image rates a 7.5 -- not too bad a rating for a screen full of nothing. The colors appear a bit too light and pale to my eye, which is the reason the image rates no higher. The calculation time of 3-2/3 minutes should cause no one to feel impatience. And even the possibility of impatience may be eliminated by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Morning sun and afternoon clouds with a temperature of 45F 7C made the fractal cats happy, but otherwise left little to comment on here at Fractal Central on Saturday. My day was equally uneventful. The next FOTD is due in 24 hours. Look for it at this same spot on the internet. Until then, take care, and be one. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= SomethinFromNothin { ; time= 0:03:38.86-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 passes=1 float=y center-mag=-1.01132/0/5.754019/1/90/0 params=-3/1.5 maxiter=1500 inside=bof60 logmap=yes periodicity=10 colors=000tzzqzwoztkzqkynkxkkwhkvektbir_hpXfnUelSc\ jRbhP`gO_eMZdLXbKW`IUZHTXFRVEQTDORBNQAMP9OQ8QR8SS8\ UU8WV8YX8ZZ8`_8ba8dc8fe8hf8ih8kj8nk8qm8tn8xp8ys2vq\ 8poElmLhkQeiWagaYedUceQafM`gN_hOZiPZjQYkRYlSXmTXmU\ WmVVpWVoXUpYUqZTr_Ts`StaSubRvcQwdQxePyfPz00U00U00U\ 00U00U00U00U00U00U00U00U00U00U00U00U00U00U00UUcYBd\ GCaHDZIFVKGQLIMNJIOLDRKEPKEOKFNJFLJGKJGJJGILFLNENP\ DPRCRTBTVAVX9XZ8_`7ab6cd5ef4gh3ii2kh4jh5jg6jg7jg8j\ fAjfBjfCjeDjeEjdGjdHidIicJicKicMibNibOiaPiaQiaRibT\ ibVicXicYjd_jdajecjedjffkghkgjkhkkhmkioliqljrljtlk\ vllxmlummrmmolnklnhkoekoajpZjpWiqTiqPhrMhrJgsFgsCf\ t9fu5eu5du6cu6bt7at8`t8Zs9Ys9XsAWrBVrBUrCSrCRqDQqE\ PqEOpFNpFLpGKoHJoHIoIHnJFnKGnLInNKoOMoQNoRPpTRpUTp\ WUqXWqZYq__raara_q`Yq`Wp_Uo_SoZQnZOmYMmYKlXIlXGkWE\ jWCjVAiV8hU6hU4gT2fS0cU3`W6XY9U_DRaGNcJKeMHgQDiTAk\ W6m_7m_8m`9maAmbBmcCmdDme } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 29-11-08 (The Mystic Twelve [8])
by Jim Muth 28 Nov '08

28 Nov '08

FOTD -- November 29, 2008 (Rating 8) Fractal visionaries and enthusiasts: Today's image is named "The Mystic Twelve". The name does not refer to the twelve apostles but to the 12-part symmetry of the features surrounding the very obvious order-12 minibrot at the center. As is always the case with Mandeloids, the number of lobes in the minibrot itself is one less that the exponent of Z. In this case, eleven. But this in no way detracts from the significance of the number 12 in the image. Actually many things in our everyday world are based on the mystical number 12. The number of signs of the zodiac, the number donuts in a dozen, the number of months in the year, the number of apostles, the number of piano keys in an octave, and the number of people on a jury are just a few. And if you think the number 12 is mystical, just open the bible and check the number of times the number 40 appears. (It must be the Deity's favorite number, as well as the number of thieves.) On its surface, the parent fractal of today's image is a huge Mandelbrot set. But as today's image shows, in its depths, it is entirely different. Today's scene is located on a short filament extending from a small radical on the northern shore line of the large minibrot on the main spike of the parent. With its rather moody coloring, today's image rates an 8. Once the image starts to appear, the calculation time of 6-1/4 minutes should seem to pass in a flash. But to avoid a 'flash in the pan' the finished image is posted for immediate viewing and enjoyment on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The intermittent sun here at Fractal Central on Friday kept the fractal cats guessing, while the temperature of 45F 7C made the shopping rush bearable. My day was busy enough to keep away thoughts of poverty, yet slow enough to allow time to relax. The next in the seemingly endless series of FOTD fractal images will be posted in 24 hours. Until then, take care, and make your fractals look alive. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Mystic_Twelve { ; time=0:06:14.04-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 center-mag=-175.3115666712\ 27/+1.321886950465596/1.838955e+011/ params=12/100 float=y maxiter=5000 inside=0 logmap=889 periodicity=10 mathtolerance=0.05/1 colors=000A28A2AA2CA2EA2GA2IA2KA2MA7OACQAHSALUBQYC\ VdDZkDclKhrUlzcuzmzzczvUwrJtmMqhPocSmZVkXYiV`gTbeV\ ccXcbZcaYc`Xc_WcZVcYUcXUcWUcVUeVUgVUiVUkVWiSYgQ_eO\ acMc_KZWIUSGPOEKKCFHACKD9MGCPJFRLJUOMWRPZUS`WWcZZe\ aahddjfhmikolnqnqressXutOwuFygCmU9aG6Q24EKFaaQxZOt\ WMpUKlRIhPGeMEaJCYHAUE8QC7NJLUQZ_XlecykZvgUtdQq`Lo\ YHlUCjR8hOB_gESzCTtATn9Ti7Uc6UZ4UT3UO7XQB_SFaTJdVN\ gXRiYVl_Zn`VkbRhcNfdJceFafBZg7XhDVaJTVOSOUQH_OAdN3\ hQ9lTFoVLsYRv_XtXTrVQpTMnRJlOFjMChK8fI5KlEJjCIiBHg\ AGf8Fd7Ec6E`8EY9EVAESBEPCENDEKEEHFEEGEBHE9IdC4eF9e\ HDeJHeLLeNQePUeRYeTaeVeeXjeZne`rebvedzdfudgqdildjh\ dlcdm_doVdpRiqQmqQilSfgUbbW_YYXU_gXVr_QByqItdPoSVk\ FPYTJKeD7rMJoVVmcfjlqhmdkYJf00PRM`nTnpabziSzqGzy5z\ tDzpLzkTzg`zh0z7PzW_zsizIDzRMzZVzfcznkzsOcx0mz4mzB\ mzHmzNmzTmzXmz_nzcqzftzbwzZzzVzzWzzWzzWzzOzzGzzEzz\ DzzCzz_zzwzzXzz7zzyzzZzzH } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 26-11-08 (Where is the Minibrot? [No Rating])
by Jim Muth 27 Nov '08

27 Nov '08

FOTD -- November 26, 2008 (No Rating) Fractal visionaries and enthusiasts: An exceptionally busy day could not keep down today's FOTD, though it did cut short the discussion. The image is a scene in the East Valley of the large minibrot on the main spike of the HyperMandelbrot set. I named it "Where is the Minibrot?" because the minibrot that should be at he center is nowhere in sight. I could not give a rating to an image that I put almost no effort into, so I let it go unrated. The calculation time of 8 minutes is longer that I would have liked, but still well within reason. Even more reason may be found at the FOTD web site, where the completed image is posted for instant gratification. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Lack of sun and a chilly temperature of 41F 5C kept the fractal cats in a bad mood on Tuesday here at Fractal Central. My bad mood was caused by the graphic work, which was even heavier than expected. The heavy work will continue tomorrow, so I cannot guarantee that there will be a FOTD, but the odds are in favor of it appearing. Until next time, take care, and walk with the angles in heaven. They are all right. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Where_is_the_Mini? { ; time=0:08:10.77-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=HyperMandelbrot2 passes=1 float=y center-mag=-1.749893677210895/-0.0000129789285012/\ 2.887599e+010/1/-40/0 params=0/0/0/0/0.1/0/1e-045/0 maxiter=9200 inside=0 outside=summ periodicity=0 colors=000GGXEFYDEYBDYABZ8AZ79Z58_47_44`36_37_38_3\ 9Z3BZ3CZ3DY2EY2GY2HX2IX2JX2LW2MW1NW1OV1QV1RV1SU1TU\ 1VU0WU0XX0Y_0_b0`e0ah0bk0an0`q0_t0Zs0Ys0Xs0Wr0Vq0W\ p4Xo5Yn5_m6`l7al8ck9dj9fiAghBhgCjfDkeGkgEkfDkeCjdB\ hdAfc9db7d`8bb8`c9Zd9YeAWfAUgAShBRiBPjCNkCLlDKmDIn\ DGoEEpEDqFBrF9sF8tH9qJAnLBlMBiOCgQDdSDbTE_VFYXFVZG\ S_HQaINcILeJIfKGhKDjLBlM8lK4mM6mO7mP8mR9mSAmUCmVDm\ XEmYFn_GnaInbJndKneLngMnhNnjPnkQomRooSopTorVosWouX\ ovYoxZqzZoy_ny`mxalxbjwciwchvdgveeufdugcuhbth`ti_s\ jZskYrlWrmVqmUqnTqoRppQpqPorOorMnsLntKmuJmvEqyGowI\ mvJltLjsMhrOgpQeoRcmTblU`kWZiYYhZWf`UeaVgbWicXkdYm\ eZoe_qe`seasease`se`se`sf_tf_tfZtfZtfZtfYtfYtgXugX\ ugWugWugWugVugVuhUvhUvhUvhTvhTvhSvhSvgRyhSwhSvhTth\ TshUrhUphVohVmhWlhWkhXihXhhYghYehZdhZbh_ah_`h`Zh`Y\ haWhaVhbUhbShcRhcQfaRe`Rc_SbZS`YS_WTYVTXUTVTUUSUTR\ URPVQOVONVNMWLLWKKWIIXHHX } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 28-11-08 (Overstuffed Cubic [No Rating])
by Jim Muth 27 Nov '08

27 Nov '08

FOTD -- November 28, 2008 (No Rating) Fractal visionaries and enthusiasts: Due to too much feast and food activity on the Thanksgiving holiday here at Fractal Central, today's FOTD must go without the usual discussion. But it's still an interesting image of a cubic minibrot, well worth the 2-1/2 minutes required to run the included parameter file. The image may be seen without being bothered by a parameter file by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing it in finished form there. I gave no rating to the image. The reason for the name "Overstuffed Cubic" is obvious. Morning clouds gave way to afternoon sun on Thursday, much to the pleasure of the fractal cats. But I was too busy feasting to notice. The next FOTD will be posted in 24 hours. Until then, take care, and a skeptic once told me that fractals are not real, but merely images in the brain. Hmmmm.... I wonder if any fractals would show up on the screen if they scanned my brain. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Overstuffed_Cubic { ; time=0:02:31.17-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 passes=1 center-mag=+0.6218176846270137/-0.003812180759794/\ 1.59654e+009/1/-42.5/0 params=3/1.5 float=y maxiter=1500 inside=0 logmap=278 periodicity=10 colors=000MKeOKhQKjSKmVKoVKqXKv_KzaKzcKzeKzeIzeFzj\ DzmDzoMzqXzshzvszxzzzzzzzzzzzzzqzzcozSSzFSWcFXt9Ys\ 5Zr0_q0`p0ao0bn1cm5dk9eiDfgIgeMicKk`ImYFoVFqSDtPDw\ MBzIBzD9z99z57z17z07z0Fz0Ow0Xq0eh0oa0mX0mS0cR0`K0M\ K1DM74MF0OM0OS0Q_0Qe0V_0_V0aO1eK7jDFm9Mq4Vv0cx0jz0\ sz0zz0zu0zo0zi0zc0zZ0zU0zP0zK0zF0zA0z54z07z0Bz0Fz0\ Kz0Mz0Sv0Xq0cm4hhBmc7oa5q_1qX0sV0sX0v_0va0xc0xe0zh\ 0zj0zm0zo0zq0zs0zv0zx0zz0zz0zz9xzKxzVxzexzqxzzsvzq\ mzzczzVzzMzzDzz5zz1zz0zz0zz0zq0ze0zV0zM0vF0q70m10h\ 00e00c00c00a00a00_01_07X0BX0IV0MV1SS4XS4MV1DX05_00\ a00c00e00h00j00m70oF0oO0qX0sh1vq5vz9xzDzzFzzSvzcqz\ qozzjzzhzzczz_zzVzzSsvOmsKeoIamDVe9Oe7Ia4B_05X01_0\ 4_04_05a05a07a07c09c09c0Be0Be0De0Dm5IqBKxIMzOOzVQz\ aSzhVzoXzv_zzazzSzzKzzDzzszzhszXezMSzIOzVKzeFzsBzz\ 1zz0zz4zz0zzhzmQzq9zv0zzzz0oz0OzK0zeQzzDzz1zz0zzzz\ z0z00zSzzvXzzzzQzzaXzj4zs } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 27-11-08 (Outward Bound [No Rating])
by Jim Muth 26 Nov '08

26 Nov '08

FOTD -- November 27, 2008 (No Rating) Fractal visionaries and enthusiasts: Due to a holiday work rush, today's image is a near repeat, simply a small outzoom and slight perturbation of yesterday's. I gave it no rating, though I did name it "Outward Bound". The image is a scene in the 4-D hypercomplex Mandelbrot set. There is really very little I can say about the image, since I know very little about it. It's still total mystery how such infinitesimal changes in parameters can make such great changes in the image. The calculation time of 7 minutes is reasonable. Going to the FOTD web site and viewing the finished image there is even more reasonable. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Lots of clouds and a temperature of 37F 3C made tha fractal cats unhappy here at Fractal Central on Wednesday. Lots of work and too little time made me unhappy. The next FOTD is due in 24 hours. Wait for it with bated but not abated breath. Until then, take care, and see you around the fractal town. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Outward_Bound { ; time=0:07:14.47-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=HyperMandelbrot2 passes=1 float=y center-mag=-1.749893677213578/-0.0000129789280232/\ 1.078439e+010/1/-90/0 params=2.5e-005/0/0/0/0.1/0/\ 1e-045/0 maxiter=9200 inside=0 outside=summ periodicity=0 colors=000eV`gX_jZZkVQl`Ymfdnllquwnrslppjnmhkjfifd\ gcbd``bYY`UWYRUWOSULQRHOPEMNBMM9KL8JL7HL7GL6EL5DK5\ BK4AK38K37K26K2DNBJQKQTTWWabZjh`scXlZTeUPZPLSKHLFD\ E684A97DAAGADJBFMBIQCLTDNWDQZETI4CaEVwQptOmqNjnLgk\ KehIbeH_cFY`EVYCSVBPS9NP8KM6HU3DK5F78BA7GD6KG6OJ5T\ M4XP4`S3dV2iY2m`1qb1u_3rX4oU5lR7iO8gL9dIBaFCZCDWAE\ UBFWBFXBFZBF_CFaCFbCFdCFeAClCFfEIaGLWIORKRLMUGNXBL\ YCJZCHZCG_DE_DC`DAaE9aE7bE5bF3cF2cFHSNVGVe6`h5ak4b\ n3cq3ct2dw1ey1ev3dt5cr7cp9bmBbkDaiF`gH`dJ_bL_`NZZP\ ZVNVSLSPJPMHMJFIGDFDBCA99412786AEADLEGRIJYMFpZLcPR\ RGXE7_DBaDFcDJeCMgCQjCUlBXnB`pBdrBgpEfnHelKdjMdhPc\ fSbdVabXa`_`Zb_XeZVgZTjYRmXLrTPoXTl_Xib`feddihallZ\ opWrsUufcqVmmIylJvjKthLrfMpdNnbOl`PjZQhXRfVSdTTbRU\ `PVZNTYMWXLYWL_VLaUKcTKfSKhRKjQJlPJnOJqNJsMIuLIwKI\ yJIrIMlIPfHS`HVVHZPGaJGdDGgPQZ`ZRlgJxpBvmEukHtiKsg\ NrePqcSpaVnZYVMeYPc`RbbTa } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 25-11-08 (Mandelbrot Mystery [7.25])
by Jim Muth 24 Nov '08

24 Nov '08

FOTD -- November 25, 2008 (Rating 7.25) Fractal visionaries and enthusiasts: I named today's FOTD image "Mandelbrot Mystery" because I'm not sure if it's a real fractal or some kind of artifact. But whatever it is, the image lies in the Seahorse Valley area of its parent fractal, which is a Mandelbrot set with lots of extra detail around the edges of the main bay and buds. The ridiculous real(p4) parameter of 10^(-45) seems far too small to produce such a change in a normal Seahorse Valley scene, but maybe that's the way the four-dimensional Hyper- complex Mandelbrot set is actually shaped. Changing this parameter to zero reduces the image to the expected Mandelbrot scene. Much of the coloring effect was achieved by rendering the scene with the outside set to 'summ', though the normal 'iter' setting gives almost as good a result. The rating of a 7-1/4 includes 1/4 point for the 5 minutes extra coloring time I put into the image. And the calculation time of under 2 minutes is quite nominal. As always, the finished image is posted for instant ecstasy on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Increasing clouds in the morning led to a cloudy afternoon and a cold evening rain here at Fractal Central on Monday, with a cold temperature of 37F 3C. The fractal cats were most disappointed with the lack of sun and got into a tussle when Cassie would not give up her spot on the scratching post by the warm radiator. After the spat, the duo sulked at each other for a half hour. My day was quite busy, and from the look of things tomorrow will be the same. But the next FOTD will be posted in 24 hours regardless. Until then, take care, and solve the Mandel-Mystery. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandelbrot_Mystery { ; time=0:02:50.00-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=hypermandelbrot2 passes=1 float=y center-mag=-0.749525773313297/+0.058824468328704/\ 79121.91/1/85/0 params=0/0/0/0/0.32/0/1e-045/0 maxiter=3200 inside=0 outside=summ periodicity=0 colors=000kDrq9ur9vr8vz8wz8xz7xz7yz7yz8xz9wz9vuAuo\ AtkBsfCrcCq_Dp_DoXEnVFmSFlMGkBGjiHihIhgIgdnNapOZqP\ WsQTuRQvSNxTKyTJrXIk`HdcGYgGSkFLnEErD7vD1yF5wH9uJD\ tKHrMLpOPoPTmRXkT`jVdhWhfYle_pc`sbatcatdbtebufcufc\ ugdvhdvievjewjfwkfmlgcmgUngUncKj`KfYKbV7_W8ZX8ZY8Y\ Z8Y_8Y`9Xa9Xb9Xc9Wd9Wd9W`DQXHLTLGPPBLT6OR8QQASPCUO\ EXNGZMI`LKbKMdJOgIQiHSkGUmFWoEYmIXlLWjPViSUgWTfZSe\ aRceQbhP`lO_oNYsMXvLWyKYxN_mQ`cSbUVdKXe0_gwbiwdjwg\ lwinwlownmvokvpiuqhurzd0zm0zs0zzizzmzzz`qtbqqdpnep\ kgpiiofjocln`nnZonWqmTsmQtmOsjMrgKrdIqaGq_EiZLY_RV\ ZXOZbS`_WcY_fWcjTgmRkqPntNosQosTosWosZoszoszprzprz\ prmpzppzspzuqwsqsrqpqqlophlpbjoXhmTflOdjJciFbhCagD\ _gGZiHYjKXkLWhOWeOUcPSbPQdOOeONcNLgNJeNHgOFgOEhPLg\ RJfTHfVFeXEeYCfZAf_8g_7f_KgXXdRh`OeYNcVMaRL_OKYLJV\ HITEHRBGP8FN7IO6KO6NP5PP5RP4UQ4WQ3YQ2`R2bR1dR1gS0i\ S0kS6fWCbZIZaOUeUQh_MkeHo } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 24-11-08 (Forever Ambergris [No Rating])
by Jim Muth 23 Nov '08

23 Nov '08

FOTD -- November 24, 2008 (No Rating) Fractal visionaries and enthusiasts: While taking it easy on Sunday after a busy day back at Old Fractal Central on Saturday, I stumbled upon this quick scene in the East Valley area of an oversized Mandelbrot set with quintic characteristics in its depths. I named it "Forever Ambergris", not to be confused with the novel of the same name. The reason I chose such an unlikely name must forever remain a secret. Since the image was found so casually, I could not give it a name or a rating. But even without these attributes, the calculation time of 22 seconds is so fast that nothing will be lost if the finished image disappoints. Another very convenient way to view the image is to see it in finished form on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Lots of afternoon sun and a temperature of 37F 3C here at Fractal Central kept the fractal cats happy. A slow day kept me happy. The next FOTD will be posted in 24 hours. Until then, take care, and don't be caught sleeping. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Forever_Ambergris { ; time=0:00:22.70-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 center-mag=+0.963166516023578/-0.0571977954305165/\ 1.023133e+007/1/5/0 params=5/3 float=y maxiter=750 inside=0 logmap=72 periodicity=10 colors=000kUAnb9rc7uc6uc5vb4ua4t_4rY3qW3pU3oS3mR2l\ Q2kP2kO2kO1kO1kO1kO1kO0kP0kQ0lR0mS0oT0pV0rW0sY0uZ0\ v`0xa0yb025G3AJ3EM4IP4MS4QV5UY5Z`6bc6ff6ji7nl7ro7v\ rAxuAzxAzzdzzkzzQFSRAZS6eT2kaTejr`koYllWmiUnfSodQp\ aOqZMrWKsUItRGuOEvLCwJAOHSULNZOJcRFhUAmX6r_2pOMoDe\ Rag2yimA__TSMkKPlMRmNTnPVoQXoSZpT`qUcrWesXgsZit_ku\ amvbovclrdinefkecgf`cgZ`gWXhTTiQQiNMjKIkIFkJEkJEkJ\ EkJEkKEkKEkKEkKEkLEkLEkLEkLEkPKhSQfWWdZabag`emZhsX\ kyVejR_WNUIKWLNXOPYRR_UT`XWa_Ybb_deaehcfkfhnhiqjjt\ lkvniumhtmfsmermdqmbpmaom`nmZmmYlmXkmVjmUimTimUjlU\ klVllVmlVmlWnlWokXpkXpkXqkYrkYskYskXkdXcYXWRXOKXHE\ iA8v43xEXPTORQPTNQWJRYGS_DTb9Ud6Vf3Wh0Wg6XfBYeGZdL\ _dQ`cVab_badc`id`neXj_TgVPcPM`KIXEEU9BR4AW89`C9dG8\ iK8mO7oM7qL6sK6uJ6wI5xH5yG5zF4zD4zC3zB3zA3z92z82z7\ 2z69zDGzKNzQUzX_zbQzWGzQ7zK9zIBzGDzFFzDHzCIzEIzFIz\ HIzIIzJTzJUzHYzF`zEdzDgzB } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 23-11-08 (Cometary Cloud [7.5])
by Jim Muth 23 Nov '08

23 Nov '08

FOTD -- November 23, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: The decorations went well back at Old Fractal Central on Saturday, and when I got back to New Fractal Central just before 10pm, the FOTD went surprisingly well also. The image reminds me of a cloud of comets just taking shape, which is why I named it "Cometary Cloud". The rating of a 7-1/2 includes the usual 1/2 point for my coloring, which is rather good despite being mostly accidental. The image could also be taken as a tangle of strings of pearls, which would earn it the name "Strings of Pearls". Actually, it's nothing more than an evaporated Julia set brought to life by the 'bof60' inside fill. The calculation time of 46 seconds will bring much happiness to the wide world of fractals. And those who wait for Paul to post the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> will find equal happiness there. Lots of clouds, flurries of snow and a temperature of 30F -1C characterized New Fractal Central on Saturday while I was at Old Fractal Central, where there was more sun, no snow and a temperature of a whopping 39F +4C. The fractal cats greatest disappointment was my absence. The next FOTD will appear in about 12 hours. Until then, take care and be in high anticipation. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Cometary_Cloud { ; time=0:00:46.12-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5Julia passes=1 float=y center-mag=0/0/0.441863 params=-7/3/-1.2/0.025 maxiter=500 inside=bof60 logmap=yes periodicity=10 colors=000zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzvzzrzzmz\ zhzzczzZxzUvzQuzQszPqzPozOmzOkzNizNgzMezMczOayP_xQ\ YwSZwT_wU`wWawXbwYcw_dw`ewafwbhwdiwejwfkwhlximyjnz\ lozmpznqzprzqszrtsspppmlmiikffhcce_`cXX`TUYQRWNOTJ\ LQGIOCGL7FH000HbL8JAdYiSCEI89944Gx1Ac05K0p3Nb2HQ1B\ D05fjcWZULNKABA9uh4TMxQZcHNK8BgVG6X04M02B0tiaSNJpj\ qQNR`wFOcACK5NEeB7LsJI`CCI66Q5LJ3FD2A615cI1UD0K90A\ 403sO1SCaL0FSoAIY59HCce6KLh_imvno5NleQioyYbiNQVBDF\ CyO8dG4K8Qt9u3af2ST1JE09EyvAig7VT3FEZWwQOhHGU88Fzl\ Mj_GVOBFC5zoZVQHv`pQ66H448221zz0ee0LLAgP6TG3E83hF2\ XB1M70B31Fk0AW05GPYsGWzCOj8GV48FAQtCgx8Tc4EKJaPCPG\ 6C8ZZmQQ`HHP88C32`21O10CDsk8`W4IG8nS6aL4PE2C7kygOV\ Mac1JK0bH7J83FfJ7L9n9weIjFjn7NPx0TU0Em10X00G000_x0\ Oc0CKuuCff9TT6EE3PB_oYRYMIHB93nS1PESbCKbFDQA6D5qyi\ RVNr_OSC9L96E6473236ydLEKA7zxJjhEVU9FF4Hsd8SKIA0C6\ 0630_g0OT0CE0J2rE1d91R40D } frm:DivideBrot5Julia { ; Jim Muth z=pixel, c=(p2), a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 22-11-08 (Julia Etal [Not Rated])
by Jim Muth 21 Nov '08

21 Nov '08

FOTD -- November 22, 2008 (Not Rated) Fractal visionaries and enthusiasts: Today's image is a Julia set of a totally evaporated image, made visible by the 'bof60' inside fill. (I think this is the first time I have checked the Julia aspect of an evaporated fractal.) Today's image isn't much, but I have the impression that I have just scratched the surface of what lies in this area. The days to come will feature further adventures in the nowhere. Having given so little time to the image, I could not give it an honest rating. The name "Julia Etal" refers out the generic nature of the scene. Perhaps the best feature of the image is its very brief calcula- tion time of 1-1/3 minutes. And it could be even faster to surf to the FOTD web site and view the finished image there. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Friday dawned with 4 inches 10cm of fluffy snow decorating the ground and trees here at Fractal Central, with the temperature a relatively mild 30F -1C. The rest of the day was cloudy with occasional light snow and a temperature no higher than 34F 1C. The fractal cats didn't mind the snow, but they complained about the lack of sun. My day was quite busy with work and preparations for tomorrow's trip. There will probably be no FOTD for Nov. 23. I'm going down to Old Fractal Central early on Saturday to spend the day decorating, and don't expect to return until near midnight. Until the next FOTD appears, either in one or two days, take care and prevail. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Julia_Etal { ; time=0:01:22.38-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5Julia center-mag=-0.0126632/0.0571198/0.3025147/1/-12.5 params=-5/3/-1.15087/0.01037 float=y maxiter=500 inside=bof60 logmap=3 symmetry=none periodicity=0 colors=000zzzRKMRLNRMOSNPSOQSPRSQSTQTTRUTSVUTWUUXU\ V_UWbVWeVXhVYmVZrW_vW`zWazXbzQKJPLIOLHNMGMMFLNEKND\ JOCIOBHPAFQ9RMJQOJPRJPTJOVJNYJN_JMaJPdJUfJZhJckJhm\ JmoJrrJwtJwvJwyJPMKNPMKSNIVPFYRD_SfLKzbUzzV6hX3kZ3\ jY3hX4fW4dU4cT5aS5_Q6YP6WO6VNFaiEbkEcmDdnCepBfrOZG\ YZC000000VlYXjUZhQ`fNadJcbGe`CqOjnR`kUShXIJBgOG`TL\ UYQNbVGCJySRZNcXRbTUaPX`L`_HcZD6gIPbDIlmOlnUlo_loe\ lpjlpYadMSUPTRSUOUVMXWJ_XG`bAaYEdZBSti_iRIDFMGEPJD\ SMCVOCYRB`UAcX9IpANl9Sh9Xe9aa91C88G9FK9MO9TS9_W9fY\ gfZZfZQfZH8CIFHGMMETQC_VAUFDXJCZMB`PBbTAdW96pQPgH5\ 8pBCiGGcMKYRORXSLaWFGuvDFHJJFPNDVRC`VAGmfUeQ6RvBSo\ GTiKUcPVYUWRYXLbYFIsMMpKQmITjGXgE_dCcaAaUZqQRkVIiH\ ahMUgQNfVG3ApNNVqI6oL7nN7lP8kR8jT8hV9gX9nP9mR9lS9k\ T9jU9iW9hX9gY9ZuE`qDamCbiBdeAea9KtZ8AZQNMVAFZJDbRB\ `NlaPgbQbcSYcTTdVOeWJfYEic`haUg`Nf_GR2AVB9ZJ9bR9ZB\ q`FiaJbbNVdROeVG1refbbf`O } frm:DivideBrot5Julia { ; Jim Muth z=pixel, c=(p2), a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 21-11-08 (Cogwheel Conundrum [6.5])
by Jim Muth 20 Nov '08

20 Nov '08

FOTD -- November 21, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: More work than expected means less time to write a discussion than expected. Today's image is a Julia set that shares the Seahorse Valley features of the Mandelbrot set with features of a Z^16 Julia set. I named it "Cogwheel Conundrum" because the words fit together in a rather satisfying way. The rating of a 6.5 includes a 1/2 point bonus for my coloring, even though the colors were not as successful as they might have been. But the calculation time of 5 seconds is an absolute pleasure. An equal pleasure may be enjoyed by zooming out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoying the already-calculated image there. Heavy clouds, intermittent snow, and a temperature of 32F 0C kept things unpleasant here at Fractal Central on Thursday. Early in the day the fractal cats saw that they would have no sun, and took up their positions by the warmest radiators. Except for the work, my day was average. The next FOTD, hopefully a little better than average, will be posted in 24 hours. Until then, take care, and make waves. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Cogwheel_Conundrum { ; time=0:00:05.23-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5Julia center-mag=0/0/0.2869\ 198 params=16/3/-2.251/-0.653 float=y maxiter=500 inside=0 logmap=3 symmetry=origin periodicity=0 colors=01000`00b55eAHhFJlKMrPQtUVxZ`zcezhmzmtzrvzv\ xzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzozSoyLruSrqYsnb\ slhrjjohjmejlcjj_jhYjfUjdSjbPjaNjzzW_ozzlbPczueRFQ\ zlYD4AsbP002jUH06CaLS2zz2zz4zz6zz8zzAzzDzzFzzHzzJz\ zLzzNzzPzzRzzUzzWzuYzw_zwazybzydzyfzsdznbzhazc_LzY\ JzYHzWHzUFzSDzRBzNDzRDzSDzUFzWFzYFz_HzaHzbHzdulful\ huljullulpulrulsuluulwulyulzulzulzulzulzulzSEzSEzR\ FzPFzMFzLFzJFyHluFlsDlpBllAlj8lf6ld4la2l_0cW0cS0cR\ 0cN0cL0cH0cH0cF0cD0cB0cA0c80c80c60c40c20a00c00e00h\ 00j00l00u00n00h00c00c04c08c0Bc2Hc4Fc2Fc0Fc0Fc0Fc0F\ c0Fc0Dc0Dc0Dc0Dc0Dc0Dc0Dc0Dc0Bc0Bc0Bc0Bc0Bc0Bc0Bc0\ Bc0Hc0MUF0PlRfazzWwySuwRssNrqLmnJllFjhDhfAdc8ba6aY\ 2_W0YU0UW0SY0R_0Pa0Mc0Jc0He0Ff0Dh0Bj08j06l04n02p00\ q00q00s00u00w00y00u00y00z00z20z40z60z84zA6zBAzDBzF\ DzHHzJJzLMzNPzPSzRUzSYzU_zWdzUazW_zYYz_WzaUzbRzdPz\ f0zB0zU0zl0zz0zz0lz0Uy01z } frm:DivideBrot5Julia { ; Jim Muth z=pixel, c=(p2), a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 20-11-08 (Julia-Type Fantasy [7])
by Jim Muth 19 Nov '08

19 Nov '08

FOTD -- November 20, 2008 (Rating 7) Fractal visionaries and enthusiasts: NEW FORMULA ALERT! Today's image was created with a new formula, the DivideBrot5Julia, which I wrote to calculate the Julia aspect of the Mandeloids created by the DivideBrot5 formula. It does its job quite well, and as today's image shows, does it in record time. The calculation time of today's image is no mistake. It finishes in a bit over 2 seconds. True, the XY-axis symmetry helps, but even with no symmetry, the image finishes in a mere 9 seconds. The name "Julia-Type Fantasy" came about when I first saw the image and thought 'that's fantastic'. Well, the truth is that I have occasionally seen similar Julia sets in my travels through Fractal Land, but today's image strikes me as one of the better ones. The rating of a 7 might have been higher if I had put a bit more effort into the coloring. And if the calculation time of 2 seconds is too fast, things may be slowed down by surfing to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there in a slightly slower time of one minute. Brilliant morning sun with a temperature of 23F -5C gave way to increasing clouds in the afternoon here at Fractal Central on Wednesday. The fractal cats would have preferred a bit more afternoon sun, but seemed happy enough, especially when the tuna treats appeared. My day was average. I expect a repeat tomorrow. The next FOTD will be posted to the Fractint list in 24 hours. Until then, take care, and when does that new world of peace, plenty, love and harmony get here? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Julia-Type_Fantasy { ; time=0:00:02.22-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5Julia center-mag=0/0/1.64892 params=16/1/-2.00004/0 float=y maxiter=260 inside=0 logmap=3 periodicity=0 symmetry=xyaxis colors=000HKhHOkHSnIWqI_tIcwOgzXksgnlrqezt_XiOB_DM\ SNSKXfNfpMpzLzlImZFa712K6GSAT_FffJscMrfOqhWpgbpgoo\ dlnagmZfmUfkKbj0ZhXhgRmfLrdFpc9sbcwZmzVzzz9mN9mJ9p\ GIzNRQT_K_hEeq8lz2rgOM`LEVI7WFDWCJXAOX7UY5ZY2dY0i_\ 3ea5bb7_d9XfBUgDRiFOjHL7RvCSrHTnMUjRUgWVc`W_dWXifT\ Fp6qkgM4FWLJeaMiI`kUXmeTShmcm`qWX`1VdFTgSSkdQNMwUU\ n`aegiXT09cRHd`nXzbbwYhtTj_RlhQmObnbWS534b2SjEyEz6\ 4sI_PZhP8JrNVh`fZzGhtZZ6FfTZYxR`sdV`cizzzZe_fkUJTh\ UaadiVqDkpRcodWAhcLk_VmWdoSNUnXaeeiX3zYRuTo2NnKOn`\ PFZsQ0oXEhbRahdVJBRRMQZXQfgP504HEASRFcdKmSvndeON0X\ Y9egHVsFarJhqM5UYLaV_iSGNFPVIYbKfjNKDCSOG_YJggMWjG\ enLOXRNJCF7YOJVXVTefRQfAXiEblIhoMWIAbUFheK3dv9sTNr\ R`qQUBn`QegcXoLrnUjnacniWL_GTdJ_hLgmNmvVntTnrRwh8S\ 4C_LHgaL_arCUpJNsQGuPDqOAmN7iM5eRTmWptPqeIrSBsE4t0\ 8`QCInITcOcUUnJ_x9O_5CB1tkJh50UO1Ge2MBWJLTHVQFdNSu\ YZvTCtrN12NgDLdAIa8GZ6H`E } frm:DivideBrot5Julia { ; Jim Muth z=pixel, c=(p2), a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 19-11-08 (Iterative Zygote [8])
by Jim Muth 18 Nov '08

18 Nov '08

FOTD -- November 19, 2008 (Rating 8) Fractal visionaries and enthusiasts: I have heard it said that life is the most complex thing in the universe. I hate to throw doubt on that near-mystical state- ment, but with their infinite complexity, fractals are more complex than even physical life. As far as I can tell, today's image is not alive however. It is only a fractal. This is not as rational as it might seem, for who can say with absolute certainty that fractals, in all their mathematical complexity, cannot be alive? The quantum theory of the sub-atomic realm is basically composed of number gyrations, and living things are composed of that sub-atomic stuff. The name I gave today's image is "Iterative Zygote", which needs some explanation. Before a human is an adult, he is a child. Before that he is an infant, a fetus, an embryo, and first of all, a zygote, which is a fertilized egg. Today's image reminds me of a fertilized egg just starting the countless divisions that will culminate (hopefully) in a mature adult human being. The image is located in the Seahorse Valley area of the large minibrot on the main negative spike of the parent fractal, which is a grossly enlarged Mandelbrot set. The tiny blips on the hairline arms and major arms surrounding and extending from the 16-lobed minibrot in the image are actually small Z^2+C Seahorse Valley Julia sets filled with similar 16-lobed minibrots. Some of the arms terminate in very curious fragments of Julia sets, while other arms simply die out into infinity. I was so impressed when I found such a picturesque minibrot of order-17 that I rated the image at an 8. The fireball calcula- tion time of a mere 19 seconds is also quite impressive. And as always, the already-calculated image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The fractal cats soundly disapproved of the clouds and freezing temperature of 32F 0C that prevailed here at Fractal Central on Tuesday. The occasional heavy showers of snow, which left a 1cm coating on the grass, did nothing to help things. My day was about average. Tomorrow will likely be the same. The next FOTD will be posted in 24 hours. Until then, take care, and when Sister Mary Thomas told me my questions about God were childish, and told me to sit down and shut up, I reminded her that the bible says we must become like children before we can get into heaven. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Iterative_Zygote { ; time=0:00:19.39-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 center-mag=-176.8801503226196/+0.238662432514931/\ 45067.88/1/-15/0 params=17/100 float=y maxiter=400 inside=0 logmap=138 periodicity=10 colors=000KFlKImKLnKOoMQpQSqTVrXYs``tdcuhhummvtttw\ wwzzzsgvscvt`utYutUutRtuNtuKtuHsuDsvAsv6rv3rv0rt2s\ s3sq5sp6sn8sm9skBtjCthEtgFteHtdItcJt`HqZGoXFmUEkSD\ iQBfNAdL9bJ8`G7ZE5WC4U93S72Q51O63R75T86V88X9AZABaB\ DcBFeCGgDIiDJk9Me6P`3SW0VRBZaUakcdumblv`dzZXzXPzVH\ zU9zTAzSAzRAzRAzQAzPAzPAzOAzNAzNAzMAzLAzLAzKAzJAzJ\ AzM7zP5zS3zU1zW6zYBz_Gz`KzbPzdUzeYzdVzdTzdRzcPzcNz\ cLzcJzbHzbFzbDzbBzcAzcAzdAzdAzcHzbNzaUz`_OzzIzzCzz\ `zz2zzAzzIzzPzzXzzczzkzzrzzozzmzzkzzizzgzzdzzbzz`z\ zZzzXzzEzzJzzNzzSzzWzz`zzdzzizzmzzqzznzXkzWhzVezUb\ zT_zSXzRUzQRzPOzOLzNJzMQzRWzVazZhzcnzgtzkrziqzgpze\ ozdnzbmz`lz_ez__z_Uz_Oz_Iz_Cz_EzWGzSIzOJzKLzGNzCPz\ 8Qz4Jz7Dz97zBAzBCzBEzBGzBIzBGzIEzPDzWBzb9zi8zp9zbA\ zPAzCAzDAzEAzFAzGAzGEzIIzJLzKPzLSzMWzN_zObzPfzQizR\ mzSpzT7zFAzGDzHGzIIzJLzKOzLQzMTzNWzOYzP`zQczRezShz\ TkzUmzVkzUizTgzTezSczSWza } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 18-11-08 (A Higher Viewpoint [8])
by Jim Muth 17 Nov '08

17 Nov '08

FOTD -- November 18, 2008 (Rating 8) Fractal visionaries and enthusiasts: Today's image shows a downright attractive minibrot of order 17, which means it has 16 interior lobes with 17-part symmetry surrounding it. It might not be fully worth the rating of an 8, but I gave this rating because it's a surprise to see something this interesting and attractive in the range of Z^17 fractals. I was tempted to add an extra half-point for my coloring skill, but my humility made me decide against it. The name "A Higher Viewpoint" refers to the high-order circular minibrot that fills the center of the image. The mathtolerance entry in the parameter file is necessary because of the extreme magnitude of the image, which is already causing a breakdown of resolution. The scene is simply a blow-up of a minibrot in the center of the kind of fractal objects that have appeared in the FOTD's of the past two days. But this will be the last of the series. I must be moving on. An infinity of fractals lies out there, waiting to be discovered. The calculation time of 31 seconds is lightning fast, though the result may not be quite as shocking. As always, the calculating may be avoided by surfing to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoying the finished image there. *****Philosophy alert!***** With extra spare time on Monday, my philosophical energies came to life. I thought of how unlikely it is that I should be here at this particular time and place, or how unlikely that I should ever have existed at all. I'll not go through the mathematical calculation, but as I figure it, the chance of myself, (and of everyone else as well), ever coming into existence is exactly zero. It's impossible for any one of us to be here, yet here we all are. It's a miracle that reason cannot explain, a miracle so subtle and omnipresent that even its existence is difficult to recognize. The high priests of science are helpless to explain it. They brush aside talk of the miracle by claiming it is a childish way of thinking. The high priests of philosophy are also helpless. They claim that, however unlikely it may be, we are here now, and this makes the probability of our existence 100 percent. The high priests of religion are a bit more able to offer an explanation. They claim that each of us is here because God had each of us in mind for all eternity before He manifested us as individuals. However, this is only a different way of stating the miracle. But religion at least goes one step beyond science when it claims that God will never forget us. The problem with the religious explanation is that God has concealed Himself so deeply that many of us doubt He is there at all. At this point it is best that, as Sister Mary Thomas told me in the seventh grade, I should sit down and shut up. *****Weather and Cat report***** Clouds and sun alternated here at Fractal central on Monday, while the temperature reached only 41F 5C. The fractal cats complained when the clouds predominated during their afternoon nap in the southwest window. A little tuna and coffee cream ended their complaints. My day was unexpectedly slow. And tomorrow has a very good chance of being exactly the same. The next FOTD fractal will be posted for all the world to admire in 24 hours. Until then, take care, and every one of us is a necessary part of the complete universe. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Higher_Viewpoint { ; time=0:00:31.26-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 center-mag=-17.65025751604\ 944/+0.1182307735644347/1.952449e+012/1/-95.5/0 params=17/10 float=y maxiter=305 inside=0 logmap=54 periodicity=10 mathtolerance=0.05/1 colors=0000EU2HW4JX6MZ8O_ARaCTbEWdGYezzztzzmzzcxzB\ szAmwAhsCbmEYhGUeERbGOaHMZJOaMRbPUgSZlVcqYiuzzzwoo\ wemzWlzQjuNht0ZzzizzLzvTzsazrizrqztbzuOzvAzdRWNgTP\ dRQbOS`MTZJVXHWVbaGwf2te4qd6nc7lb9iaAf`Cd`DbcH`eK_\ gNYjRWlUVzXQz0zz4zzAzzGWzMYhS_hYahcbhh_haYhWWhQXcU\ YcYZca_ce`ciacmaepbdnbdmbdlbdjcdicdhcdfcde5mu7lz9l\ zAkzCkzDjzFjzHjzIizKizLhzNhzPhzQgzSgzTfzVfzXfzYez_\ ez`dzbdzIezKgzMizOjzQgzRdzSazTZzUWzVTzQdzmzzmzzmzz\ mzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzDzzGzzIzzKz\ zMzzPzzRzzTzzVzzYzz_zzazzNzzOzzPzzQzzRzzSzzTzzUzzV\ zzWzzXzzYzzZzz_zz`zzazzbzzczzXzz_zzazU6z68z8AzABzB\ DzDEzEGzGHzIJzJKzLMzMNzOPzQRzRSzTUzUVzWXzYYzZ_z``z\ abzcXz7Yz9YzBZzDZzEZzG_zI_zJ_zL`zN`zO`zQazSazUazVb\ zXbzZDziDzkFzjGzjIziJziKziMzhNzhOzhQzgRzgczjSzgUzf\ VzfWzfYzeZze_zeazdbzdCztEzsGzrIzqJzpLzoNznPzmQzlSz\ kUzjWziXzhZzg`zfRzmOzuCzg } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 17-11-08 (Ring Around a Fractal [7])
by Jim Muth 16 Nov '08

16 Nov '08

FOTD -- November 17, 2008 (Rating 7) Fractal visionaries and enthusiasts: In yesterday's discussion I said that the image is located in the interior of the main bay of its parent fractal. But I made a mistake. Yesterday's image is actually located in an island near the distorted northwest shore line of a small minibrot on the main spike of its parent fractal. I'll try not to make such a non-apocalyptic error again. Today's image, with its overlapping and squashed minibrots of order 17, is much the same as yesterday's, but with more vibrant colors. It is located in a similar location in its parent fractal. After a modicum of thought, I named today's image "Ring Around a Fractal". Then, because I felt like it, I rated the image at a reasonably glorious 7. The calculation time of 6-1/3 minutes will vary according to the speed of the individual machine. The time required to hop out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> will be shorter in almost all cases. Heavy clouds and blustery winds made the temperature of 43F 6C feel colder than it actually was here at Fractal Central on Sunday. The fractal cats, who have been getting very little sun lately, continued to complain. A saucer of half-and-half and a teaspoon of tuna eased their disappointment. My day was good enough, and if all goes well, tomorrow will be even better. The next FOTD will be posted in 24 hours. Until then, take care, and if the current economic 'crisis' was caused by having too much cheap credit available, how can it be cured by getting even more credit flowing? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= RingAroundAFractal { ; time=0:06:19.67-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 passes=1 center-mag=-162.7372066644226/+0.2393249187302109/\ 2304584/1/-55/0 params=17/100 float=y maxiter=5000 inside=0 logmap=209 periodicity=10 colors=000Kc8Hb6Ea5M_LTZ__Yn`Xi`WeaVaaUYbTUbSQbRMc\ QIcPEdOAdN6dN2bO7aOB`OF_OJYPOXPSWPWVP_UPcSQhRQlQQp\ PQtOQxLpRIjYGddE_kCUrAPy9Tx8Xw8_v7cu6ft6js5mr4qq4t\ p8qqCorGmsIloKklMjiNifPhcRg`TfYUeVWdSYcP_bM`aJb`Gd\ _DeZAiT9lN9pH8sB8w57z07y36y66y96yC5yF5yI5yL5yO4yR4\ yU4yX4y_3yb3ye3yh3vf4td4qc4oa5m_5jZ5hX5eV6cU6aS6ZQ\ 6XP7UN7SL7QK7NN7zUzwPwrNnrLonJokGogEodDoaFoYIoVKoS\ NoOQoLSoHVoEXoB_o7ao4do1fo3eg5e`7eU9eNBeGDe9Fe2Lh4\ Qk5Wn7`q8ftAkwBpyCrrBtkAeWFRGJC1NK9QSHSZPUfXWndYzw\ _zwYzwXzwWzwVzwUzwTznSznQdnPcoOaoN_oMYoLXoKVmPTlUR\ kZPjcOhgMglKfqIevHdzIawJ_uJXsKVqKSoLmmLmkMmiMmgNme\ NmcOmaOm_QmZRmYSmXTmWUmVVmUXmTYmSZmR_mQ`mPamObmOZm\ QWmSTmTQmVNmWKtYHyZGuaFrcEoeDlgChiBekAbm9_o9XqQ`Xe\ dCd_HdzLdzPdzTdzXczaczecziczmczqezogzmhzljzjlzhmzg\ ozeqUcrYbta`veZwhYqjVkkSfmP`zMWzKYzN_zPazRczTdzVfz\ XhzZjz`kzbfzZbzVYzRUzNPzJ } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 14-11-08 (Webs of Intrigue [7])
by Jim Muth 16 Nov '08

16 Nov '08

FOTD -- November 14, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's image is a scene just east of East Valley of the large minibrot on the infinitely-divided negative spike of the Z^(2.000001)+C Mandeloid. As the 'Y' parameter of 0.000005... shows, the scene is actually located at the edge of the spike. The mathtolerance entry is necessary to assure that the para- meter file runs at the correct magnitude. I named the image "Webs of Intrigue" because of the cobweb-like features surrounding the central minibrot. I was going to name it "Web of Desire" but decided that this sounds too much like the title of one of those latin tele-novellas (limited soap operas) FL, who speaks Spanish, watches so many of. The rating of a 7 pleases me and does not exaggerate the worth of the image. After all, this is not the first time we have seen such fractal cobwebs. The calculation time of just under 1-1/2 minutes is easy to digest. And just to make sure there is no indigestion, the completed image is posted for immediate viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds and occasional rain kept the umbrellas busy here at Fractal Central on Thursday, while the temperature of 48F 9C kept the overcoats in action. Early in the day the fractal cats gave up hope for sun, and spent the afternoon sleeping near the radiator. My day was busy enough for me to forget the rain. The next FOTD will be posted in 24 hours. Until then, take care, and the over hyped theory of everything could actually be a theory of nothing. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Webs_of_Intrigue { ; time=0:01:26.11-SF5 on P4-2000 reset=2004 type=manzpower passes=1 center-mag=-1.741009418786829/+0.0000054663417767/\ 1.41155e+012/1/87.5/0 params=0/0/2.000001/0 float=y maxiter=1900 bailout=16 inside=0 logmap=150 periodicity=10 mathtolerance=0.05/1 colors=0000FW0F_0Fc0Fg0Fk0Jo0Ns0Sw0Xz0az0fz0jz3mxA\ opKnhUl`UiSUfLUaDUXAUS8PN8KJLA0030A69V3Db1Ih0Mq0Oz\ 0Rz0Tz5Sz9QxCPoIOjPMbWL_bJYiIWpJUvPQzdPzrOxvCpz2me\ QiMph5zmJnuYPuk1zb0zu0pz2gz5_z6Sz8Lz9DzA2hD0PGF_ib\ izYbzUWzQOuMGpI9iF2dA0Y80UA0`D9hFJnIUvJdzM_sPWiSQ`\ UMS_IJeDAmA2uF2zI2zL2zO2zQ2zU2z_3ze5zk6zi2zi0xi0sh\ 0nh0kh0Gz00z00z00n03e08X0DO0IF0M60L80L80J80I90I90G\ A0FA0DC0DC0CD0AD0AD09G09I08J08M18O26P36S56U60xX5W9\ 5XA3_C3`D3bF2eG2gI2hJ1iM1mO0nP0pQ0sS0uU0vWp02m13k2\ 5i35h56g88e98dA9bC9`FA_GCYICWJDUMFSOFQPGPQGOSIMWJL\ XJJYLI_LGbMDdOCeOAgP9iQ8kQ6mS5nS3rU2sW1uW0vX5A03C0\ 3D03F03G03I03J03L03M03O03P03Q03S03U03W03X02Y02_02b\ 02e0zh0zk1zn1zr2zu2zxzzzzzzzzzzzz5zz5zz6zz6zz6zz8z\ z8zz9zz9zz9zzAzzAzzCzzCzzCzzD1zz1zz1zz0zz0zz0zz0zz\ 0zz0zz0zz0zz0zz0zz0zz0zz0zz0zM0zO0zO0zP0zP0zP0zQ0z\ Q0zS0zS0zSzz1uzDdzPMzb6zn } END PARAMETER FILE=========================================

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FOTD 16-11-08 (Fractal Convention [6])
by Jim Muth 15 Nov '08

15 Nov '08

FOTD -- November 16, 2008 (Rating 6) Fractal visionaries and enthusiasts: Today's image shows a Julia set of the main bay of the Mandelbrot set stuffed to overflowing with the circles of Z^(33)+C minibrots. If fact, it is so overstuffed with minibrots that they actually overlap. The scene is located in the interior of the main bay of its parent fractal, which on the surface resembles a huge Mandelbrot set. It is only in the depths of the parent fractal that the strange things seen in today's image start happening. I rated the image at a 6, which is at least a bit above average. Then, when I saw the minibrots packed like sardines, I named it "Fractal Convention". The calculation time of under 1-1/2 minutes will keep impatience at bay. But if impatience breaks loose, the finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds and occasional downpours of rain spoiled the unusually warm temperature of 68F 20C here at Fractal Central on Saturday. The fractal cats somehow managed to get through yet another day without sunshine. My day was good enough. But due to the rain, FL and I had to cancel the antiquing expedition we had planned. The next FOTD will be posted in 24 hours. Until then, take care, and look on the bright side. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fractal_Convention { ; time=0:01:26.55-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 passes=1 center-mag=-157.5333645695505/+0.02931181123341/\ 1807947 params=33/100 float=y maxiter=1000 inside=0 logmap=86 periodicity=10 colors=000E03F04G05H16I27J38K49K5AJ6BI7CH8DG9EFAFB\ BGECHGDIIEKKFMMGOOHQQISUJUXKWZLYaM_cNafOYhPWiQTkRO\ lSFmTGoUFqVFsWEuXEwXEvXGvXHuXJuXKtXMtXNuWNtXOpXPlX\ PgXQcXR_YRVZSR_TN`TIaUEfVzdTzzVzzWzwXzsYzoZXf_ag`f\ cajdboecsfdk__cTVWNQOGzG9z93zC4FF5HH6KK6MM7PP8RR8U\ U9WXAYZA`aBbcCefCghDjkElmEnkFmjGliHkhIjfJjeKidLhcM\ gaMg`Nf_OeZPdXQdWRcVSbUTa`TVTTaMThETo1Ux7TvDStISsO\ RqTRoZQncQliPjnPijQjgQjdQjaQkZQkWRkTRlQRlNRlKRmHSm\ ESmBSn8Sn5Sn2Sn9UkGWiNYgU_d`abgc`qfWmdZibae`daZgYX\ jUVmQTpMRsIQuLbbKdaJe`If_Ig_HhZGiYGjYFkXElWEmWDnVC\ oUBpTBqTArS9sR9tRzUKzTJzTIzSIzSHzUBzSHzQNzPTzNZzMd\ zKjzJpeSk`_gWhcRp_Yladhcpekjdedc_ZzUTzPNzJHzDBz8Hz\ 9Mz9Rz9Wz9azAfzAkzApzAxz8uzAszCqzEnzGlzIjzKhzMezOc\ zQazSZzUXzWVzYTz_QzaOzcMzeLzhKzgJzgJzgIzgIzgHzgGzg\ GzgFzgFzgEzgEzgDzgCzgCzgBzgBzgAzgAzgFzfJzfNzfRzfWz\ kVzfKz0Kz0Kz0Kz0Kz0Kz0Kz0 } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 15-11-08 (Broken Branches [6])
by Jim Muth 14 Nov '08

14 Nov '08

FOTD -- November 15, 2008 (Rating 6) Fractal visionaries and enthusiasts: Today's fractal is definitely neither real nor unreal. It is something halfway in between -- an image of a minibrot in the Z^(2.1)+C Mandeloid. I named it "Broken Branches" when I noticed the breaks in the streams of chaos extending out from the central midget. The rating of a 6 indicates a repetition. I have posted some very similar images in the past. The calculation time of 20 seconds could exceed the speed of light. This would mean that the finished image would appear on the screen several seconds before the <enter> key is struck. I'll not speculate on what would happen if, after the finished image had appeared, the fractalist would decide not to strike the <enter> key that caused the image to appear several seconds before. All this confusion may be avoided by surfing over to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Philosophy alert! On Friday I received an envelope in the mail from a scientific book club, offering a selection of three books, this month about the nature of physical reality. As is obvious, the offering gave my philosophical side a shot of energy. One of the books presents a modified theory of gravity (MOG), which, if true, might explain the mystery of the missing dark mass and energy. If this latest new theory is right, then Einstein's general theory of relativity is lacking, and maybe his status as the premier brain of the 20th century needs to be re-evaluated. As for me, I feel we're getting all of nowhere in explaining things, in fact we're digging an ever-deeper scientific hole. Before we try to explain 'physical reality' we should step back, take a break, and try to find a way to prove that physical reality is actually as objectively real as is conventionally assumed. We can't explain it if we don't know what it is. I, and everyone else as well, have never observed a 'real' world that exists out there independently of the observation. All I have ever observed is an ever-changing series of images formed in my mind by stimulation of my sense organs. To be considered a rational thinker, I know I should believe that these images faithfully reflect a universe that actually exists apart from myself exactly as I experience it through the images. But for some reason, I cannot shake the feeling that this belief is an unproved and perhaps unfounded article of faith. True, if we assume the mental images accurately mirror an outer world, then the scientific method works quite well. But we are still left with all the unexplained things called paranormal or supernatural. These reports keep coming despite the skeptics' denial of the paranormal and their attempts to give the reports a natural explanation. Does this mean I am a believer? Well, I certainly know that there are many reports of strange things, and I doubt that all of them can be fully explained by the gullibility, credulity ignorance or wishful thinking of those who do the reporting. Finally, I am once again left to wonder why the proposed 'theory of everything' totally ignores the conscious intelligences, whatever they are, that are searching for a theory of everything. Low heavy clouds obscured the surrounding hilltops here at Fractal Central on Friday. And the humdrum temperature of 54F 13C did nothing to improve things. The fractal cats don't care about hilltops. Their problem was the lack of afternoon sun in their southwest window. Like the day's fractal, my day was . . . average. The next attempt at greatness will be posted in 24 hours. Until then, take care, and how will we know what's real if our scientific ideas about reality keep changing? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Broken_Branches { ; time=0:00:20.09-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotN center-mag=-1.275442910495\ 823/+0.013776353035086/1.01901e+010/1/-105/0 params=2.1/0/0/0/0/0 float=y maxiter=750 inside=0 logmap=55 periodicity=10 mathtolerance=0.05/1 colors=000YGkXEqUJqRMrNRmJVhE`dRf_VkVcoRltWwx_zzWc\ STRKQQHMINJASGEWII_KJbFJfAJi6ClK6qY0xkOToj4rjJtjYv\ jlxjzzizzixzhuzhrzkpzmmzplzrizuhzwfzyezw_ouVesPWqK\ MpFChKNaOYVShOWsQXrRXrVVmZTibReePaiNYmLUpKQiLMbLJW\ MGPMCIN9BN65N3CL6JK8PJBWIDbGGhFIoELuDNnJKgPH`VEU`B\ Nf8Gk5FcAEXEEPIDINCARC3VATc9rlHZhDTbLXXHTXDQXKXV8f\ g9Xaf1Za4YY7YUAYQCYLFXHIXDLXpGHjHJeIL_JNVKPzLRzMTz\ NVgicWa`KUZzCgzGczK_fwGVjMzZSz_TzYUzWUOVVzTVzRWzQW\ zOXz7CzDJzIQtkwjfq`alSXfISaakdNZ`z59LxlzFGzQSh_cad\ aWh_QmYKqWEvU8zT9pUzL`9fVzXWz4Cz9IzENzJSza3zZ9zWFz\ TLzQRzMCzNHzNLzNPzNTzkCz2wz9nzGez1gz7dzCazIZzHqzIm\ zJjzKfzLczM_zv3zp8zjDzdIzZNzTSzm8z_Lzvgzdbz_`zW_zR\ YzrRzzTzzVzzm7zjzzhzzf8zdzzbzz`9zZEzzDztCznBzhAzbp\ zqVzf7zf8zd8zb8za9z_9zYDzxBznAzewzClzHbzLTzPJzTizc\ bzaXz`Rz_LzZFzYbzVYzWUzWQzWLzXHzXDzX8z89zC9zF9zI9z\ L9zO9zR9zUwztnzpfzlYzhZze } frm:MandelbrotN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 13-11-08 (The Eyes Have It [7])
by Jim Muth 13 Nov '08

13 Nov '08

FOTD -- November 13, 2008 (Rating 7) Fractal visionaries and enthusiasts: An unusually busy day on Wednesday left little time for a discussion. Today's image lies in the interior of the parent fractal that results when 0.25 part of 1/Z is combined with 0.5 part of Z^2. The stairstep effect was created by rendering the scene with the outside set to 'tdis'. The rating of a 7 is pretty close to what I think of the image. The name "The Eyes Have It" came to me when I thought I saw eyes staring out of the image at me. The calculation time of 1-1/3 minutes is quite reasonable, as also is the trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the already-calculated image there. Mostly gray skies and a temperature of 52F 11C made Wednesday passable here at Fractal Central, while two hours of hazy sun in the afternoon kept the fractal cats satisfied. My day was busy but adequate. The next FOTD will be posted in 24 hours. Until then, take care, and where will we find the last fractal? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Eyes_Have_It { ; time=0:01:22.80-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.6024187609298886/-0.166206626874756/\ 3241287/1/90/0 params=0.25/-1/0.5/2/0/0/0/0 float=y maxiter=1500 inside=0 outside=tdis periodicity=10 colors=000HU2OWAVXHdl3ck4cj5cj6ci7ci8ch9cg9cgAbfBb\ fCbeDbdEbdEbcFbcGbbHaaIaaJa`Ja`Ka_LaZMaZNaYOc0Ob7O\ bEOaLOaSORoMSnNSmNTmNTlNUkNUkNUjNViNViNWhNWgNWgNXf\ NXeOYeOYdOYcOZcOZbO_aO_aO_`O`_O`_OaZOaYOiOlhPjgQhg\ RffSdeSbeT`MSRGIWA8`JDXSIU_NQhSNqXJyaGpWMhQS_LXSFb\ J9hB4mJAoRFqZLsfQumVvlXtkYrjZqi_oh`mgalfbjfcia`dXZ\ _TWVOURJSMFPHANC6L8BUKFbVJkeQjgXihcijjhkqgmxgnoheg\ hY_hQRhIJhABh2jtode_ZRKTD4OC8KCBFBEBBI6AL2AOLRfbfx\ adracmaaha`caZZaYUaXPYOUZRS_TR`WPgvsfqmemhdicceYba\ TdLhcMgcMfcNecNdcOccOccPbcPabQ`bQ_bR_bRZbSYbSXbTWb\ TWbUVaUUaVTaVSaWSaWRaXQaXPaYOKXMNYNQYNSYNVYOXYO_YO\ 4EuAIoGLiLOdRSZXVT4Xw9YrDYnHYiLYeQY`UYXYYSGtXOlUVd\ RVbWWaVXaUY`TmOTlPSlPSkQSjRRiRRiSRhSRgTQfUQfUQeVPZ\ _SdVPcWPcXObXOaYOk7hiDcgI_eOWcTSd3Sc4Rc5Rc6Rc7Rc8R\ c9RcARcBQcCQcDQbEQbFQbGQbHQbIQbJPbKPbLPbMPbNPaOPaP\ PaQPaROaSOaTOaUOaVOaWOaXO } 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 for Nov 12 test
by JimMuth＠aol.com 12 Nov '08

12 Nov '08

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FOTD 12-11-08 (Mystical Minibrots [8.5])
by Jim Muth 12 Nov '08

12 Nov '08

FOTD -- November 12, 2008 (Rating 8.5) Fractal visionaries and enthusiasts: Yes, there is a minibrot in the lower part of today's image, and there is a less obvious upside-down cubic bud in the upper part. And this has anything to do with the number of iterations a par- ticular point takes before reaching an arbitrary distance from the origin. Escape time is not involved in the image because it consists entirely of trapped points that have been made visible by the 'bof60' inside fill, which colors the points according to how close to the origin they come in their trapped wanderings. The most amazing thing is that the small Mandelbrot set and the ghostly cubic bud are actually there at all. The more I work with fractals, the more I come to see the Mandelbrot set as a universal presence, created in potential by mankind when he invented and defined complex numbers. With all this in mind, I named today's image "Mystical Mini- brots". Of course, only one obvious minibrot exists in the image, but I see other brilliant yellow points scattered about. Could these be other minibrots? Only a further investigation will tell. The rating of an 8-1/2 includes a self-awarded half point for the effort I expended in getting smooth gradation with only 256 colors. The calculation time of 3-3/4 minutes is extrapolated from the 14 minutes the image took to run on the P200 machine. The 2000mhz unit is still out of action. The image may also be seen and hopefully enjoyed by surfing out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing it without effort there. Leaden gray skies and a chilly temperature of 43F 6C made Tuesday a rather forgettable day here at Fractal Central. The fractal cats again complained when the sun failed to appear as scheduled on their shelf in the southwest window. I eased my own gloom by treating myself to a genuine New York egg cream. The next FOTD will be posted in 24 hours, a fact that hardly needs to be repeated. Until that (IMO) wonderful moment, take care, and choose wisely. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mystical_Minibrots { ; time=0:03:45.72-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 passes=t periodicity=10 center-mag=-2.5071809/0/91.53/1/-90/0 params=-3/100 float=y maxiter=1000 inside=bof60 logmap=yes colors=000zzzzqmzjcreUmZEcVEUSEOODKMDKLDKMEKKQFFXA\ Ac55j65j76j86j97jA7jB8jC8jD9jE9jFAjGAjHBjIBjKCjLDj\ MEjNFjOGiPHhQIgRJfSKeTLdUMcVNbVOaUP`UQ_URZUSYTTXTT\ WTTVSTUSTTSTSSTRRTQRTPRTOQTNQTMQTLPTKPTJPTIPTHOTGO\ TFOTENTDNTCNTBMTANS9NSANSBNRDNREOQFOQHOPIOPJOOKPOM\ PNNPNOPMQPMRPLSQLTQKVQKWQJXQIZRI_RH`RHaRGcRGdRFeSF\ gSEhSEiSDjSDlTCmTCnTBpTBqTArTAsSBrSCrRDqREqRFpQGpQ\ HpPIoPJoPKnOLnOMnONmNOmNPlMQlMRlMSkLTkLUjKVjKWiKXi\ JYiJZhJ_hI`gIagHbgHcfHdfGeeGfeKheQjdWldancgpcmqchk\ `c`YURVKHSL9PM1MN2NN2NN2NN2NN2NN3NN3NN3NN3ON3ON3ON\ 4ON4ON4ON4ON4ON5PN5PN5PN5PN5PN5PN6PN6PN6PN6QN6QN5P\ N4OL3NI2MF1ID0FA0A505000N8RN8RN9RN9RN9RN9SN9SN9SNA\ SNASNASNASNASM9RNASNBSOBSOCTPCTPDTQDTQEURFURFURGVS\ GVSHVTHVTIWUJWUJWVKWVKXVLXWLXWMYXNYXNYYOYYOZZPZZPZ\ ZQZ_R__R_`S_`S`aT`aT`bU`bVacVacWacWbdXbdXbeYbeZcfZ\ cf_cg_cg`dg`dXVEXVEXVDXVD } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 12-11-08 (Mystical Minibrots [8.5])
by Jim Muth 11 Nov '08

11 Nov '08

FOTD -- November 12, 2008 (Rating 8.5) Fractal visionaries and enthusiasts: Yes, there is a minibrot in the lower part of today's image, and there is a less obvious upside-down cubic bud in the upper part. And this has anything to do with the number of iterations a par- ticular point takes before reaching an arbitrary distance from the origin. Escape time is not involved in the image because it consists entirely of trapped points that have been made visible by the 'bof60' inside fill, which colors the points according to how close to the origin they come in their trapped wanderings. The most amazing thing is that the small Mandelbrot set and the ghostly cubic bud are actually there at all. The more I work with fractals, the more I come to see the Mandelbrot set as a universal presence, created in potential by mankind when he invented and defined complex numbers. With all this in mind, I named today's image "Mystical Mini- brots". Of course, only one obvious minibrot exists in the image, but I see other brilliant yellow points scattered about. Could these be other minibrots? Only a further investigation will tell. The rating of an 8-1/2 includes a self-awarded half point for the effort I expended in getting smooth gradation with only 256 colors. The calculation time of 3-3/4 minutes is extrapolated from the 14 minutes the image took to run on the P200 machine. The 2000mhz unit is still out of action. The image may also be seen and hopefully enjoyed by surfing out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing it without effort there. Leaden gray skies and a chilly temperature of 43F 6C made Tuesday a rather forgettable day here at Fractal Central. The fractal cats again complained when the sun failed to appear as scheduled on their shelf in the southwest window. I eased my own gloom by treating myself to a genuine New York egg cream. The next FOTD will be posted in 24 hours, a fact that hardly needs to be repeated. Until that (IMO) wonderful moment, take care, and choose wisely. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mystical_Minibrots { ; time=0:03:45.72-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 passes=t periodicity=10 center-mag=-2.5071809/0/91.53/1/-90/0 params=-3/100 float=y maxiter=1000 inside=bof60 logmap=yes colors=000zzzzqmzjcreUmZEcVEUSEOODKMDKLDKMEKKQFFXA\ Ac55j65j76j86j97jA7jB8jC8jD9jE9jFAjGAjHBjIBjKCjLDj\ MEjNFjOGiPHhQIgRJfSKeTLdUMcVNbVOaUP`UQ_URZUSYTTXTT\ WTTVSTUSTTSTSSTRRTQRTPRTOQTNQTMQTLPTKPTJPTIPTHOTGO\ TFOTENTDNTCNTBMTANS9NSANSBNRDNREOQFOQHOPIOPJOOKPOM\ PNNPNOPMQPMRPLSQLTQKVQKWQJXQIZRI_RH`RHaRGcRGdRFeSF\ gSEhSEiSDjSDlTCmTCnTBpTBqTArTAsSBrSCrRDqREqRFpQGpQ\ HpPIoPJoPKnOLnOMnONmNOmNPlMQlMRlMSkLTkLUjKVjKWiKXi\ JYiJZhJ_hI`gIagHbgHcfHdfGeeGfeKheQjdWldancgpcmqchk\ `c`YURVKHSL9PM1MN2NN2NN2NN2NN2NN3NN3NN3NN3ON3ON3ON\ 4ON4ON4ON4ON4ON5PN5PN5PN5PN5PN5PN6PN6PN6PN6QN6QN5P\ N4OL3NI2MF1ID0FA0A505000N8RN8RN9RN9RN9RN9SN9SN9SNA\ SNASNASNASNASM9RNASNBSOBSOCTPCTPDTQDTQEURFURFURGVS\ GVSHVTHVTIWUJWUJWVKWVKXVLXWLXWMYXNYXNYYOYYOZZPZZPZ\ ZQZ_R__R_`S_`S`aT`aT`bU`bVacVacWacWbdXbdXbeYbeZcfZ\ cf_cg_cg`dg`dXVEXVEXVDXVD } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 11-11-08 (Out of Order [6])
by Jim Muth 10 Nov '08

10 Nov '08

FOTD -- November 11, 2008 (Rating 6) Fractal visionaries and enthusiasts: Today's image is a mathematical mystery, even if not an artistic wonder. The first parameter of the formula is 19, which should result in midgets of order 19. Such midgets have 18 lobes, but in today's huge central midget I count 37 lobes, and the lobes on the upper right shore line of the midget are strangely doubled, so that it is impossible to say exactly how many lobes are in this supposed minibrot. There is no problem in the surrounding circular midgets. They all have 18 lobes like a well-behaved minibrot of order 19 should. Most likely, today's central midget is actually a merging of 2 or more proper order-19 midgets, but if it is, I have not found the place where they merge. At any rate, the image has a certain abstract symmetrical simplicity about it, which earns the rating of 6. The parent fractal resembles a Mandelbrot set with rounded features. Today's scene is located in the suburbs of a smaller midget just east of the largest midget on the rudimentary main stem of the parent. The name "Out of Order" refers to the wrong number of lobes in the minibrot. The calculation time of 1-1/2 minutes will cause no one any heartache. And as always, the already calculated image is posted on the FOTD web site for instant viewing at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Dark lumpy clouds, (strato-cumulus), blustery winds and chilly temperatures made Monday of questionable worth here at Fractal Central. Not only did the temperature of 43F 6C make the fractal cats unhappy, the lack of afternoon sun shining through the southwest window kept them unhappy. With more than enough work to get out of the way, I had no time to be unhappy about the outside conditions. Unless something unexpected arises, as it sometimes does, the next FOTD will be posted in 24 hours. Until then, take care, and forget the boring 'real' world of reason. Live in the imaginary world of fantasy instead. Skeptics don't approve of this but it's a lot more fun. And if you believe in fantasy hard enough, it can become as real as the chair you are sitting in. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Out_of_Order { ; time=0:01:29.69-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 center-mag=-5.077610928161702/+0.001263530929175/\ 1.070948e+008/1/-167.5/0 params=19/3 float=y maxiter=2400 inside=0 logmap=159 periodicity=10 colors=000KDEJEFIEGHEHGEIFDJECKDAKC9KB7KA7Ka2dz6Yz\ cSzcMzIFzM9w3lmP0eQ1aQ1bQ1bQ1cQ1cQ2dQ2dQ2eQ2eQ2fQ3\ fQ3gQ3gQ3hQ3kv0js1jp1jm1jk1ih2ie2ib2i`2hY3hV3hS37E\ p9FmBGkDGhFHfHHdIIaKI_MJXOKVQKTRLQTLOVMMXMJZNH_OEa\ OCcPAeP7gQ5tUhsTfrTdrTbqT`qTZpSYpSWoSUoSSnSQnSOmRN\ mRLlRJlRHkRFkRDjQCjQAiQ8iQ6hQ4r_qqZmpYioXfoXbnWZmV\ WmVSlUOkTLjSHjSDiRAhQ6LV3OU3RT3TT3WS3ZS3`R3cR3fQ3c\ D1dE2dF2dF2dG2eG2eH2eI2eI2fJ2fJ2fK2fL3fL3gM3gM3gN3\ gO3hO3hP3hP3hQ31M85N79N7DO6HO6LO5PP5TP4XP4`Q3dQ3Kj\ gOgaRdXUbSX_N_XIbVDeS82FK5GU7Hc9HmBIzDIzFJzIJzKKzM\ KAOL9QM8SM8UN7XN6ZO6`O5bP4dP4fQ3Vx3Wv3Xt3Yr3Yp3Zn3\ _l3`k3`i3ag3be3cc3ca3z`3zZ3zX3zV3zS3zV3zZLzcJzhIzm\ HzrGzvFzzDzzCzzBzzAzz9zz7zz6zz5zz4zzRzzPzzOzzNzzMz\ zLzzKzzJzzIzzHnzGmzFmzElzDlzCkzBkzAjz9jz8iz7iz6hz5\ hz4FzOHzMJzLLzJNzIPzHRzFTzEVzCXzBczedzcdzadz`dzZez\ XezWezUezTezRfzPfzOfzMfzK } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 10-11-08 (Mandel What is It [No Rating])
by Jim Muth 09 Nov '08

09 Nov '08

FOTD -- November 10, 2008 (No Rating) Fractal visionaries and enthusiasts: Today's image shows a minibrot on the eastern side of the north branch of Seahorse Valley of the Hyper-Mandelbrot set. So far, so good. We've seen many minibrots in Seahorse Valley. But today's minibrot is truly different. It is not empty on its inside. Instead of the expected blank interior, the minibrot is filled with a spidery network of very high iteration arms. The image was created by the HyperMandelbrot formula, which is a generalization of the type=hypercomplex formula. I am not sure if the arms inside the minibrot are real or if they are arti- facts, since it seems quite unlikely that a value as tiny as the 10^-150 of the real(p3) parameter could make such a difference in the appearance of a minibrot. But there it is in the image, and it behaves as though it is real. I named the image "Mandel What is It" but gave it no rating. It's kind of hard to give a name to something I know nothing about. The calculation time of 4-1/4 minutes will cause no pain. The finished image is posted for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Brisk winds, dark gray clouds and a chilly temperature of 48F 9C made the outdoors unpleasant here at Fractal Central on Sunday. The fractal cats complained about the failure of their afternoon sun to appear. My day was uneventful, which is how I wish more days would turn out. The next FOTD will be posted in 24 hours. Until then, take care, and do it quickly. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandel_What_Is_It { ; time=0:04:15.44-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot passes=1 center-mag=-0.748577741895/+0.06049221491/1466442/\ 1/-57.5/0 params=0/0/-4.6/0/1e-150/0 float=y maxiter=1500 inside=0 logmap=-464 periodicity=0 colors=000PcCPc9Pc8OY7FK66546C9PSwPUxVVs_WneXjjXep\ YauZXzZTraXkd`cfdXigPlkInoAqs3sv4ba4MH7RN6RV4Rb2Rj\ 0QsLNseJteOoeTjeYeeb`egWfmRYhNOcIEZE4U9AQIGMRMH_SD\ hY8qUFrPNsLVtGbuCjv7rw2zx9iwGTuOCsMLfKVUHdGF_FDVDB\ QC9LA7G95B7265B7ML8cIDbEIaAO`6T_2ZZ9V_GQaNMcUHd7jm\ DkhIldOn_UoVZpRYjVXeZW`bVWfURjTMmjxYbn_WeaPWcINdHK\ eGHfFDhEAiD7jG8lJ9mMAnPBoSCpVDrYEs`FtcGufGvdJrcMoa\ Pl`RiZUfYXcW_`VaYTdVSgSRiPOgLMfIKeFIdCFb9Da6B`39_0\ D`1Ha1Lb1Pc1Td1Xe1_e2cf2gg2kh2oi2sj2vj2j_RZPoYQpXR\ pXSpWTpWUpVVpVWpUXpTYpTZpS_pS`pRapRapLhjGoeBv`FmVJ\ ePMXJQPDTH8SJBRKDQLGPMIONLNPNMQQMRSLSVKTXJV_IWaHXd\ GYfGZhL_cQ`ZV`U_aPdbKibFncAsd5xd0va5tZAsWEqTJpQNnN\ SmKWkH`jEdhBig8me5rd3vf8ohDijHblMXnQQpVKrZDtc7ug1p\ e7ldDhbJdaO`_UXZ_TYdPUZLQUHNPKmJKaEKQ9KK4GP8TPCeKG\ q0Kr6LzCLsHLoNLoTLoYLl_LhaMdcM`fNaiNblNdoNerNgzOcz\ PzzRzzTzzRzzOzzMzzJzzHzzE } frm:HyperMandelbrot {; periodicity must be turned off a=(p1),b=(0,0): q=sqr(a)-sqr(b)+pixel, b=(p2+2)*a*b+p3, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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Re: [Fractint] NOVA fractal program
by JackOfTradeZ＠comcast.net 09 Nov '08

09 Nov '08

. I cant play it online. The sound comes but the video freezes. Must be an internet thing. I'll just wait and order the DVD ... .

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FOTD 09-11-08 (To the Point [No Rating])
by Jim Muth 09 Nov '08

09 Nov '08

FOTD -- November 09, 2008 (No Rating) Fractal visionaries and enthusiasts: The lateness of today's FOTD tells that things were busy here at F.C. on Saturday, as a couple more customers called in, needing quick changes on their jobs as a result of the recent election. This left but little time for work on the glorious (IMO) FOTD. I could give today's image no rating because it's not a finished image, it's only a study in getting a smooth color gradient from a palette of 256 colors. But the result turned out good enough to qualify as the FOTD for November 9. The image shows parts of both Seahorse Valley and East Valley. The solid area at the left is part of Seahorse Valley of the Mandelbrot set, while the sharp spike shooting in from the right and stabbing into Seahorse Valley is actually a part of the East Valley of a second Mandelbrot set, which partially overlaps the first M-set. The 2 overlapping M-sets form a four-dimensional unit that can be explored in limited orientations by the hypercomplex formula. There are entries for four parameters in the formula, but only the last two have any effect on the image. Apparently the form- ula is still in an unfinished condition. But finished or not, the formula creates some images that can be quite unusual, with elephants eating seahorses, and minibrots filled with smaller minibrots. I have written several formulas that are supposed to expand the range of the hypercomplex form- ula, though they produce such weird results that I'm not sure exactly what they do. The name "To the Point" refers to the point of East Valley jabbing into Seahorse Valley from the right. The calculation time of 2 minutes will cause no impatience. And the finished image will soon be posted to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> but due to the odd hour of this posting, there may be a delay of several hours before Paul gets it calculated and posted. Early morning rain was followed by afternoon sun here at Fractal Central on Saturday. The fractal cats enjoyed the sun to the maximum. The temperature rose to 64F 18C by 2pm, but by sunset, just before 5pm, it had dropped to 52F 11C. As stated earlier, my day was busier than expected. The next FOTD will be posted in around 12 hours. Until then, take care, and wait for the new world with bated but not abated breath. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= To_the_Point { ; time=0:04:45.54-SF5 on P4-2000 reset=2004 type=hypercomplex function=sqr passes=t center-mag=-0.24440456/+0.04924533/207.7403 params=0/0/0.05/0.5 float=y maxiter=5000 inside=0 logmap=28 periodicity=10 colors=000jUKkULlUMmUNnUOoUPpUQqURrUSsUTtUUuUVvUWw\ UXxUYxUXxVYwWYvXXvYXuZWt_Wt`VsaVraUraUqaTp`Tp_SoZS\ nYRnXRmWQlVQlUPkTPjSOjROiQNhPNhNMgMMfLLfKLeJKdIKdH\ JcGJbEIbDIaCH`BH`AG_9GZ8F`6GZ7FY7FX7FW7FU8FT8FS8FR\ 7ER8FR9GRAHRBIRCJRDKRELREMRFNRGORHPRIQRJQRKRRLSRLT\ RMURNVROWRPXRQYRRZRS_RS`RTaRUaRVbRWcRXdRYeRZfRZgR_\ hR`iRajRbkRclRdmRdmVhaZlRbpGes5du3dw1ct4br7apA`nD_\ lGZjJYhMXfPWcSVaVU_YTY`SWcRUfQSiPQlQNnPOoPPoPQoPRp\ PSpOSpOTpOUqOVqOWqOWqNXrNYrNZrN_sN`sM`sMasMbtMctMd\ wLfzMdzNbzOazP_zQYzRXzSVzTTzUSzUQzVOzWNzXLzYJzZIz_\ Gz`EzaDzbBze8zbAz`BzZCzXEzUFzSGzQHzOJzMKzJLzHNzFOz\ DPzCSzBQzBPzBOzANzAMzALz9Kz9Iz9Hz8Gz8Fz8Ez7Dz7Cz7A\ z69z68z67z56z55z54zTKzpZzn_zl`zkazibzhczfdzeezcezb\ fz`gz_hzYizWjzVkzTkzSlzQmzPnzNozMpzKqzJqzLqzNqzPqz\ RqzTqzVqzXqzZqz`qzbqzdqzfqzhqzjqzlqznqzpqzrqzvxzsq\ zwmzpjzigzbdzWbzP_zIXzBUz } END PARAMETER FILE=========================================

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FOTD 07-11-08 (Totally Chaotic [No Rating])
by Jim Muth 06 Nov '08

06 Nov '08

FOTD -- November 07, 2008 (No Rating) Fractal visionaries and enthusiasts: Because of a lack of time, today's hasty image, for what it is worth, is presented without comment. Due to the calculation time of just under 14 minutes, I recommend viewing the image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> An unusually mild temperature of 68F 20C was spoiled by clouds here at Fractal Central on Thursday. The fractal cats slept through it all. With a big rush expected on November 7, there will be no FOTD for November 8. The FOTD for November 9 will be posted on schedule. Until then, take care, and be at ease. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Totally_Chaotic { ; time=0:13:51.90-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+0.052763137/-1.438769024/27360/1/-77.5/0 params=-4.4/-1.4/-1.4/-4.4/0.6/50000/0/0 float=y maxiter=2000 inside=zmag periodicity=10 colors=000XSaVT`UT_cC3dD4eD5eD6fD6gD7gE8hE9hE9iEAj\ EBjFCkFClFDlFEmFFmFFiYLgWMfVMeUNcTNbSNaRO_QOZPOYNP\ WMPVLPUKQTJQRIQQHRPGRNFRMDSLCSJBSIATH9TF8TE7UD6UC5\ UB7VB9VBBVADVAFWAHW9JW9LW9NW8PX8RX8TX7VX7XY7ZY6`Y6\ bY6dY5fZ5hZ5jZ4lZ4n_4p_3r_3t_3v_5tZ6sY8qX9pWBoVCmU\ DlTFjSGiRIhQJfPLeOMcNNbMPaLQ_KSZJTYIUWHWVGXTFZSE_R\ DaPCbOBcMAeL9fK8hI7iH6jG6`NHSTSIZb9dl8ek8ek8fj8fj8\ gj8gi7hi7hi7ih7ih7jg7jg6kg6kf6lf6lf6me6me5ne5nd5od\ 5oc0000000004qb4rb4ra4sa4sa6t_7tZ8tYAtXBtWCtVEtTFu\ SGuRIuQJuPKuOMuMNuLOuKQvJRvISvHUvFVvEWvDYvCZwB_wAa\ w8bw7cw6ew5fw4gw3hv4hv4hv5hu5hu6hu6iu7it7it8it8it9\ is9jsAjsAjsBjrBjrCjrCkrDkqDkqEkqEkqFkpFlpGlpGlpHlo\ HloIloIloIknKknLkmNkmOkmQklRklSkkUkkVkkXkjYkj_kj`k\ iakickhdkhfkhgkgikgjkfkkfmkfnkepkeqkerifshgsggsfhs\ eisdiscjsaks`ks_lsZmtYmtXntWotUotTptSqtRqtQrtPstOs\ tPsqPsoPsmQsjQshQsfRscRsa } 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 06-11-08 (Incomprehensibilities [6])
by Jim Muth 05 Nov '08

05 Nov '08

FOTD -- November 06, 2008 (Rating 6) Fractal visionaries and enthusiasts: Things were quite busy here at FC on Wednesday. Several jobs that were waiting for the results of the election needed to have the blanks filled in and finished fast. But in the end all was worked out and delivered to everyone's satisfaction. The image of the day is a nondescript scene in the parent fractal that results when 1.8 parts of Z^5 is subtracted from 3 parts of Z^3. This parent is absolutely humongous in size -- too large to fit onto the screen even at the least available magnitude. It consists mostly of oval holes, but a distorted Mandelbrot set lies not too far from the origin, and today's scene is located in some extra stuff extending east from the East Valley of this M-set. I named the image "Incomprehensibilities" because the parent fractal is one of the largest in FOTD history, and the word 'incomprehensibilities' is the longest word I knew how to spell in the third grade at Saint Martin's Elementary School. It also happened to be the longest word that any student in Sister Andera's class knew how to spell. (Apparently no one knew the word 'antidisestablishmentarianism', which, BTW, I now doubt is the longest real word in the English language.) The calculation time is 1-1/4 minutes -- fast enough to make running the included parameter file worth the effort. Viewing the completed image on the FOTD web site takes even less effort. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Clouds and mild temperatures made Wednesday fair enough here at Fractal Central. The fractal cats were too distracted by foraging squirrels to notice that, even though the temperature reached 63F 17C, their afternoon sun was missing. I was too distracted by FL's enthusiasm to notice that the sun was missing. The next FOTD will be posted in all of 24 hours. Until then, take care, and only my humility keeps me from telling how great I am. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Incomprehens-etc { ; time=0:01:14.76-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-3.960133085501834/+0.0473117827526381/\ 1646927/1/80/0 params=3/3/-1.8/5/0/0/0/0 float=y maxiter=1500 inside=0 logmap=75 periodicity=10 colors=000YcrZds_et`fuagvbhwcixdjyelwfnwgpwhrwitwj\ vwUaPU_POWOGRN8LM0GL7LJDPHJUFPYEVbC`gAfk8lp7oscP`L\ EVSLZRSbQZfPejPlnOsrNzzNueMnYMXMLNALQFQSJVUO_XScZX\ h``mbdqKlz2tz8zzDfhJ_hOThUMhZFhd8hi1hg8bfFXdMRcTLa\ _F`f9_m3T_NNMeH8xAuwHsjNrZTzNVjPXcQZYS`RTbKVcEWgMb\ jThm`npgtodunavmZvlWwkTwjQxjOxoXytdzxlzajhFhSJiQNj\ PRjNVkMZlKblJfmHimGehMadRZ_WVW`SSeQQhOPjNOlLMoJLqI\ KsLPmNUgPYaRbWTgQVkKXpEZt9`VRa6gbJacVWcfRLdrk6pg9l\ cBh_DdWGaSIYOKUKMREPT8SU2VV3WW3XX3YX3YY4ZZ4_Z4`_4`\ _BbWIcSPdPWfLbgHhhExy2svAosIkpQgnXckd_hlWfsSelPdfL\ d_IcUEcNBbH8bBDaJI`QN_XRZcWYj`XqdWxZQqTLkNUeHc_BcU\ 6cOAcNDcMHcLKgKNrKKtHHuEEvBBw88x5zozzpzzqzzrzzszzt\ zzu`zvbzwezxzzyzzzzzzzzzzzzYzzQYzIezAmz2`zFPzSCzd0\ zqAzrJzsSzt`ztRzsIzr9zq0zp7ziEzbLzXRzQYzJdzDkz6qz0\ 6zREzNLzJSzFMzGHzICzJNzILzJJzJHzJFzJDzKBzK9zKDzCCz\ EBzFAzGgzVfz_ezddzicznbzr } 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 05-11-08 (Ring of Butterflies [No Rating])
by Jim Muth 04 Nov '08

04 Nov '08

FOTD -- November 05, 2008 (No Rating) Fractal visionaries and enthusiasts: Looking at today's image, I see a ring of arctangent butterflies fluttering around the central minibrot, which is why I named the image "Ring of Butterflies. The parent fractal is a grossly overblown and out-of-proportion Mandelbrot set with a vast emptiness where its East Valley should be. Today's image is located on the southern shore line of the main bay, rather near the edge of the emptiness. Since I put so little effort into the image, I did not feel it was worth a rating, so I gave it none. But even an unrated FOTD is worth the short trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the image posted there already calculated. Those who decide to bite the bullet and run the included parameter file can expect a wait of a mildly dragging 3-3/4 minutes. Persistent clouds and a temperature of 61F 16C kept things within the comfort zone here at Fractal Central on Tuesday. The fractal cats were more concerned with two stray cats wandering about in the yard. When the voting was accomplished, (Thanks to FL's nagging, I finally did decide to vote.), my day was fair enough. The next FOTD will be posted in 24 hours. Until then, take care, and may the better man win. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Ring_of_Buterflies { ; time=0:03:45.72-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 passes=1 center-mag=+118.916225137266/-30.13184975452475/\ 83775.68/1/32.5/0 params=1/150 float=y maxiter=2400 inside=0 outside=atan periodicity=10 colors=000TBaWCfYAQ_89a9Ac9Ad9Bf9Bg9CiACjADlADmAEo\ AEpAElCHhDKdFN`GQXISTJVPLYLM`HObDPe9Rh5Sk1TmAJiJ9e\ S0aQ1_O2ZM2YK3XI3VG4UE5TC5SA6Q86P67O57NABPEERIHSMK\ URNWVQXZTZbW_PkcUefZ`ibVlgQnlLqpFtuAwy5ys4tn4oi4kc\ 4fZ4aU4YP4TJ4OE4K94F44B56A6897A88C79E6AG5BH5CJ4DL3\ EN2FP1GR0GS0QTAZUJhVSqV`pTYoRWoQTnORnNOmLMmKJlIHlH\ EkFCkEAlH9mK9nN9nP9oS9pV9pY9q_9rb9re9sh9tj9tm9up9v\ s9vu9rtDotGltJhtMetPbsS_sVWsYTs`QscNsfLqcKo`JmYHkV\ GiSFgPDeMCcJBaGA`ED_NFZWIYdKYmJTdIOXHJOGEGF98JAENA\ KRAQNIVKP_GWdDbiAin9hl8hk7hi6hh5hf4he3hc2hb1ha4eZ7\ cWAaTD_QGXNJVKLTHOREROBUM8XK5_I2aG0`I4`J8`KB`LF`MI\ `OM`PQ`QT`RX`S_aUYaVWaXUbYSb_Qb`ObbMccKceIcfGchEdi\ CdkAdl8dm7fk8gi9hgAifBjdCkbDlaEm_FnYGoXHpVIqTJrSKp\ QMnONlNPkLQiJSgITeGVdEWbDY`BZZ9`Y8aW6cU4dT3eU4gV4h\ W4iX4jY4kY4mZ4n_4o`4pa4qa4sb4tc4ud4ve4we4xc5ua5s_5\ pZ5nX6kV6iT6fS6dQ7aO7_M7X } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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NOVA fractals
by Vortex Swirling 04 Nov '08

04 Nov '08

>thanx for the heads-up vortex but too freakin' late! >it aired on oct 28 > >I HATE it when that happens! As mentioned already, it is on line. Here it is in chapter format. http://www.pbs.org/wgbh/nova/fractals/program.html I recorded it. PBS tends to replay the current episode many times during the week. Around here it is still on the listings. I was most interested in the scientific community's reaction Benoit Mandelbrot's discovery. At the time he presented, it was widely believed that the Mandelbrot fractal was an computer "artifact". If anyone bothered to read more than the first page of the paper they'd see that it is a graph of the bailout of a recursive algorithm. What does belief have to do with science, especially math in science? By the fractal patterns shown clearly had nothing on JOT's movies. Nor any mention of Fractint, which could have deserved at least a sentence, or a cameo. They must have spent 5 minutes of it on this *esoteric* "fractal pattern clothing". Roger

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Re: [Fractint] NOVA fractals
by JackOfTradeZ＠comcast.net 04 Nov '08

04 Nov '08

. thanx for the heads-up vortex but too freakin' late! it aired on oct 28 I HATE it when that happens! .

4 4

At Nov. the 4th ..
by Guy Marson 03 Nov '08

03 Nov '08

Hi fractinters, .. a little .par: Alienation { ; time= 0:24:00.42--SF7 on a P4 3.00GHz reset=2004 type=mandel(fn||fn) function=atanh/cotan passes=1 center-mag=0/1.04/1.2126 params=0/0.18586/0.57066 float=y maxiter=480 inside=atan periodicity=0 colors=000<8>21822922A32B32C32D<44>FCtFCuFDv<2>GDyGDzGDy<55>116115104<2>\ 001000100<56>tZ9u_9v_9<2>yaAzbAyaA<61>000 } Cheers, Guy

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FOTD 04-11-08 (Ultraviolet Sunrise [6])
by Jim Muth 03 Nov '08

03 Nov '08

FOTD -- November 04, 2008 (Rating 6) Fractal visionaries and enthusiasts: It's the day before election day as I write this, and FL is worried that her guy might lose. As for me, I have no guy, so I'm not very worried. The only thing I *am* waiting for is the end of the speeches, and while I'm waiting I'll take a little diversionary trip into fractal land. Today's FOTD image is notable for its . . . well it must be notable for something. I guess the mixture of zig-zag filaments and smooth areas makes it kind of notable. But I have seen and posted many similar scenes in the past. The image rates a relatively modest 6. A careful examination revealed little that might make it worth more. The name "Ultraviolet Sunrise" was inspired by something in the image that I have since forgotten. The calculation time of just under 4 minutes is my best estimate of the time the image would take to finish on the 2000mhz unit, which still will not start and I have yet to check. The parent fractal is a distorted Mandelbrot set with a gaping hole where its East Valley should be. Today's image is located in a small but curious bit of chaos at the tip of a zig-zag filament extending from a bud on the northwest shore line of the main bay. As always, the image is available for immediate gratification on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The Monday temperature of 57F 14C was mild enough here at Fractal Central. The persistent clouds spoiled the fractal cats' afternoon however. My day was a bit busier than usual, but nothing out of control. The next FOTD will appear in 24 hours. Until then, take care, and be of stout heart in the abstract sense only. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= UltravioletSunrise { ; time=0:03:57.80-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 passes=1 center-mag=-0.807745426104596/+0.6920600237179639/\ 16070000/1/-90/0 params=1/2 float=y maxiter=2600 inside=0 periodicity=10 colors=000kQXlXZmc`njboqdmrbkrais`hs_fsZdtYbtXauW_\ uUYuTWvSVvRTvQRwPQwOOxNMxMKxKzyJzyIzzHzzGzzFzzEzzD\ zzC8yD9xD9wDAvDBuDBsDCrDDqEDpEEoEFmEFlEGkEHjEHiFIg\ FJfFJeFKdFLcFLbFPcETcEXcE`dDddDhdDleCpeCteCweCwdDv\ cFvbHvbIuaKu`Mt_Nt_PsZQsYSrXUuZEr_Dp`Dm`DjaCgbCecC\ bdB_dBXeBVfASgAPhAMh9Ki9Hj9Ek8Bl89l8OsEbzKpzQnzRmz\ SkzTjzTiyUgxVfvWeuWctXbsY`qZ_pZgXZbbZXgYSmYNrYIxYD\ zYCzUCzQCzNByJBxFBwCAv8Au4Au1Bs3Br4Bq5Bp6Bo7Bn8Bm9\ BlABkBBjCBhDBgEBfFBeGBdHBcICbJCaKC`LC_MCZNCXOCWPCV\ QCURCTSCSTCRUCQVCPWCOXCNYTPfiQozzzzzzzzzzzzzzzzzzz\ wzztzzqzzozzmzzkzzizzgwzetzdqzcnzbkzahz`gzZfzXexUd\ vSctQbsOaqN`oM_mLZlKYjJXhIWfHVeHUcHRaGQ_GQYGPXGOVF\ NTFMRFMQFLOEKMEJKEIJEDVGtgIzkKzmMzkOuhQrfRmcSh`TcZ\ UZWVUTWPRXKQYIPZJP_KO`LNaMNbNMcOMdPLeQKfSKgTJhUIiV\ IjWHkXHl_GlcFnfFoiEomDqmDqmCrrCtvBtzAvzAvz9xz9xzDu\ vHkqLhmPeiTceX`b`Y`dV_hSY } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 03-11-08 (Minibrot in Doubt [7.25])
by Jim Muth 02 Nov '08

02 Nov '08

FOTD -- November 03, 2008 (Rating 7-1/4) Fractal visionaries and enthusiasts: Today's image appears to have a large brilliant blue minibrot near its center, with other minibrots scattered generously about. But actually this is an illusion. To begin, the image is evaporated. Everything in it consists of 'inside' stuff made visible by the 'bof61' inside fill. And also, the real(p1) parameter of minus-11 means that any minibrots must be of order minus-11. A problem immediately arises -- minibrots of order minus-11 are an absurdity. If such things actually existed, they would have minus-12 lobes, which is meaningless. Yet there it is in the image, a minibrot, which must be one of order minus-11. Well, maybe according to rules the minibrot is supposed to have minus-12 lobes, but I count plus-10 lobes, making the minibrot one of order plus-11. I guess nature has made sure that some- thing impossible, such as a negative minibrot, does not happen, just as it conspires to prevent backward travel in time or the simultaneous knowledge of both the exact position and momentum of a sub-atomic particle. I named the image "Minibrot in Doubt" because of this confusion. I rated it at a 7-1/4, which includes a 1/4 bonus for my work with the limited number of colors that actually appear in the image. The calculation time of 4-2/3 minutes is user-friendly. The trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the completed image there is even more friendly. Sun in the morning was followed by clouds in the afternoon here at Fractal Central, while the temperature bogged down at 48F 9C. The fractal cats grew testy when their much-anticipated after- noon sun failed to appear. But my day was acceptable. The next FOTD, in all its glory, (if any), will be posted in 24 hours. Until then, take care, and in two days it will all be over and we can start hoping we chose correctly. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Minibrot_in_Doubt { ; time=0:04:42.50-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 passes=1 center-mag=-1.2076051079214/+0.01488191850166877/\ 4927746/1/-95/0 params=-11/11 float=y maxiter=2500 inside=bof60 logmap=yes periodicity=10 colors=000zrcvqcrpcmochnccmcZlcUkcRicSgcTecUccVbcW\ acXacYacZ`c_`c`_ca_cbZccZcdYceYcfXcgXchWciWcjVckVc\ lUcmUcmUcmUcmUcmUcmUcmUcmUcmUcmUcmUcmUcmTcmScmRcmQ\ cmOclNckMcjKciJchHcgGcfFceDbdCacBabCZaDW_DTZCQXBMW\ AKU9JS8IQ7HO6GM5FK4FI3FG2FE1FC0FA0F80F60F40F00F00F\ 00F00F00F00F00F00F00F00F00FZzz3G50112F52E42E42D42C\ 42C42B32A31A31931821821721621621510410410310200200\ 10000eP3dO2cO2bN2aN2`M2`M2_L2ZL2YK2KLaJK`II_HHZGGY\ FEXEDWDCVDBVYKv_Pp`TkaYfba`dfWejRfoLgsGhwBjmJlcRmU\ YoKepBloFnnIonLqmOrmRslVukYvk`xjcyjfzUqLSrPRrSQrVP\ rYOs`NscMsgLsjKtmJtpItsHtvGutGurFupFunFulEujEuhEug\ DueDucCuaCu_CuYBuWBuUBuTHvTMwTRwTWxT`xTeyTjyTozTtz\ TpvUmsVjpWglXdiYafZZb_W_`TXaQUaSVbUVcWVcYVd_WdaWec\ WeeWffWfTeXFoN2xD1sC1nB1iA1d91_81V70Q60L50G40B3062\ 012011011000000agQ`fP_eP_eOZdOZcOYcNYbNXaMXaMW`MV_\ LV_LUZLUZKTYKTXJSXJSWJmOF } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 02-11-08 (The Worst Minibrot [3])
by Jim Muth 01 Nov '08

01 Nov '08

FOTD -- November 02, 2008 (Rating 3) Fractal visionaries and enthusiasts: Today's discussion is brief because I spent quite a bit of time trying to explain to FL why we will elect no messiah on Tuesday. Basically, the reason is that I see no messiah on the ballot. But I prefer to avoid getting involved in politics, so let's get on with the fractal talk. Today's image is perhaps the least attractive minibrot of all time, which explains the name "The Worst Minibrot". But unattractiveness does not always mean hopelessness. Yesterday's unusually attractive image is actually located deep in the stuff filling the interior of today's minibrot. What we have in today's image is a minibrot caught about halfway through the process of morphing from quadratic to quintic. And like a caterpillar halfway through its metamorphosis into a but- terfly, the present appearance is rather unattractive. Considering all this, I could rate the image no higher than a humble 3. The good news is that the image calculates in a hyper 51 seconds. The better news is that the finished image is posted for instant viewing pleasure on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Morning clouds gave way to afternoon sun here at Fractal Central on Saturday, while the temperature reached a high of 61F 16C. The fractal cats were glad when the sun appeared just in time for them to enjoy their afternoon nap in the sunny window. My day was about average. The next FOTD will be posted in 24 hours. Until then, take care, and line up to choose your messiah. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Worst_Minibrot { ; time=0:00:51.05-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 passes=1 center-mag=-20.72757404199032/+111.7489204233713/\ 316.95/1/137.5/0 params=5/100 float=y maxiter=2500 inside=0 logmap=24 periodicity=10 colors=0007FT9GUBHVCIWEJXFKYHLZJM_KN`MOaNPcPQeRRgS\ SiTTiRSkQRhMQdIOaCMXFITJDOWIPeLTnNUvNPuQQrSQnUQkWQ\ iYQf_QfaQecRdeRcgRbiRakR`mR`oRZmPXlOWkNUjMSiLRgJPf\ INeHMdGKcFIaDH`CF_BDZADV4CY9B`DAcI9fM8iQ6gR5iR4kR3\ mS2mS1mS5mR8mQCmPFmOJmNMmMQmLTmLRmOPmRNmULmXJm_Hmb\ FmdDmgBmj9nm7qp5ts3wv1yx7yjCyXIyJNy6Mw9MvBLtDzsFzt\ KzuPzvUzwZzxczyhzzmzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzAzzIzzQ\ zzMzzSzzZzzYzzYzzYzzYzzYzzYzzYzzYzzYzznzzkzzhzzezz\ bzz_zzgzzfzzezzdzzczzbzzazz`zz_zzZzzYzzEzzHzzKzzNz\ zQzzTzzWzzizzhzzgzzfzzezzdzzczzbzzazz`zz_zzZzzYzz0\ zz3zz5zz7zz9zzBzzDzzFzzHzzKzzMzzOzzQzzSzzUzzWzzuzz\ rzzpzzmzzkzzizzfzzdzzazz_zzezzbzz_zzozzmzzkzzizzgz\ zezzczzazz_zzazzKzzMzzOzznzzlzzizzfzzczz`zzYzzVzzS\ zzQzzRzzXzzSzzTzzTzzUzzVzzWzzWzzXzzYzzYzzYzzYzzYzz\ YzzYzzYzzYzzuzzszzizzkzzn } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 01-11-08 (Ins and Outs Of It [8.5])
by Jim Muth 31 Oct '08

31 Oct '08

FOTD -- November 01, 2008 (Rating 8.5) Fractal visionaries and enthusiasts: I named today's image "Ins and Outs Of It". I chose this name because the image is filled with both basins and peaks. The central minibrot is obviously a basin, but the five elements surrounding it are peaks. A collection of smaller basins and peaks is scattered about the image. The peaks have bright solid centers, while the basins have pentagonal shapes surrounding the tiny minibrots at their centers. The scene lies in the partially-filled interior of a larger minibrot that lies on a filament on the north side of the parent fractal, which on the surface resembles an overblown Mandelbrot set. I might make the larger minibrot with the active interior the FOTD for November 2. It is unusual and interesting enough to merit FOTD status. After some consideration I rated today's image at an 8-1/2, including a reward of 1/2 point for my coloring. The calcula- tion time of 47 seconds will pass faster than the time it takes a bat to fly out of you-know-where. But the most convenient way to see the image is to view it in all its finished glory on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Conditions were absolutely perfect here at Fractal Central on Halloween Friday. The sky was cloudless, with a temperature of 64F 18C and light winds. The fractal cats had a moment of excitement when a stray cat stopped by the porch to take a drink from the watering can. But they did not enjoy the many trick or treaters that showed up in the evening. My day was about average; tomorrow looks like it will be slow. The next FOTD will be posted in 24 hours. Until then, take care, and serious science does not search for ghosts because there is no scientific evidence that ghosts exist. There is no scientific evidence that ghosts exist because serious science does not search for it. Happy belated circular-logic Halloween. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Ins_and_Outs_Of_It { ; time=0:00:47.48-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 center-mag=-20.72785398290\ 719/+111.74900338823/1.864e+008/1/30/0 params=5/100 float=y maxiter=2500 inside=0 periodicity=10 colors=000gzUczQ_zNWzJTzGPzCLz9Hz5Ez2EzMEzdEzwHzrJ\ zmLziNzdPz_RzWTzRVzMXzIZzJ`zKazLczLdzMfzNhzNmzOrzP\ vzPzzSzzVzzXzz_zzzzzzzzzzzzzzzzzzzzzzzzzvzwomtlbqi\ bmgbiebecbca`aZZ_WYYTWWQVUNTSKSQHQODPN9NM6ML3KK0JI\ 1MH2PF3RE3UD4XB5ZA5a86c77f67i48k39n29p48q57q66q76q\ 95qA4qB3rC3rE2rF1rG0rH0rF4qE7qDApCDpAGp9Jo8Mo7Po6S\ n4Vn3Yn2`m1cm0fm4hn7inAknDloGnoJooMqpPrpStpVupe`mp\ GknOblWUjbMhjDfq5iiEkaNmUVoMcqEklFngGpbHsYIuTJwZRv\ dYujdtpkti_pcOmXCjR0gU2iX3k_4la8kcCkeGjgKjhOijSilW\ hn_hpcgqggskfuofwseywezzezzdzzczzbzzazz`zz_zzZzzYz\ z0zz3zz5zz7zz9zzBzzDzzFzzHzzKzzMzzOzzQzzSzzUzzWzzu\ zzrzzpzzmzzkzzizzfzzdzzazz_zzezzbzz_zzozzmzzkzzizz\ gzzezzczzazz_zzazzKzzMzzOzznzzlzzizzfzzczz`zzYzzVz\ zSzzQzzRzzXzzSzzTzzTzzUzzVzzWzzWzzXzzYzzYzzYzzYzzY\ zzYzzYzzYzzYzzuzzszzizzkzznzzqzzpzzpzzpzzozzozzozz\ ozznzznzznzznzzmzzmzzZzzY } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 31-10-08 (Trick or Fractal [Spooky])
by Jim Muth 30 Oct '08

30 Oct '08

FOTD -- October 31, 2008 (Rating Spooky) Fractal visionaries and enthusiasts: It's Halloween, and in recognition of the event, I named today's image "Trick or Fractal". The rating of 'spooky' pretty accurately describes the hypernatural things going on in the image. The parent fractal is a grossly oversized Mandelbrot set with quadratic characteristics on the surface and quintic characteris- tics in its depths. Today's scene is located in an elephant trunk in a larger elephant trunk in the East Valley of the large midget on the main spike of the parent. The minibrot at the center of today's image is purely quintic, but the surrounding pattern is not. It has been caught in the act of changing from quadratic to quintic. Surprisingly, the resulting numerical chaos is totally free of discontinuities. The calculation time in the parameter file is 1/4 of the time it actually took to calculate the image on the old 200mhz unit. The 2000mhz unit is still out of action. The fastest way to fractal ecstasy is to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the already-calculated image there. Gorgeous Halloween weather prevailed here at Fractal Central on Thursday, which is a bit strange, since Halloween comes on Friday. Regardless, the fractal cats kept the ghouls, witches, and all the other various goblins, well under control. The work was well under control also. If all goes as planned, the first fractal of the new month will be posted in 24 hours. Until then, take care, and some fractals are hauntingly beautiful. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Trick_or_Fractal { ; time=0:06:01.08-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 passes=1 periodicity=10 center-mag=-174.9609778835375/-0.0095685074016842/\ 1.66389e+010/1/-115/0 params=5/100 float=y inside=0 maxiter=3600 logmap=-744 mathtolerance=0.05/1 colors=000FU_IUZLUYOUXRUWUUVXUU_UVbUWeUXgUYiUZkU_l\ T`mSalRbkQcjPdiOehMegKefIceG`eEZdDWcCUbBRbEQaHPaKP\ _LLYPIWUFU_CSf9Qo6Xv3Tr3Pl3Lf3Ha3DW39Q35K32F3MGLgE\ hdGjbKcbJhfIkiHlmHsrGuuFvxEywEtuCpqBlmAhi9de8`a7XY\ 6TWHMUINSKORLPQOQTRSWUUZXWa_Yeb_ieamhckiekj`jkWjlR\ imMmoJqoFkmHdfJY_LSTNOOGHIKUnfjocopazpZoqXHrUFrSCs\ PAsN9qP8sw8zz7mT7lV6kW6iY5hZzgzmez3dc3cd2af2`g1_i1\ Zj1bd1f_1jV1nQ1qL4rO6rQ8rSArUDsWFsYHs_JsaLscSiWZ_P\ dRHkHAq83mD7iIAeNDaSGYWJU`NQeQMjTIoWEsZImdMgiQbnUX\ sXSxPM8PLGPLOPKWPKbPJjPJrPJyRHwSGvTFuUEsVDrWCqYBoZ\ Anc9mh8km7jr6iv5hz5qzAyzFuzKqzPmzUizZezcazhYzmUzrQ\ zvRzzRzzRzzRzzRzzRzzRzzSzzSzzSzzSzzSzzSzzSzzSzzRzz\ PzzNzzNzzMzzLzzKzzKzzJzzIzzHzzHQzzVzz_zzdzzmzzizzf\ zzczz`zzazzbzzbzzZzzWzzSzzPzzJzzMzzRzzPzzOzzNzzLzz\ KzzAzzFzzJzzOzzOzzSzzWzz_zzbzddzfezgfzigzjhzkizmjz\ nEzxkzofzmazkXziTzhOzfJzd } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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Re: [Fractint] Fractint Digest, Vol 68, Issue 8
by Vortex Swirling 29 Oct '08

29 Oct '08

Hi, I didn't see it mentioned but the current running just made PBS Nova episode is about the "new" field of fractals. I think it can be watched on line but usually plays several times a week. Check local listings. http://www.pbs.org/wgbh/nova/fractals/ Roger

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FOTD 30-10-08 (Glorious Outzoom [7.5])
by Jim Muth 29 Oct '08

29 Oct '08

FOTD -- October 30, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is an outzoom from yesterday's image. It's not exactly glorious, but I felt like exaggerating when I chose the name, so I named it "Glorious Outzoom". The rating of a 7-1/2 includes 1/2 point for my extra coloring effort. Coloring in GIF mode takes effort. It's not easy to get smooth colors with only 256 colors to choose from. The purplish spot just southwest of the minibrot at the center of today's image is the source of the break in the smooth sequence of bifurcating features surrounding the minibrot, which itself has been caught in the act of shifting from quadratic to cubic. This purplish spot is in fact yesterday's anti-minibrot image. Today's minibrot itself resembles one of order 2.718 but lacks the discontinuities that I always thought 'must' exist in such fractals. I have not yet figured out what is happening, but whatever it is, it sure is interesting. (And since the universe is a giant fractal, and keeps breaking the rules that seem so intuitive to us, why should it be surprising to see our small- scale fractals doing the same?) Since my 2000mhz fractal machine is still out of action, and will remain so until I find the time and energy to tackle it, today's image was run on the ancient but faithful 200mhz unit. On the old unit it takes 4-1/2 minutes to finish. On the ailing 2000mhz machine, it would finish in about 1-1/4 minutes. But why worry about calculation time when the completed image is or soon will be posted for instant enjoyment on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> What a minor let down! Gerald D. has informed me that yesterday's 'anti-minibrot' is actually an example of 'reverse bifurcation', which I assume is relatively rare, but not totally unknown. And a further examination of yesterday's image has shown that in this image at least, the symmetry totally vanishes beyond the stage of 2-part symmetry. (Then again, what else could it do?) In yesterday's trivial closing comment, I speculated that every- thing is an illusion, and wondered what then is having the very convincing illusion that I myself exist. Alex Dukay replied that in his opinion it is the conscious mind that creates the illusion of an individual identity. Now I wonder what is having the illusion that the conscious mind exists. (The logic seems to be going in circles here, but the flaw is hard to pin down.) Chilly temperatures around 39F 4C, mostly cloudy skies, and occasional showers of cold rain and wet snow made Wednesday less than perfect here at Fractal Central. The fractal cats agreed and wasted little time hunched on their shelf by the drafty window, watching the TV show outside. My day was about average, which still leaves some things to be desired. The next FOTD will be posted in 24 hours. Until then, take care, and prosper. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Glorious_Outzoom { ; time=0:04:28.53--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 center-mag=+29.20416308310227/-1.333596110856609/\ 6355680/1/100/0 params=3/100 float=y maxiter=2000 inside=0 logmap=168 periodicity=10 colors=000cUncUmcUlcUkcUjcUicUhcUgcUfcUecUdcUdcUcb\ VbaW``WaZX`YX_VXZUXYTWXTVWTUVTTUSRTSPSQNRNLQKJPGHO\ CCN99OC6QF9SIBULCWODYRFZUG_XH_`FVdDQhBLl9Hp7Ct57w4\ 3t65r76p88nA9lBAiCCgEDeFFcGGaIHZJJXKKVMMTNNRQOPUTN\ _YLdbKjgIolGuqFzuRsjbm`nfQy`Gy_Fy_Ey_Ex`Fx`Fx`FxaF\ waFwaFwaFwbFwbFvbFvcFvcGvcGvmGuhGucGuZGuUGvPLuKGtA\ GteGtfGtfHtfHsgHsgHsgHsgHzzzzzzzzHrvHrrHqiIqiIqjIq\ jIqjIpkIpkIpkIpkIplIolIolJomJomJomJnmJnnJnnJnnJmoJ\ moJmoJmoKmpKlpKlpKlqKlqKlqKkqKkrKkrKkrKksLjsLjsLjs\ LjtLjtLitLiuLiuLiuLW7nYCkZGi_Kf`OdaTabX_d`XedVfiSg\ mQhqNWMFXNGXOGXPGYQGYQGYRGZSGZTHZTHZUH_VH_WH_WH`XH\ `YH`ZIa_Ia_Ia`IaaIbbIbbIbcIcdJceJceJdfJdgJdhJdhJei\ JejKekKflKflKfmKgnKgoKgoKgpLhqLhrLhrLisLitLiuLyvdv\ watxZryWozTmzQkzNVzsWzrWzqWzqWzpXzpXzoXzoXznXznYzm\ YzkXziXzhWzfWzdVzcVzaUz_UzZVz`VzaVzbVzcVzdVzeVzfVz\ gWziWzjWzkWzlWzmWznWzoWzp } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 29-10-08 (Anti-Minibrot [8.5])
by Jim Muth 28 Oct '08

28 Oct '08

FOTD -- October 29, 2008 (Rating 8.5) Fractal visionaries and enthusiasts: It's rare that I stumble upon something entirely new in the world of fractals, but today it appears to have happened. I named today's image "Anti-Minibrot" because that's what it is. The image is exactly the opposite of a minibrot. Instead of growing larger as the center of symmetry is approached, the iteration count grows smaller. And instead of the expected 2...4...8... sequence of symmetry as we near the center, we have an 8...4...2... sequence. The backwardness is immediately noticeable in the reverse direction of the color cycling. Instead of visualizing today's image as the expected bottomless pit of a minibrot, we must see it as a mountain peak. The rating of an 8-1/2 reflects the mathematical interest of the image and includes 1/2 point for my coloring effort. Its artistic worth alone is closer to a humdrum 5. I have not yet had a chance to open my P4-2000mhz machine dedicated to fractals to see why it will not start, so today's image was created on the P200 unit with the broken exhaust fan, which served the fractal world faithfully for over 10 years. The 4-1/2 minute calculation time on the older machine would be closer to 1-1/2 minutes on the 200mhz unit. However, calculation time is of no consequence for those who view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Cloudy skies, cold rain with a few wet snowflakes mixed in, high winds with gusts to 50mph 80kph, and a temperature of 41F 5C allowed the fractal cats only brief periods of comfort on their TV seats in the side window. They complained, but were silenced by several treats of half-and-half coffee creamer. My day was appropriately busy. The next FOTD will be posted in 24 hours. Until then, take care, and if nothing is real, then everything is an illusion. Since I am included in the set of everything, what is having the illusion that I exist? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Anti-Minibrot { ; time=0:04:24.63--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 passes=1 inside=0 center-mag=+29.20416304833718/-1.333596074674975/\ 1.586862e+009/1/70/0 params=3/100 float=y maxiter=2000 periodicity=10 colors=000zzz_UdbUc3slHtlVulhvlwwknsFlzIac`SIrQRmP\ _hNhdMq_LyWQsUVmT_gSdaRiWQnQPsKOwENmDTdCZVBdMAjC9p\ 39u9BiFCYKDNNKJQQFSWBVb7Yh3_n0Wk1Th2Pf2Mc3J`4FZ4CW\ 59U5EOBJJGOELPKJPQHPVGQ`EQeDQgBQjAdX6fV5gT5iS5jQ5l\ P5mN5nL5pK5qI5sH5tF5uE5nL7hR8aY9WcBPjCJpDLmENkEPhF\ RfFTdFVbGY_G_YHaWHdTIfRIiOJkMJmKKpHKrFLuCMVQC3c15`\ 38Y6BV8ESBGPDJMGMJIPGLRDNUAQX7S_4V_7U`BT`ISzzQzvPz\ rOzmNzhLyeKxdJtfHlgKcgNafQ_cTZ_WXXZRVXQSVNQUGQO9PM\ 2OL2P63Q64R75T76W87Z88a89d9Ag9BjAJj`RkcRjfQieQhcPg\ aPfZOeVNcQM`QKYPIVPHSOFPODMNCJNAGM8DM7AO57R33U7GVC\ HYHI`OJcSKfXLf`MfcMfdLfcKgbJaaIW`MWWQXSUXNYYIaZEeZ\ 9i_4m`6mZ8nXAoUCpSEqPGqNIrLLsINtGPuDRuBTv9Vw6UsATo\ ESkIRgMQcQP_UOWYNSaMOeLKiMOkOTmQYoSbqUgsWlvUkvRjuO\ itMhsJgrGfrDeqBdp8co5bn2am4al6aj8ahA`gD`eF`cH_bJ_`\ L_ZOZXARCASFAUIAVLAXOAZRA_UAaXAb_AdbAfeAghAikAkoDg\ nGblJYkMTiOTiQThTTgVTfYUe } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 28-10-08 (Scattered Minibrots [7])
by Jim Muth 27 Oct '08

27 Oct '08

FOTD -- October 28, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's image has in it one of the most incredible assemblage of minibrots that I have yet stumbled upon. There are cubic ones, quadratic ones, some that look like disembodied cubic buds, plus quite a bit of odds and ends. And strangely enough, none of this actually exist, since the entire image consists of blank inside stuff made visible by the 'zmag' inside fill, which adds detail where none exists. I named the image "Scattered Minibrots" when I turned on the radio and heard the local forecast of scattered showers. The image rates a 7. If I had found a chance to further tweak the colors, it might have rated an 8. The calculation time of 27 minutes is not as bad as it seems, since the time is on the old P200 machine. On the usual P4-2000mhz unit it would take about 6 minutes. The calculation time may be totally eliminated by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the completed image is posted for instant viewing. Thick clouds, a chilly temperature of 50F 10C and occasional light rain spoiled Monday here at Fractal Central. The fractal cats vented their dis-satisfaction by attacking and tearing up their scratching post. My day was frustrating, spoiled by a job that simply would not do what I wanted. And to make things worse, my fractal- dedicated P4-2000 mhz machine did not start up when I turned it on. It simply beeped 1-3-2, which must be some kind of coded message, and stopped trying to start. I suspect some memory might have worked loose. We'll see how it goes when I get the chance to check it. The next FOTD will be posted in 24 hours regardless. Until then, take care, and stalk the wild fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= ScatteredMinibrots { ; time=0:27:25.96--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 passes=1 periodicity=10 center-mag=1.28707/0.94564/29.06118/1/-70/0 params=-3/10 float=y maxiter=1000 inside=zmag colors=000GkWGlWGlXGmXGmXHlYIkYIkYJjZKiZKiZLhZMg_M\ g_Nf_Ne_Oe`Pd`Pc`QcaRbaRaaSaaT`bT_bU_bUZbVYcWYcWXc\ XWdYWdYVdZUd_Ue_Te`Se`SeaRfbQfbQfcPgdOgdOgeNgfMhfM\ hgLhgLhdPaaTW_XQX`KUdESg8Tf9Te9TeATdAUdBUcBUcCUbCV\ bDVaDVaEV`EW`FW_FW_GWZGXZGXYHXYHXXIYXIYWJYWJYVKZVK\ ZULZULZTM_TM_SN_SN_RO`RO`QO`PP`PPaOQaOQaNRaNRbMSbM\ SbLTbLTcKUcKUcJVcJVdIWdIWdHWdHXeGXeGYeFYeFZfEZfE_f\ D_fD`gC`gCagBagBbhAbhAch9ch9ciAbiBaiCajD`jE_jF_kGZ\ kHYkHYlIXlJWlKWmLVmMUmNUnOTnPSnPSoQRoRRoSQpTPpUPpV\ OqWNqXNqXMrYLrZLr_Ks`JsaJsbItcHtdHtdGueGufFugEvhEv\ iDvjCwkCwlBwlAxmAxn9xo8yp8yq7yr6zs6zt5zt5yr6xq6wp6\ vo6un6tm7sl7sk7rj7qi7ph8og8nf8me8md8lc9kb9ja9i`9h_\ 9gZAfYAfXAeWAdVAcUBbTBaSB`RB`QB_PCZOCYNCXMCWLCVKDU\ JDUIDTHDSGDRFEQEEPDEOCENADOBEPBEPBFQBFQBGRBGSCGSCH\ TCHTCIUCIUCJVCJWDJWDKXDKXDLYDLZDLZDM_EM_EN`EN`EOaE\ ObEObFPcFPcFQdFQeFQeFRfFR } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 27-10-08 (A Huge Trunk Full [7.5])
by Jim Muth 26 Oct '08

26 Oct '08

FOTD -- October 27, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image, with both Z^2 and Z^6 features, lies in the East Valley of a parent fractal that resembles a ragged Mandelbrot set. I named it "A Huge Trunk Full" because it is a scene in a trunk-spiral in a larger trunk-spiral. I rated the image a 7.5, allowing myself 1/2 point reward for the 1/2 hour I spent working on the colors. Unfortunately, the colors will not blend as smoothly on a monitor with a different color balance. Though the generating expression combines both Z^2 and Z^6 elements, there are no discontinuities in the image, such as would exist with a generating formula of something like Z^4.5. Yet with the DivideBrot5 formula, we can produce Mandeloids in all the stages of morphing between Z^2 and any other power of Z. But strange things happen when we try to morph a Z^2 Mandeloid into something with an exponent less than 2, especially including the negative exponents. This area needs much more exploration, which of course, I will be doing in the days to come. The calculation time of just under 2 minutes is as brief as a bikini. The trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the completed image there is even briefer. Sunday began quite foggy here at Fractal Central, but by 10am when the fog lifted, the rest of the day was near perfect. The fractal cats fully appreciated the warm sun and temperature of 61F 16C, but had a bit of a spat about who got the sunniest spot on the shelf. My day was fully occupied by doing nothing. But with the work already waiting, tomorrow will be less peaceful. The next FOTD will be posted in 24 hours. Until then, take care, and keep the fractal exponents straight. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Huge_Trunk_Full { ; time=0:01:57.18-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 center-mag=+1.545328108316\ 62200/-0.00573785680965751/7.048239e+008/1/-120/0 params=6/6 float=y maxiter=3600 inside=0 logmap=279 periodicity=10 colors=000Y9SX9SW8RV8QU8QT7TT7VT6YT6_S6bS5dS5gS4iR\ 4lR4nR3qR3sR3uT5sU7qW8pXAnYBm_Dk`EjaGhcHgdJeeKdfJc\ fIcfIceHcdHccGbbFbaFcaEe_IgWMiTQlQUoNYqKauHeuIivKm\ vLovNovOpvQpvRqvTqvUrvWrvXsvZsv_tv`tvYrrVqoTolQmiN\ leLkbIi_GfXHcVI`UIYTJVRKSQKPPLNOMKMMHLNEKOBIOFHPKG\ PPFVUL`ZQfcVlh`rmevpjnmaehTXcKOZBFV3ER8EOCDLGDLKCL\ PCKTBKXBK`DJYEJVFISGIPIHMJHJKGGLGDNFAOF7PE4QE2TI3V\ M4XP5_T6aW7c_8fb9hfAjiBmmCopDqtEswFtuEttEusDuqDupD\ voCvnCwlBwkBwjBxiAxgAyf9ye9yd9wcEvbIuaMs`Qr_UqZZpY\ bnWfmUjlRikQgjOeiMchKagI_fGYeEWdCUcDSgMQhOOiQMQLKz\ hMzeOvcQv`StZSqWRlURkRQjQOhPQ_ORRNTHCcJMUDPKKVLTT4\ R_MRggQecQd_PbWPaSP_OOZKOXGLXAOWDzWGTVJzVLZVOzURcU\ UzOBzUWzapzZoSoozXnt1jpFmmTpzfszclz`ezYZzWSzTLzQEz\ N7zL0zI5zFAzCFz9Kz6Pz3Uz0Yz7`zDbzKezQgzWizXWzYIzY4\ zVBzSHzQNzNTzK_zIezFkzDqzAnz8kz6hz4ez5_z5Uz5Oz5Iz5\ Cz56z50zMfzKbzIZzGVzERzCN } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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Fractint version 20.04 patch 9 is now available
by Jonathan Osuch 25 Oct '08

25 Oct '08

Folks, Fractint, Xfractint, and Winfract versions 20.04 patch 9 are now available on the developer's web sites: www.fractint.org and www.fractint.net What's new: Added new Fractal type DivideBrot5 by Jim Muth. This Fractal type has AP math support. Note that image skewing and inversion are not supported by the AP math routines. See Arbitrary Precision and Deep Zooming for other features not supported. Fixed several obscure bugs in the AP math. Added MakeFile changes from Michal Januszewski (xfractint maintainer in Gentoo Linux) to increase distribution compatibility. Jonathan

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FOTD 26-10-08 (A Non-Existent Bud [8])
by Jim Muth 25 Oct '08

25 Oct '08

FOTD -- October 26, 2008 (Rating 8) Fractal visionaries and enthusiasts: Pay careful attention to today's image. Even though you might think you see it on the screen, nothing actually exists. The whole thing exists only in the mind of the individual fractal viewer. Those who still believe today's image is real should change the inside from 'bof60' to 'numb'. And equally surprising is the fact that there is no parent fractal either, only another blank screen that consists totally of inside stuff. But there the image is on the screen, evasive, ephemeral, like a ghost in a ghost show. Actually, I have no idea what it is that I have captured in today's FOTD. It makes no sense at all. The main feature is a Mandelbrot bud with a main-spike appearance. But the expected large minibrot is little more than a vaporous mass of fractal ectoplasm, caught in the act of evaporating back to its natural state, whatever that may be. Yet the equally ephemeral features along the bottom of the image actually resemble distorted and shadowy East Valley elephants. And there are more buds scattered through the debris choking the lower side edges of the scene. I did a tiny bit of stretching in the horizontal direction to change the large bud from an oval to a more-natural circle. Except for the bit of tweaking I did on the colors, the rest of the image is untouched. I rated the image at an 8, which includes 1/2 point for my coloring effort. Then I named the image "A Non-Existent Bud", since that's exactly what it's a picture of. The calculation time of 2-1/3 minutes is reasonable, as is the minute or so required to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the finished image there. Rain fell in heavy squalls most all day Saturday here at Fractal Central in central Pennsylvania, but the temperature remained a relatively mild 61F 16C. The fractal cats didn't mind the rain, but they were were disappointed with the lack of sun. Due to the rain, I escaped an antiquing trip, which left me with an average day. The next FOTD will be posted in about 24 hours. Until then, take care, and be at large in the world of fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Non-Existent_Bud { ; time=0:02:23.57-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 passes=1 center-mag=-2.05685/0/9.739925/1.0323/-90/0 params=-1/10 float=y maxiter=1500 inside=bof60 logmap=yes periodicity=10 colors=000zqUwoVtlWqiXnfZmd_la`k_bkZcjXdjVfiTgiShh\ QjhOkgNlgLnfJohJofIpeIpdIpcIpbIpaIp`Ip_IpZIpYIpXIq\ WIqVIqUIqTIqSIqRIqQIqPIqOIqMIrLIrKIrJIrIIrHIrGIrFI\ rEIrDIrCIsBIsAIs9Is8Is7Is6Is5Ir4Ir4Jq3Iq3Iq3Hq3Hp3\ Ho3Gn3Gm3Fl3Fk3Fj3Ei3Eh3Eg3Df3De2Cd2Cc2Cb2Ba2B`2B_\ 2AZ2AY29X29W29V28U28T28S27R17Q16P16O16N15M15L15K14\ J14I13H13G13F12E12D12C24E36G38H4AJ4CK5EM6GO6IP7KR7\ LS8NU8PV9RXATZAV_BXaBYbCZdB_fC_eD_dD_cE_bEZbFZaFY`\ GY_GXZHWZHWYIVXJVWJUWKUVKTULTTLSSMSSMRRNRQNQPOQPPP\ OPPNQOMSOLTNLTNKVMJVMIUMHXKLXKKYJLYIMYHMYGMYFMYEBY\ FAYGAZH9ZI8_J7`K5_L7ZM9ZNAYOCYOEXPFXQHWRIWSKVSMVTN\ UUPUVQTVSTWUSXVSYXRZYRZ_Q_aQ`bPadPaeO`fO_fN_fNZfMZ\ fMYfLXfLXfKWfKWgJVgJVgIUgITgHTgHSgGSgGRgFRgFQhEPhE\ PhDOhDOhCNhCMhBMhBLhALiAKi9Ki9Ji8Ii8Ii7Hi7Hi6Gi6Gi\ 5Gl4Hp3Hs2Hv4Ju5Lu7Nu8Pu9RuBTuCVuDXuFZuG`uHbtJdtKf\ tLhtNjtOltPntRptqpPpoRpmS } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 24-10-08 (Pentaheptahexabrot [7])
by Jim Muth 24 Oct '08

24 Oct '08

FOTD -- October 25, 2008 (Rating 7) Fractal visionaries and enthusiasts: I named today's image "Pentaheptahexabrot". The outer pentagon surrounding the central minibrot encloses an area with 7-part symmetry, while the minibrot itself has 6-part symmetry. It's an unlikely combination I know, but there it is. Images on the screen do not lie. I could also have included the 2-part symmetry that exists far out beyond the edges of the frame and led me to the scene, but none of this symmetry shows in the image. The scene lies near a larger minibrot near a larger minibrot near a still larger minibrot in the chaos on the bud side of the northern branch of Seahorse Valley of the parent fractal, which on the surface resembles an oversized but otherwise perfect Mandelbrot set. I rated the image at a 7, mostly for mathematical interest. The calculation time of over 12 minutes is admittedly slow, but full relief may be found on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image has been or soon will be posted in GIF format for immediate gratification. Clouds moved in during mid-morning here at Fractal Central on Friday, while the temperature hovered around 54F 12C all day. The fractal cats meowed and resigned themselves early to a sun- less afternoon. My day was busy, but not as busy as recent days. The next FOTD will be most likely but never certainly be posted in 24 hours. Until then, take care, and if fractals are abstractions, how can it be that we have concrete pictures of them? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Pentaheptahexabrot { ; time=0:12:24.13-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 passes=1 center-mag=-75.63892599433935/+6.415672693923542/\ 7.228203e+010/1/174/0 params=7/100 float=y maxiter=6450 inside=255 logmap=1625 periodicity=10 mathtolerance=0.05/1 colors=0000_p8ZoBYnEXmHWkKVjOThRSfUQeXPcYKa_ObaRbb\ UcdXce_dgcdifejiellfmofkndjmbim`gl_fkYekWcjVbjTaiR\ _hQZhOZhMYgKYgKXgG_i1_f3_c4_`6_Y7_V8_SA_PB_MC_JE_G\ F_DG_AI_7J_4KZ8JZCJZGIZKIZOIZSHZWHY_HYcGYgGYkGYoFY\ sFatGYtFVtFSrFPqFLoEImEFkEDiACjCCjEBkGBkIBlKAlLAmN\ AmP9nR9nT8oU8oW8pY7p_7qa7qb7qb7qc2sd7qfBphFojJneKm\ cLmaMm_KmYJmWFmVClU8mW4nY0oY1pZ1q_2r`2sa2ta9k`Gb_N\ U_ULZU6e_DZeKSkRLpXFoTIoPLoLOnHRnDUnAXDIzIHsNGmSFg\ XE`aDVmHCiFJeDPWEUZDVaCVdBVgAVj9Vm8Vv5Up8VjBWdEWZH\ XTKYNNYHQZAEQBLVBSZBYbCdfCkjFnpDpoCqnAsm9tm8ol6pk5\ lj4lj6gl8bn9_p9Xo9Wo9Wo9Vo9Uo9Uo9To0Ry9TyHMfQFXY8O\ _OUKXe`b_wfLtgQqhVni_ljdikiflncmsakwfisjdPz`8lXAka\ BjQDiNEgKGfGHeDJZ4GdAKiFOoLStQVwaLzsAymCxhDxbEwYFv\ THvNIuIJsAMtCLuDKuEKvFJvGJnGQgGW`Ga0IrFHlUGgl7RnPZ\ gGbm3gf6f`8eVBdPDcJGU7NKAKADI0FF0ID0KA0N80U20P60LA\ 0GE0CI04L06M08M09M0BM0zzz } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 24-10-08 (Dynamic Structures [7])
by Jim Muth 23 Oct '08

23 Oct '08

FOTD -- October 24, 2008 (Rating 7) Fractal visionaries and enthusiasts: Due to a huge rush, today's image is an ultra-quickie, a Z^8 minibrot with East Valley Z^2 characteristics. I named it "Dynamic Structures", which is a fair description of all fractals. The rating of a 7 seems about right. There are two ways to see the image -- run the included parameter file and wait a minute or so, or see it in finished form on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Absolutely perfect autumn conditions prevailed here at Fractal Central on Thursday -- total sun and a temperature of 54F 12C. The fractal cats enjoyed the afternoon sun to the fullest. In keeping with the season, my day was spookily busy, and tomorrow, when the next FOTD is scheduled, could well be a repeat. Until then, take care, and don't get left out of the fractal parade. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Dynamic_Structures { ; time=0:01:26.50-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 center-mag=+13.81891327868127/-0.3498656617738474/\ 1.017278e+008/1/-22.5/0 params=9/50 float=y maxiter=1500 inside=0 logmap=200 periodicity=10 colors=000RHPSGPTFPUEOUDOVCNWBNWAMX9MY8LY7KZ6K_5J_\ 4J_3I_4IZ7HY8HX9HWAHVBGUCGTDGSEGRGGOHFLJFIKFFLFEMF\ HNEKODNQDQTCTWCWZBZbBaeAdiAgl9in9jkBkhDlcEmZGnUHoP\ JoMHqJXsGcuDmqArmCwjDvfFucGt_HsXIsTKrPLqMMpIOoFPnB\ Qm8Rm6Vn5Zo4bpA_jGYdMVZSTTYQNcOHiLBoJ5mM9kODiQHgTL\ eVPcXTa_X_a`YcdWfhUhlSjpUkmVljXmgYndZoa`pZaqWcrUds\ RetOguLhvIjwFkxClxAkwBkwCkwDkwEkwFkvGkvHkvHjvIjvJj\ uKjuLjuMjuNjuOjuOipLikJhgHhbFgZDgUBfQ9fL7eH5eC3e81\ gG7iOCkVHlXKlYMlZPl_Rl`TlbWlcYld_leblfdlgfd`jXVmPO\ qHItACwCDvDDuFDtGDsHErJErKEqLEpNFoOFnQFnRFmSGlUGkV\ GjWGjXEdYC_ZAV_8P`6Ka5FW9HQCIKFJEJK8ML2PM8ONEONKOO\ QOOWOPaOPgOPhQOiSNiTMjVLkWKkYJlZIl`HmbGncFneEofDph\ CpiBqkAqlA`m8Ln7RoGXpPaqYgramsdstgyujsvinwiixidyia\ zi_zibziezihzikzinziqzitzhwzhzzgzzgzzfzzfzzezzezzd\ zzdzzczzczzbzzbzzbzz_zzXzzUzzRzzOzzLzzJzzPzzVzzWzz\ XzzYzzZzz_zz`zzazzbzzczzd } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 23-10-08 (All Roads Lead to Here [No Rating])
by Jim Muth 22 Oct '08

22 Oct '08

FOTD -- October 23, 2008 (No Rating) Fractal visionaries and enthusiasts: Due to the continuing rush here at Fractal central, today's image is another quickie that fails to merit a rating. But I did give it a name. When I saw all the complex filaments converging on the order-13 minibrot at the center, I named it "All Roads Lead to Here". Even with no rating, the image is worth a quick glance. That glance may be enjoyed by running the included parameter file and waiting a brief 1-1/2 minutes, or by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and glancing at it posted there in already-calculated form. Cloudy skies and blustery winds spoiled Wednesday here at Fractal Central. Being stuck in front of the LED screen all day, I was not bothered by the temperature of 43F 6C. But the fractal cats complained when they missed their afternoon sun. The next FOTD image will be posted in 24 hours. Whether it is accompanied by a discussion depends on how well the load of work goes. Until then, take care, and in yesterday's FOTD I ex- pressed some doubt that 3.5 billion years of geologic time could by pure chance accomplish the miracle of creating life and eventually intelligent human beings. Lee S. replied: By pure chance? No way! But with natural selection accompanying and assisting those chance mutations, yes, I believe so. This begs the question: if natural selection assisted the favorable mutations, (perfectly logical), what then other than pure chance guided the mutation process to produce mutations that were favorable? (No, I don't necessarily endorse the 'In- telligent Design' [God did it.] theory, but with a near-infinity of mutations possible, and with such a miniscule number of them favorable, it seems to me that it would take closer to a google years for intelligent life such as man to evolve by chance.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= AllRoadsLeadToHere { ; time=0:01:35.88-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 maxiter=14500 inside=0 center-mag=-0.6406320652144715/+3.903884528896754/\ 7.155811e+012/1/-70/ params=13/6 float=y logmap=216 periodicity=10 mathtolerance=0.05/1 colors=000kiWkhZlg`lfbmeemdgncinblo`noZpoWrmUpkSnj\ QlhOkgMieJgdGfaHc_H`YHYWHVUHSSHPPHMNHJLHGJHDHHAFH7\ DH4HJ9LLDPNHTPLWRP_TTcVXgX`jYdWeiHlnImkIniIngIoeIp\ bIp`IqZJrXJrVJsSJtQJtOJuMJuKKuJLuJLuIMuIMuIOvMQvPS\ wSUwWWxZYxaZxdXvbWtaUs_TqZRoXQnWOlUNkTLiRKgQIfOHdN\ GcMHbPIaSJ`UK`XL_ZMZaNZdOYfPXiQXkLamHeoDiq8ms4qu0u\ v1qt2ms3jq4fp5cn5_m6Wl7Tj8Pi9MgAIfAFeCVLDj0Fg3Gd5H\ a8IZAJWDKUFLRIMOKNLNOIPPGSQDURAXS7ZT4aU2cY4aa5_e7Y\ i8WmAUqBStCQmJNfPL`VIUaGNgDHmBHlAHl9Hk9Hk8Hl8Hm7Hn\ 7Ho6zp6zq5zr5Hs4zt4zu7zv9zwCzxEzyHzzJC0MB0OA0QA0T9\ 0VzzYzz_zzbzzd60fC0iI0kN0mT0oZ0rc0tizvnzx`zqNzj9zc\ 8zc8zc8zc7zc7zc7zcBzbEzbHzaLzaOz`Rz`Vz_Yz_`zZdzZgz\ YjzYnzXqzXtzXqzWozWlzVjzVgzUezUczU`zTZzTWzSUzSSzSS\ zRSzQSzPSzOSzNSzMVzMXzMZzM`zMbzMdzMfzMhzMjzMlzMhzP\ ezSazUZzXVz_SzaOzdLzfMzcNz`NzZOzWPzTPzRQzORzLRzJPz\ KOzLNzMLzNKzNJzOizPjzSzzU } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 22-10-08 (Globular Clusters [No Rating])
by Jim Muth 21 Oct '08

21 Oct '08

FOTD -- October 22, 2008 (No Rating) Fractal visionaries and enthusiasts: Another hyper-busy day here at F.C. means another abbreviated discussion. Suffice it to say that today's image lies in an evaporated fractal. What is seen on the screen is nothing but empty 'inside' stuff made visible by the 'bof60' inside fill. (The image is actually a zoom into yesterday's image.) Today's image reminds me of a deep-sky photograph, perhaps taken by the now broken-down Hubble Space Telescope. The object at the center so closely resembles a globular cluster surrounded by smaller clusters that I named the image "Globular Clusters". I could not rate the image, which I found almost automatically. But I feel that running the 10-minute parameter file will result at least in fractal satisfaction, even if it does not rescue the economy. To enjoy the image without trying to rescue the economy, view it in finished form on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A mostly cloudy, blustery autumn day prevailed here at Fractal Central on Tuesday, with occasional showers of falling and drifting leaves keeping the fractal cats occupied. The tempera- ture of 55F 13C was not too chilly, but in the wind it was unpleasant. My day was very busy, with a repeat expected tomorrow. The next FOTD will be posted in 24 hours. The only question is whether a discussion will accompany it. Until then, take care, and 3.5 billion years of geologic time can accomplish the miracle of creating life and eventually intelligent human beings by pure chance. . . or can it? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Globular_Clusters { ; time=0:10:14.56-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 passes=1 center-mag=+2.274695262209428/-0.3912954702661584/\ 1e+012/1/90/0 params=-0.75/-12 float=y maxiter=1500 inside=bof60 logmap=yes periodicity=10 colors=000zzzqwzhsuantXjpXfo`cmdaldZkaViWRhSKgLEfE\ 9e84c00_00W00U00S00S00O00M00K00A000000000000000000\ 0000000000000000000000000000000000000aa0_Z0YX0XV0V\ T0TR0SO0QM0OK0NI0LG1JD1IB2G93E73D51G90JD0MG0PK0SN0\ VR0YU0`Y0c`0fd0ig0he0hc0ha2h_5hY8gWBgUEgSIgQLgOOfM\ RfKUfIXfG_fEbfC_8RY6OW4LU3IS1GQ0DO0AN08L05J02H00F0\ 0D00C00E00F05G0BH0HJ0OK0UL0_M0e0B01D02F04H05J06K08\ M19O3BQ5CR8DTAFVCGXEHYGJXKKWNLVRMUUNUXPSYQQZRO_SM`\ TKaUIaVGbWEcXCdYAeZ9e0DD2HB5KA9N8CR7FU5JX4M`2Qc1Tf\ 0Wi0Vh0Vg0Uf1Ue2Ue2Td3Tc4Tb5Sa6Sa6S`7R_8RZ9RZ9MTFH\ OLDJR8DX38b03h05i07i08i0Ai0Ci0Di0Fj0Hj0Ij0Kj0Mj0Nj\ 0Mg0Md0Ma0MZ0MWLM60MU0MR3MO6ML9MIBMGEMDHMAKM7NM4_M\ BZMAYM9XM8WM7VM6UM6TM5gp4RM3QM20FF1GE3GD5HC7HB9IAB\ I9CJ8EJ7GK6IK5KL4ML3OM2N0UO2SO4QO5OO7MO8KOAIOBGPDE\ PFCPGAPI8PJ6grpR02Q02ZnoQ02Q02Q32P62P92PD2PG2Xenpu\ vD0aE0ZF1WG3TH5QI7OZnoKBI } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 21-10-08 (A Negative Attitude [No Rating])
by Jim Muth 21 Oct '08

21 Oct '08

FOTD -- October 21, 2008 (No Rating) Fractal visionaries and enthusiasts: Today's fractal is not too bad, but I have no time to write a discussion. So enjoy the image by running the included parameter file or viewing it live on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather was chilly but pleasant on Monday. The fractal cats were happy. If all goes well, the next FOTD, complete with discussion, will be posted in 24 hours. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_NegativeAttitude { ; time=0:04:09.50-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 periodicity=10 center-mag=2.28375/-0.398497/17.41524/1/90/0 params=-0.75/-12 float=y maxiter=1500 inside=bof60 colors=000DA5A83652O6UN5WN5XM4ZM3`L3aL2cK1eK1fM4gN\ 6hP8iQBjSDkTFlVImWKnYMoZOo_RpaTqbVrdYse_tgauhdvjfw\ khxljxhgtedpbal_ZhXWdUTaRQYONULKQIHMFEJCBF01198B65\ 7323H`TDTNAMH6EB375wz8ns6ah5YZ4FS3AM2581egO`bLXZJT\ UGPQELMCLH9CD7884442543432432432332322321221221211\ 211111110100000000000000000000IAC9560004gH3`E2TB2M\ 81E5072Aiz9fw9dt8bq8`n7Zk7Xh6Ve6Tc5R`5PY5NV4KS4IP3\ GM3EK2CH2AE18B1680450229Sf8Pb7N_6LX6JT5HQ4FN4CJ3AG\ 28D269146023nFWjDTfCRcBP_AMW9KT8IP7GL6DI5BE49A3672\ 4312rT5oR4mQ4jP4hN4fM3cL3aK3ZI3XH3VG2SF2QD2NC2LB1J\ A1G81E71B61950730420200000000000000000I2kH2hG2fF2c\ E1aD1ZC1XB1UA1R91P81M71K60H50F40C30A2071050029QuQu\ 0Or0No0Mm0Lj0Kg0Ie0Hb0G_0FY0EV0DT0BQ0AN09L08I07F05\ D04A0370250120kUFeQD_MBUI9OF7IB5C73631M4OK3MJ3LI3J\ G3IF2GE2FC2EB2CA1B919718617505304202101rfLncJk`IgY\ HdWF`TEYQDUOBRLAOI9KG7HD6 } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 19-10-08 (Nine-in-One [No Rating])
by Jim Muth 19 Oct '08

19 Oct '08

FOTD -- October 19, 2008 (No Rating) Fractal visionaries and enthusiasts: Today's image is posted late and without comment. It may be seen by running the included parameter file or by viewing it on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Nine-in-One { ; time=0:12:57.04-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 center-mag=+2.622068463886969/-0.0218057613201577/\ 3497525/1/-27.5/0 params=9/10 float=y maxiter=10000 inside=0 logmap=996 periodicity=10 colors=000aUkdUcgUWjUOmUGpU9rUFsUKtUQvUVwU`xUewUdw\ UdvTcvPcuLcuHbtDbt9bqEanI`lM`iQ_fV_dZZabZZfYXjYVkW\ UkVTkTRlSQlQPlPNlNMmMLmKJmJImHHnGFnEEnDDnCBkJ9hP8e\ V6ba5_g3Xm2Us5Tq8TpBToETnHTmJTlMTjPTiSThVTgYTf_Tea\ SfbRfcQfePgfOggOgiNhjMhkLhmKinJioJimKhlLfkNeiOchQa\ fR`eSZdUXbVWaXU`YTZ_RY`PWaOVcMUdKSeJSeHTdIUcGVbFWa\ EX`K_aPbbUdcZgedjfimgnohslfridrgbqd`qbZq_XpYVpVTpT\ RoQPoNNoLLnIJnGHnDFmBDm8Bm69l37l15l27j38i49h5Ag6Bf\ 7De8Ed9FcAGbBHaCJ`DK_ELZFMYGNXHPWIQVJRUKSTLTSGOYMU\ RS_KXdDZbG``Jb_LdYOfWRhVTjTWkSYmQ`oOcqNesLhuJkwImy\ GpzFrvJkrNeoRZkVThZMdbGbdCaeAdB9eM8fW7ge7ho6zz6vw8\ rv9mtAhsBeqCdpDcnEbmFblGajI`iJ_gKZfLZdMYcNXaOW`PW_\ QZVJaRDdM7gI1dJ4cJ6bJ8aJA`JCZKEYKGYKI`LLcMNhNPmORm\ PTmQVmRXmSZmTXmUVmWTmYRr_OvaNzcNzcMzcMzcLzcLzhKzmK\ zrJzvJzzIzzIzzIzzHzzGzzGzzxzz5zz9zzDzzHzzKzzOzzSzz\ VzzZzzbzzfzzizzmzzszzszzs } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 18-10-08 (Deep Seahorse Scene [No Rating])
by Jim Muth 17 Oct '08

17 Oct '08

FOTD -- October 18, 2008 (No Rating) Fractal visionaries and enthusiasts: A fiery fractal with the speed of light, a cloud of iterations and a hearty "Hi-Yo Fractint". From out of the past come the thundering convolutions of the great fractal Mandelbrot. The Lone Mandelbrot rides again. Return with us now to those thril- ling days of yesteryear . . . Well, I had to say something to stir up a little excitement. Today's image is indeed a flashback to the past, even if only an under-iteratered scene deep in Seahorse Valley of the all-too- familiar Mandelbrot set. And this is why I named it "Deep Sea- horse Scene". I gave it no rating because these kinds of images were one of the first things I was producing in those ancient days when I was a young tyro fractalist. (Now I'm an old tyro fractalist.) The one thing that keeps the image from being totally hackneyed is its magnitude of 2.4x(10^14), which lies just beyond the range of conventional math. The resulting calculation time of almost 48 minutes begs impatience, but a quick though blurred preview of the scene may be viewed in 7 seconds (less than 1/300 the ap time) by switching to conventional math with the command mathtolerance=0.05/1 But all this math-switching and resulting impatience may be avoided by viewing the finished image posted in full arbitrary- precision definition on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Morning clouds gave way to afternoon sun on Friday here at Fractal Central, while the temperature dropped to a far more seasonable high of 59F 15C. The fractal cats enjoyed the afternoon sun that they missed yesterday. My day was average. Most likely but not certainly, the next FOTD will appear in 24 hours. Until then, take care and have fun at the same time. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= DeepSeahorseScene { ; time=0:47:56.28-SF5 on P4-2000 reset=2004 type=mandel passes=1 periodicity=10 center-mag=-0.7485177858185152687/0.05757462599937\ 39027/2.4e+014/1/25/0 params=0/0 float=y bailout=9 maxiter=8000 inside=0 logmap=1725 mathtolerance=/0 colors=000USFUSEUTCUUBUUAUV9UUBUUDUUFUUHUUIUTKUTMW\ TOYTP_TRaTTdSVfSWhSYjS_lSanSbmP_lNXkKVjISiFQhDNgBL\ hCKhDJhEIiFHiGHiHGjIFjJEjKDkLDkMCkNBlOAlP9lQ9mR8mS\ 7mT6mT6kR5jQ5hO5gN5fM5dK5cJ5aH5`G5_F5YD5XC5WB5XC6X\ D7XD8YE8YF9YFAZGBZHBZHC_ID_ID_JE_KF`KG`LG`MHaMIaNI\ aNJbOKbPLbPLbQMcRNcRNcSOdTPdTQdUQeUReVSeWSfWTfXUfY\ VfYVgZWgZXg_Xh`Yh`Zha_ib_ib`icaicahd`hd`hd_ge_geZg\ eZfeZffYffYefXefXegXdgWdgWdgVchVchUchUbhUbiTbiTaiS\ aiSajS`jR`jRakQbkQckQdkPelPflOglOhlNimNkmNmmMmmMmn\ LjnLgnLdnKaoKZoJWoJVoJXpKYpL_qM`qNbrOcrPdrQYqXSpcL\ ojFnq9mz8hz7ez6bz6Zz5Ur4Qm3Mh3Jc6KZ9TKCWLFZLI`MLZM\ NWMMVLMSLMOKMMKMKKMJJMJhMIhMHhMGhMFIMEHMEHLDHLCGLB\ GLAGL9FL8FL8Fw7ELcUw5ELcUw3DLcUN8COCCPHBRKCSKETKGV\ KIWKKXKMZKO_KQ`KUaKZbKccKccKcdKfeKieKlfKogKrhKuhJw\ iFxkCym9zmAzmDzmHzmLzmPzmUzmZzmZzmZzmZzmZzmZzmZzmZ\ zmZzmZzmZzmZzmZzmZzmZzmZz } END PARAMETER FILE=========================================

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FOTD 17-10-08 (Absolute Complexity [8.5])
by Jim Muth 16 Oct '08

16 Oct '08

FOTD -- October 17, 2008 (Rating 8.5) Fractal visionaries and enthusiasts: Today's image brings a much-anticipated improvement in FOTD quality. In fact, it actually earns a rating -- one of 8.5. The parent fractal is a mandeloid whose negative stem has collapsed into an area of fractured chaos, forming a kind of west valley. But today's scene is not located in this valley. It is found on the northeast shore of the main bay, near a larger minibrot in a cut-off section of a kind of elephant trunk. The cut-off nature of the general area is reflected throughout the image. The name "Absolute Complexity" means little, since nothing can be so complex that it could not possibly be more complex. (Except maybe fractals, which are infinitely complex.) The calculation time of 4-1/5 minutes means that some patience must be shown in the rendering process. Or the image may be seen almost instantly by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing it there. A partly cloudy morning with a temperature of 75F 24C here at Fractal Central on Thursday gave way to a cloudy afternoon with falling temperatures, which had dropped to 64F 18C at FOTD post time, which was 1800 hrs. The fractal cats were disappointed when the afternoon sun failed to appear in their favorite south- west facing window. My day was acceptable. The next FOTD will be posted in 24 hours. Until then, take care, and how can numbers possibly create a whole infinite world? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= AbsoluteComplexity { ; time=0:04:12.28-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 passes=1 maxiter=2750 center-mag=+1.270555855677304/+0.5674181658563614/\ 3.9665e+011/1/-137/0 params=1.2/2 float=y inside=0 logmap=428 periodicity=10 mathtolerance=0.05/1 colors=000UYAW_AYaAZc9`e8ag7cf6dh5fi4gi4ii3jj3lk2m\ m2ol8pkEqjKrkQslWtmaungvomodchVVaLM`KN`JO`JP_IQ_IR\ _HSZHTZGUYFVWFWVEXTEYQDZTD_VC`XCaYGcZJd_Mf`PgaSibV\ jcYkeameenhirmmwrrzvvzzxzzyzzzzTPHRQGQSFOUEMWCL_BJ\ cAHg9Ge8Ed7Dc6BeKAfX8hj7iwHdoR`g_X`iTTrPMmNLiLKeJJ\ aHJYGIUEHPCHLAGH9FD7F95E53D12D34E46F58G79G8BH9DIBE\ ICGJDIKFJKGLLHNMIOMKMJLKHNIEOGCPEAQFDQFGRFIRFLSGNS\ GQTGSTGVUHYUH_VHbVHdWIgWIiXIlXInZIk_IhaIebIbdI`eIY\ gIVhISjIPkINmIKnIHpIEqICoKFnLHmMJgITaEbWAlQ6uhQazi\ IxkHvlGtmFsoEqpDoqCmsBzzAzz9hw8fx7ey6cuEbqM`nU_j`Y\ ghXcpW`wcSsjKprCmy4jwhToUQoPOnKMnFKjEHfDEcCCSQ6Hbz\ KczNczPc4Sc5Uc5Xd6_d7ad8dd9fd9feAffAfgBfhCfiCgjDgk\ EglFgmFgnGgoKgoPipUjqZlrcmshnsmptrquvrvztwzuwzvxzx\ yzxxzyzz2zzLzzUzzazzjzzrzzTzzizzHzzLzzOzzRzzVzzYzz\ `zzczzgzzjzzmzzqzztzzwzzezzhzzjzzlzzozzqzzszzvzzxz\ zLzzQzzUzzYzzazzezzjzznzz } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 16-10-08 (Etheric Mandeloid [No Rating])
by Jim Muth 15 Oct '08

15 Oct '08

FOTD -- October 16, 2008 (No Rating) Fractal visionaries and enthusiasts: We successfully weathered another panicky day here at F.C. on Wednesday, with quite a few more to come I am sure. Today's fractal diversion reminds me of a fractal caught in the act of manifesting. I named it "Etheric Mandeloid", but gave it no rating. The parameter file is slower than the recent images, taking 8-2/3 minutes to finish on the fastest machine. Time may be saved however by viewing the completed image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Wednesday was a near perfect day here at Fractal Central, just a couple degrees cooler than Tuesday. The fractal cats made the most of things. My day was frustrating and tomorrow may be the same. The next FOTD has a 67-percent chance of being posted in 24 hours. Until next time, take care, and be prepared for the sudden appearance of unseen things such as fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Etheric_Mandeloid { ; time=0:08:41.41-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 passes=1 float=y center-mag=-2.30147/0/4.149901/0.8516/90/0 params=3/3 maxiter=1500 inside=atan periodicity=0 colors=000ParOcrNfsOfpnZLkXNhVPeTRbRT_PVVM_PJdWT_c\ cVknQsyKsyKsyKsyKsyJsyJsyJsyJsxIsxIsxIsxIsxHsxHsxH\ sxHtwGqwInwKjwNgwPdwR`wUYwWUxZRx`OxbKxeHxgExiAxl7x\ n3yq7wnBtjFrgJocNm`RjXVgTZeQbbMf`JjYFnWCrT8wQ4vR6t\ S8rTApUDnVFlWHjXKhYMfZOd_Rb`T`aVZcYWdUSfQOhMLiIHkE\ DmA9o69jA9dF9_J9UOAPSAJXAE`A8eB2jE5gH9dLDaOHZSKWVO\ TZSQaWNd_KhbHkfEojBrn8vr4qkBldIgXQbQXYJcSBkTFiVJfX\ NcZRa`VZbZWdbTqOTqPTqQUqRVqSVqUWqVXqWXrXYrYZr_Zr`_\ ra`rb`rcasebpeclddhcfebgaaiY`jV_kR_mNZnKYpGXqCWr9V\ t5Uu1Tw6RpCOiHMbNJWSGPYEIbBBh84g95eA6dB8bC9aDA_ECZ\ FDXGFWHGUIHTJJRKKQLLOMNNNOLOQJGdH7sH9pHCmHEiHHfHJb\ HM_HOWHRTHTQHWMHYJH`FHbCIe8If8Ig8Ii8Ij9Jk9Jm9JnAJp\ AKqAKrBKtBKuBLwCLtDLqELnFKjGKgIKdJJ`KJYLJVNIROIOPI\ LQHHSFNWDU_B`c9fg7mk5tpBi`IYLPM5SN5VP5YR6aT6dV7gW7\ kY7n_8qa8HHGIHJJHMKHPLHSMHVNGYOG`PGcQFfRFiSFlSEnSG\ oSIpSLpSNqSPqRRqQSqQTrPUr } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 15-10-08 (Tangerine Tempest [No Rating])
by Jim Muth 14 Oct '08

14 Oct '08

FOTD -- October 15, 2008 (No Rating) Fractal visionaries and enthusiasts: Things are a little calmer here at FC, but nowhere near what I would call serene. At least, fractals never get panicky! I have picked up the latest developer's version of Fractint, which has the DivideBrot5 formula hard-coded into it, and allows the use of arbitrary-precision math with the formula. I will not use the new version for the FOTD's for a while however, to give those on the list a chance to first pick up the new version. Today's image was created with the old DivideBrot5a formula. But it could just as easily have been made with the new type=dividebrot5. I named it "Tangerine Tempest" just for the fun of it. I gave it no rating because I don't think it's worth one. The 2-1/2 minute calculation time will pass like lightning for true fractal fanatics. The others will need to wait 152 seconds or view the already-calculated image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tuesday began with dense fog here at Fractal Central, but by 10:30am the fog gave way to hot sun and a midsummer-like temperature of 81F 27C. The fractal cats had quite a thrill when one of the neighborhood stray cats caught a careless squirrel in the back yard. Except for disposing of the half- eaten squirrel, my day was routine. The next FOTD will be ready for posting in 24 hours. Until then, take care, and look for the light. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Tangerine_Tempest { ; time=0:02:32.33-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5a passes=1 center-mag=-1.350574724350784/+0.5645188431144991/\ 1.892014e+009/1/20/0 params=3/2/0/0 float=y maxiter=1600 inside=0 logmap=208 periodicity=10 colors=000zlczi`zeYzaVzYSzUPzRMvOJrLGmIDhFAcD8ZB7U\ B9PCBPCDOCFODHNDJNELMEMMENLFOLFPKGQKGSJHUJHWIHYII_\ HIaHJcGJeGJgCTb9bZ6l`FfaNabWWdcRelLgtGhqIenKclM`iO\ ZgQWdSUbTR_VPYXMVZKS`IQbFNdDLeAIg8Gi5Dk3Bm08o06p09\ m0Ck1Ei3Hg6Kd8MbAP`DRZFUWHXUKZSMaQOcOQaMS_KUYJWXHX\ VGXTEYSDZQB_O9aM8bL6dJ5fH3eG2dJ4bJ6`I8ZKAXMCVOETQG\ SSIQUKOWMMZOKaQJdSJgUJjWJlYIn_HpaFrcEtdEocGjcIecK`\ cLWbNRbPMbRuIffz3bw7_tAXqDUnGQkJNhMKePdD0_J4VOAQTG\ LYM6uS8rSAoSBlSDjSEgSGdSuKqoNmjPjeSg`UdWW`RZYM`VXc\ VUbURbUPbTMbTJbS1t05p18l8BiFEeMp`rjamdaiZadTb`ehMa\ iPYkRUmTQnWMpYJq_LjaNcbPXdQReSKgUDhW6jX0kY2hZ3e_5b\ `6_a7Xb9UbAScCPdDMeEJfGGgHDgIBiJ9kJ8mJ6oJ5pJ3rK2tK\ 0vK0xK0yK0xN0xP2xS5wU7wXAwZDv`GvcIveLuhOujRulTtiUt\ fVscWscXscYrcZrc_qc`qcaqcbpccpcdpcencbmc_lmXkmUimR\ hmOgmLfmIemFcmCbz9az6`z3_z1az3bz5dz7ez9gzBhzDjzFkz\ HizIgzIfzJdzJpzOnzMlzKjzI } frm:DivideBrot5a { ; Jim Muth z=0, c=pixel, a=real(p1)-2, d=real(p2)+16 b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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FOTD 14-10-08 (Depressed Minibrot [No Rating])
by Jim Muth 13 Oct '08

13 Oct '08

FOTD -- October 14, 2008 (No Rating) Fractal visionaries and enthusiasts: The minibrot of order 1-1/3 at the center of today's image gives me a feeling of gloom. Just look at the dark somber colors filling the screen. No wonder I named it "Depressed Minibrot". The shape of the minibrot pretty much mirrors the shape of its parent fractal, whose main spike it lies on. Putting almost no effort into the image, I could hardly give it a rating. Then again, maybe it is better than I think. Some- times I come up with these images intuitively, almost without effort, and therefore consider them worthless. The calculation time of 29 seconds is faster than light, which means that the calculation will be finished 34 seconds before it is begun. I make no comment on what will happen if, 34 seconds after seeing the finished image appear on your screen, you decide not to run the parameter file after all. All such paradoxes may be avoided by viewing the completed image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Lots of clouds marred the sky over Fractal Central on Monday, but the temperature of 68F 20C kept things quite pleasant. At least the fractal cats thought so as they checked the back yard to be sure no unwanted stray cats were in the vicinity. My day was another hectic one. I guess we'll just have to wait to see what tomorrow brings. The next FOTD will most likely be posted in about 24 hours. Until then, take care, and don't be a gloomster. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Depressed_Minibrot { ; time=0:00:29.64-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident inside=0 center-mag=-6.680899592359807/-4.08385816487839/\ 5364601/1/-31.25/0 params=1.3333333333333/0/14/0 float=y maxiter=32767 logmap=40 periodicity=10 colors=000iMqSM`SKYQIVPHTOGQNEOMDMKCJJBHI9FH8CG7AF\ 68F8BFAEFCGFEJFGMFIOFKRFMUFOZFQcFShFUmFWrF_vFczBZm\ 8Oc7GU68K51ABAAHJFNSKT`OVYPWWPXTQYRQZOR_MR`KRbHScF\ SdCTeATf7Ug5Uh3UdG_`SdXdjTpoVqmWqkXriYrg_se`scatab\ t`duZeuXfvVgvTiwRjwPkxNlxMitLfqKcnJ`jIYgHWdHahPfkW\ lncqqjrngrkerhbrf`rcYr`WsZTsWRsTOsRMsOJsLHsJFlNEmR\ EmUEmYEm`EmdEmgEmfDmeCmeBmdAmd9mc8mc7Db7Eb6Ea5Fa4G\ `3G`2H_1H_1JZ3LZ5UZ6cZ8mZ9mZBmZCmYEmYGmYHcYJ`YKbYM\ cYNdXOeWPfXQgYRhZSi_Tj`UkaVlbWmcXndYoeZpf_qgfrhmsi\ tvjtyktxlqwmovoluqjushtueswcrz`rzZqzXzzUzzSzzQzzKz\ zFzz9zz4zzGzzRzzazzlzzgzzczz_zzWzzS5zN5zJ5zF4zB4z7\ 4z39z4Ez4Iz4Nz4Rz4Wz4_z4dz4hz4mz4qz4rz9szEtzJtzOuz\ SvzXvzawzfxzkxzorzjmzehz`bzWYzRTzMOzIMzJLzKJzLIzMG\ zMFzNEzOCzPBzQ9zQ8zR6zS5zT4zTQzWjzYbz_VzaOzbNzdMze\ MzgLzhLziKzkKzlJznJzoIzpIzrHzsHztKzrMzpOzoRzmTzkVz\ jXzkZzl_zmazmczndzofzpgzp } 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 13-10-08 (Diversion [No Rating])
by Jim Muth 12 Oct '08

12 Oct '08

FOTD -- October 13, 2008 (No Rating) Fractal visionaries and enthusiasts: Today's image is a little something I whipped up in a couple minutes. Its streaks and patches of intense colors bring it to FOTD status. I named it "Diversion" because that's basically all it is. I could give the image no rating because I put almost no effort into it. The calculation time of 2-1/2 minutes is thankfully brief. Equally brief is the time required to view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Perfect weather made Sunday quite enjoyable here at Fractal Central. Total sun and a temperature of 66F 19C seemed near perfect for mid-autumn in central Pennsylvania. At least the fractal cats thought so. Unless panic intervenes, the next FOTD will be posted in 24 hours. Until then, take care, and if you must be haunted, be sure it's by a fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Diversion { ; time=0:02:31.21-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+2.9712483712/+0.2932775867/36889/1/\ 160/0 params=-4.5/-1.4/-0.8/-8/0/0/0/0 float=y maxiter=1500 inside=0 logmap=130 periodicity=10 colors=000PhoPip2BH5CK8CNACQDCTFCWICYLC`NCcQCfSCiV\ ClXCnWGiVKdUO`URWTVRSZNRbIReEUgGWiHYjI_lKamLcoMfqO\ hrPjtQluSnwTpxUriNsWGuH9v33uC8tKDsTIr`NqiSpqXoy`nu\ YnqWnmUniSneQnaOnYMnUKnQInMGnIEnECnAAn68n26o78pB9p\ FAqJBrODrSEsWFt_GtcHkXEbRCUK9LE7C74412q9TpFYpLaoRf\ oXjnbonhskkmhmhepbbrY_uSXwNUyIZgWcQih9vaMtWYsPiqJu\ pJiiJZcZMQmADjHKhORfVXhRVjOUlKSnHRpDPrAOcJHQSAC`4K\ Z6RX8YW9eUBlTCsREzQF9zBGtGNoLUiP`dUgZZnUbP4TPCbOAe\ O9hN7kN6mM4pM3sL1vL0xKAwJKwIUvHcvGmuFwuLtqQrnVpj_n\ gdldeX_fHVf2Lg2RY8QODPEIO5NN9ORCOUGOYJP`NPdQPgPKrT\ PjWUbZZVacNdhFdv2gl8jbEmTJpJPs9UpSZnjcfYdbZe_ZfX_g\ U_gR`hO`iLajDfsIajMYbRTVVPNZLFXNKWPPVRUUTYTVbSXgRZ\ lQ_pMbnJdlFfkCii8kh5mf0uh2oe3ib4d_6ZX7UU8OR9JOIrxH\ lrHgmGahGXcFRZGDOFMUEVZDbcCkhCsm7QNDXYJbhOhrXbseXt\ nRuvMvKHXPS_QZjUabYcW`fOdhHhk9rs0km2dg4Za6IghJaeJW\ bKYdLZeL`gMahMbiNdkOelOgn } 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 12-10-08 (Red Line Railroad [No Rating])
by Jim Muth 12 Oct '08

12 Oct '08

FOTD -- October 12, 2008 (No Rating) Fractal visionaries and enthusiasts: Today's fractal is not only late, it is lucky to be here at all. On Saturday, FL and I spent the day wandering aimlessly around the Gettysburg Military Park, and we didn't get back to FC until almost midnight. We saw no ghosts there, but I have no doubt that ghosts, whatever they are, actually exist in the area. I also sometimes wonder about my own credulity, since I believe in the reality of ghosts, (as well as fractals), while at the same time, I am the first to laugh at claims of UFO's carrying alien visitors from space. It's the day Columbus discovered America, and to celebrate the occasion we have a Fractal of the Day. To see the image, run the included parameter file and wait 14 seconds, or go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and see the finished product there. I named the image "Red Line Railroad" because it is filled with reds and also has the rail yard effect. Saturday was absolutely perfect in Gettysburg -- not a cloud in the sky and a temperature of 73F 23C. The fractal cats told me it was pretty much the same here at FC. If I feel fractalish, the next image will be posted in about 8 hours. Until then, take care, and sometimes fractals are hauntingly beautiful. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Red_Line_Railroad { ; time=0:00:14.01-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5a center-mag=-8.154824884965874/-0.0146428869668948/\ 1585140/1/-50/0 params=2.9/5/1000/0 float=y maxiter=1500 inside=0 logmap=30 periodicity=10 colors=000cC8fFFiIMlLTnOZqRetUlvWrtRlrNfpIanEWl9Qj\ 5LfGGbRCZ`8Vk4Su0Fab`qLYhHV_ESRBPI8N95KCDHFLFITCL`\ 9Oh7QpAPqDPqFOrIOrLNsNNsIPoERkATgtdUnbZi`bd_f_YjVW\ nQUrTUkWUeZU_aUTdUNgLHjUBUUKDUTHUXKU_OUcRUfUUdXUb_\ c`bc_ecYhcWkcUncThmVcmXYmZTm`OmbImdDmf8mhrmQpmVomZ\ mmblmfkmkimohmsgmwkmoomhrm`vmUymNtmUpm_lmfhmlzmrzm\ szmszmszmszmszmszmszmszmuzmwzzYzz8zzLzzYzzizz`zzTz\ zKzzCzzDzzDzzDzzDzzDzzDzzDziSzwJzvGzuDzuAzt7zs4zs1\ zzDzzPzzRzzSzzTzzUzzVzzWzzXzzYzzIzz2zz9UzG_zMezTkz\ Zqzewzkwzlwzlwzlwzlwzlwzlwzluziszgrzepzcnzamz_jzLh\ z6ezDczJazQ_zWYzaWzhUznSztNzoJzjFzeBz`7zXLzcZzjlzq\ zzwtzunzthzrbzqXzoRznMzmRzfMz8Tz8`z8gz8cz7`z6Xz5Uz\ 4Rz3Nz2Kz1Hz1Wz2iz2wz2hzOUzhIzlHzKoz2iz7czCYzHTzLN\ zQHzVBz_6zcGzYQzS_zMhzGizBZzGOzLDzQ3zVBzTJzSRzRYzQ\ _zO`zNbzMczKezJfzIgzHZzEQzCHz98z70z54z88zBCzEGzHKz\ KNzMNzbXzaez`nz`XzeGzirz3 } frm:DivideBrot5a { ; Jim Muth z=0, c=pixel, a=real(p1)-2, d=real(p2)+16 b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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FOTD 11-10-08 (Having the Blues [No Rating])
by Jim Muth 10 Oct '08

10 Oct '08

FOTD -- October 11, 2008 (No Rating) Fractal visionaries and enthusiasts: Friday was very hectic, so there will be little discussion, but we do have an unrated and very blue image to post. The blueness of the image inspired the name "Having the Blues". The image can be seen on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> It may also be seen by running the included parameter file and waiting 43 seconds. Total sun and a temperature of 70F 21C kept the fractal cats happy on Friday, while my day continued hectic. The next FOTD image could be posted as soon as 24 hours, with or without dis- cussion. Until next time, take care, and keep the fractal faith. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Having_the_Blues { ; time=0:00:42.57-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5b function=ident passes=1 center-mag=-0.49825068303276/+0.07466869763114337/\ 20699.78/1/180 params=1.5/3/2/1000 float=y maxiter=3600 inside=0 logmap=18 periodicity=10 colors=000zzwzyyvxxrwwmvvhuucttZssUrrKqqAop6mo7jn8\ hmAekBcjC`hDZgFWeGUdHRcJPaKM`LKZLHYFFWACV5AT07S05Q\ 02P00O02Q03RN4_05T07U08V09WPAePCYPDZOE`OFfNHiKImMJ\ oLKeLMfKNgKOhJPiHRlJQjLQiMQgOPfQPdRPcTPbVJ`UJ_UJYP\ IXPIVPIUPJWPIYPI_PHaRHcUGe`LgaKi_KiYJiWJgUIcUF_UIW\ UKSUNOWPIYRF_UEaWGcYIe`JibLhdNggOfiQcsPekRfcThXUiP\ WjIXgLZeO_cQ`aTa_WbXYcV`dTcfRegPhhMkiKmjIpkGslCtpE\ umFujGvgHveIvbKw_LwYMxVNxSPzSOxQOvPOtOOrNOpMNqLNrK\ NsJNtINuHMvFMwEMxDMyCMzBLzALz9Lz8Lz7Jz2Lz6Nz9PzCRz\ FSzIUzLWzOYzRZzU`zYbz`dzcfzfgziizlkzomzrpzwnzumztk\ zsjzrhzqgzoezndzmbzlazk_zjZzhXzgWzfUzeTzdRzcQzaOz`\ Nz_LzZKzYJzXLzYMzYOzZPzZQz_Sz_Tz`Uz`WzaXzaYzb_zb`z\ cazcczddzdezegzehzfizfgzgfzgdzgczhazh`zhZzhYziWziV\ ziVzkUziUzhUzgTzfTzdTzcSzbSzaSz`RzZRzYRzXRzWQzUQzT\ QzSPzRPzQPzOOzNOzMOzLOzKPzLPzLPzLPzLPzLPzLPzMPzMPz\ MPzMPzMPzMWzMTzPRzSOzVLzY } frm:DivideBrot5b { ; Jim Muth z=0, c=fn1(pixel), a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=(z^a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 09-10-08 (Three Dimensions [6.5])
by Jim Muth 09 Oct '08

09 Oct '08

FOTD -- October 09, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image is located near a larger minibrot in a loop near the East Valley of the largest minibrot on the negative spike of the parent fractal, which resembles a Mandelbrot set. The large minibrot itself is quite unusual, and its 'East Valley' must be seen to be believed. I named the image "Three Dimensions" because the minibrot at the center is clearly a cubic one. The unusually rich pattern of the cubic minibrot earned the image a FOTD status. After a few seconds thought, I rated the scene at a 6.5. The bit of extra effort I put into the coloring earns the extra half- point. The calculation time of just over 1 minute will cause no one any pain. The trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the finished image there, will be equally painless. Sun in the morning, clouds in the afternoon, and light rain in the evening marked Wednesday as a day that could have been better here at Fractal Central. The temperature of 63F 17C was just about normal. The fractal cats had a cussing spat over the best window shelf, but soon made up. My day had nothing of unusual interest to describe. The next FOTD will be posted in 24 hours. Until then, take care, and walk with a fractal in your heart. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Three_Dimensions { ; time=0:01:10.74-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5a passes=1 center-mag=-6.818433862246904/+0.0198539478134832/\ 5.161324e+009/1/-53/0 params=3/4/1000/0 float=y maxiter=650 inside=0 logmap=111 periodicity=10 colors=000H5WJ5UL5SN5QP5OS5MUEKXHG_K8bO1eS3hX4ka5n\ fAqjEsmFolIjhKedN``PWXSRTUNPTPUTRbhTjmRddQa_PVXOTY\ NR_MP`LOaSYdtX_vXWz_RzYMzVIuSKmQLeNMYLOQIPIGQBERy8\ JjSMXjPWeSV`UUWWURZTM`SHbSCdTBhUBlVBoWBsXAwYAzZAz_\ AzaNfcZHe`JfbLhdNiePkgRliTnkVolWcrYTx_IzaRUoXSlbRi\ hQfnOdtNazMZzLXwK`nKdeKhXKlOKpSFvWAzZ6zW7zU8zR9zP9\ zMAzKBzHCzFCzPDyZEwhEu`czI9uYLfmXSzgEp`WdUlUNz_Yze\ hzkszpzyfzgXzQRzYLzeGzmVtwhkza_zVOzODzKEvHEzEFzBFz\ 8FzFHzLJzRLzXNzbPzhRzlTzpUztVzxWzzXzqZzg_zY`zOazFb\ zKfzOizTlzXpzaszevz`ozXhzSbzOWzKQzIPzHPzFOzEOzCNzB\ Nz9Mz8MzISzRXz`bzigzsmzzrzpmzeizVezKaz7TzK_zWezgkz\ sqzrtzqwzqzzpzzpzzgLzkJzoIzrHzvFzzEzzDzzNzzWzxezwn\ zvwzjlzZazNRzBGzJFzQEzYEzdDzkDzlLzmSzmZznfzomzotzj\ DzkLzlSzm_zmfzkfzifzhfzmfzqfzufzzHzzIzzIzzSzzzzzzz\ mszdzzXzzPzzHzzMzzRzzVzz_zzczzZzzVzzQzzMzzHzzDzz9z\ zAzzBzzCzzCzzDzzczz`zzXzz } frm:DivideBrot5a { ; Jim Muth z=0, c=pixel, a=real(p1)-2, d=real(p2)+16 b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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FOTD 10-10-08 (A Hole in One [No Rating])
by Jim Muth 09 Oct '08

09 Oct '08

FOTD -- October 10, 2008 (No Rating) Fractal visionaries and enthusiasts: I'm afraid I can no longer keep the FOTD going on a daily basis with FL's continuing state of panic and a constant need for calming words. So as of tomorrow, I will stop posting the FOTD every day. When the present panicky financial situation is well behind us, I will resume the regular daily schedule. But this does not mean there will be no FOTD's until then, I will still post the FOTD on the less-panicky days. I have totally forgotten what today's image is about, but I think it lies in the east valley of its parent fractal. I gave it no rating and I named it "A Hole in One". The distorted mini- brot at the center is certainly a hole in something. The included parameter file calculates in just under 6 minutes. The trip to the FOTD web site to view the finished image is even faster. The web site can be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> An absolutely perfect day prevailed here at Fractal Central on Thursday, with total sun and a temperature of 77F 25C. This made the fractal cats happy. My day was hectic, but hopefully tomorrow will be calmer. The next FOTD will be posted who knows when. Until then, take care, and wait for the fractal rescue with bated breath. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Hole_in_One { ; time=0:05:55.48-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5b function=ident passes=1 center-mag=1457.31/223.658/0.1774922 params=1.35/4/25/100000000 float=y maxiter=32767 inside=0 logmap=86 periodicity=10 colors=000zmUwmawo`wp_rjYmdXh_WcUVZOTUJSMDRL8QK9RJ\ 9RJ9RI9RI9RHARHARGARFARFAREAREBSDBSDBSCBSKB0ZBSMC0\ ACS9CS9CS8CS8CSEGTJKUOOUTSVYWWbZWa`Y`aZ`c__d`_faZg\ bZicYjdYleXhfWozWkhVriVsjUukUvlTxmTynUwkUuhUsfUqcU\ oaUmZUkXUiUUgRUePUcMUaKU_HUYFUWCUUAXPB_LCbHDeCEh8F\ k4Ge5E_5CU5AP59J57D55854A77B89C9BDADFBFGCIHDKIEMKF\ OLGQMHTNIVPJXQKZRL`SMbRLaQKaPK`OJ`NJ_MI_LHZKHZJGYJ\ GYIFYHEXGEXFDWEDWDCVCBVBBUAAUAAUCBSDBRECQGCOHDNIDM\ KEKLEJMEIOFGPFFQGERGDTHBUHAVH9XI7YIAZJF`JKaKPbKUcK\ ZdJceIheHmfGrgGvgFzhEziDziCzjCzkBzkAzl9zl9zDlmFkmH\ jmJimLhmNgmPfmRemTdmVcmWbmYam_`ma_mcZIeYGgXEiWCkVA\ lV9kVBjWCmmEmmFmmHmmImmJmmLmmMmmOdmPcmQbmSamTamV`m\ z_mzZmzZmzYezXfzXfzZhz`izajzckzelzfnzhozjmzkiRmePo\ cUpcZrcctchucmwarx_vyYzzWzzUzzuzzuzzuzzuzzuzzuzzuz\ zuzzuzzuzzuzzuzzuzzuzzuzzuzzuzzuzzuzzuzzuzzuzzuzzu\ zzuzzuzzuzzuzzuzzuzzuzzuz } frm:DivideBrot5b { ; Jim Muth z=0, c=fn1(pixel), a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=(z^a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 04-10-08 (Disorderly Order [5])
by Jim Muth 07 Oct '08

07 Oct '08

FOTD -- October 04, 2008 (Rating 5) Fractal visionaries and enthusiasts: I named today's image "Disorderly Order". It is located in the East Valley of a minibrot floating in an area of total chaos surrounding a large Mandeloid at the center of the parent fractal. The disorderly parent chaos is reflected in the texture throughout the scene. The immediately recognizable pattern reflects the order. I rated the image at a 5. After all, how impressive can a scene lying not all that deep in an East Valley be. Perhaps the most impressive thing about the image is the fact that a negative logmap setting works best with it. The calculation time of 19 minutes is pretty impressive also, so I strongly recommend viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Early morning clouds gave way to afternoon sunshine here at Fractal Central on Friday, while the temperature reached a high of a slightly chilly 61F 16C. The fractal cats cleared the unwanted cats from the area early, then spent the rest of the day sleeping and thundering up and down the hallway at top speed, like a herd of . . . well, hyperactive cats! My day was busy. Enough said. I'll be spending most of the day Saturday back at Old Fractal Central, so the next FOTD will not appear until October 06. Until that sublime moment, take care, and maybe it's the myths that are real, and reality is the myth. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Disorderly_Order { ; time=0:11:10.97-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5a passes=1 center-mag=-0.7383216106645732/+0.107014930211066/\ 2.43737e+010/1/-167.5/0 params=-6/0.5/-13/0 float=y maxiter=12500 inside=0 logmap=-2156 periodicity=10 colors=000wnRsjVpgZmdaiaefYicVl_SpXPtUMwTNtSNrRNpQ\ NmPNkONiNNgLLfKJfIIeHGeFFdEDdDCdMGhVJlcMpbQqaTraWs\ `Zs_bt_euZhvYkvYowXrxWuyWxyUvxTtxRrxQpxPnxNlxMjwKh\ wJfwIdwGbwF`wEZwFYpFYjGYcGYYHYSHYLIYFIY9KU8MQ8OM7Q\ I7RF6TB6V75X35Y05X1AX2FW2KW3OV4TV4YV5bU6fU6kT7pT8u\ T8yZNrcakhodfqferhdtjbulawn`xpVsnPnlJjkMiiOihRhgTh\ fWgeYgd_gcbfadf`ge_ieZldYndXpdWlaYi__fY`bWb_TdXReT\ PgQNiNLjeG_xBPtGUpKYlOahSedWi`_mXcqUguWhrXhpYhmZhk\ _ih`ifbicciadjZejXfjUgjShjQnpLsvGpnRmf`j_jlWgmSdoO\ bpK_rGXsCVu8Sv4Qt8RsBSrETpHUoKVnNWlQXkTYjWZiZ_faac\ db`gdZjeWmgTphRsiPtgOtfNteMtdKubJuaIu`Hu_FvYEvXDvW\ CvVAwT9wS8wR7wQ9xPAxOCxODyNFyNGyMHyMFzOEzQDzSCzUBz\ W8zZzz`4zbzzkUztzzrRzpzznOzlzzjzzhzzfzzdzzbzz`zzZz\ zXzzVzzTzzRzzPzzQzzQzzRzzRzzSzzSzzTzzTzzUzzUzzVzzV\ zzWzzWzzXzzYzzYzzZzzZzz_zz`zz`zzazzazzbzzczzczzdzz\ dzz6zz7zz7zz7zz7zz8zz8zzS } frm:DivideBrot5a { ; Jim Muth z=0, c=pixel, a=real(p1)-2, d=real(p2)+16 b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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FOTD 08-10-08 (Beads and Things [No Rating])
by Jim Muth 07 Oct '08

07 Oct '08

FOTD -- October 08, 2008 (No Rating) Fractal visionaries and enthusiasts: NEW FORMULA ALERT! Today's image was created with a new formula. The new formula is a slight generalization of the DivideBrot5a formula, and adds a new variable parameter as well as a variable function applied to 'C'. The result takes us pretty much back to where the DivideBrot series began. Since I don't feel like writing a discussion, I will not write one. It's up to the image to speak for itself. To see the image and hear it speak, (figuratively, that is), visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or run the included parameter file and wait a few seconds. Due to the media-induced financial panic, and a panicky FL to calm down, I feel an uncontrollable burst of philosophy coming on, and when I start philosophizing, nothing is sacred. So watch out do-everything-for-everybody politics, rational science, faith-based religion and feel-good dreamy New-Age mysticism. But fear not, at least not yet. The time for philosophy has not yet come. The weather was normal for the season on Tuesday. (59F 15C) The fractal cats were their normal selves. My day was restless. The next FOTD will be posted in 24 hours. Until then, take care, but do as you will. Jim (never cynical) Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Beads_and_Things { ; time=0:00:44.89-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5b function=ident passes=1 center-mag=-0.828772682396652/+0.0511147577361402/\ 3.318738e+009/1/-167.5/0 params=1.1/3/1/0 float=y maxiter=1500 inside=0 logmap=48 periodicity=10 colors=000WD0T80R30MHnM1eH2_D2U``Fmz0IFGHMIGSKFYME\ dODjQCzRKlMShH_dCfa7lSCzJGgGKXEONCSCAW28ZUJjtTupQo\ lOjhLedJ_`GVYEQUKTRPWdDiq2vr6os9htCauFVvIOwLHwOBoP\ GhQKaQPVRTOSXHSaATe3TiAZqHcxRdk`eZjfMtfAtgDtgFtgHt\ gKtgMtgOtgQudTvaVvZXwWZxT`xQboRcgSc_ScRTdJUdBUd9Zj\ 7co5ht4myHpnTsdevVqxLpsJonHoiGldOi_VgVadQhbMoVFdN9\ VF3LM5OT6R_7Tf8Wl9YgCbbEfYGkTIoQKjNLfLNbIOZFQVDRRA\ TN8UJDYPI`UNdZRgcWji`nneqsitxnevsSulQtfOs`MsUKrOIq\ IHqikpgeke_gcUcbO_JHl0ByLYmdtaUn`Kh_AbZ9ST9HN97I7C\ H6HH5MG3RG2WF1`F0eF3bH5`J7YL9WMBUODRQFPSHNTJUQL_ON\ fMPlJRsHSyFPqDMiCJaBGV9DN8AF778667C67I66O66U65_65d\ DE_JMVPUQVaL`iHRUTHFd80o98gAF_AMTBTLC_DCf6D_OETdFM\ uEQsDTrCWqBZpAao9dn8gmE`kKViQOgWIeaBcg5aMDyOBwQ9vS\ 7uU5sW3rY1qZ0pa6rdBsgGtiLulQvoVwr_xtdyuewueuvesveq\ weowemwel`QYEBKIAPM9TP8XT8aW7e_6ib6meAfgE`iIUkLOUL\ G`KJzzzhP1tb0qY0nT0kO0hI0 } frm:DivideBrot5b { ; Jim Muth z=0, c=fn1(pixel), a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=(z^a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 07-10-08 (Enola Rail Yards [No Rating])
by Jim Muth 06 Oct '08

06 Oct '08

FOTD -- October 07, 2008 (No Rating) Fractal visionaries and enthusiasts: On Monday FL had another financial panic attack, and I had to spend most of my normal fractal time assuring that the world is not ending and we should not sell all our investments right now before they drop to zero value. I still managed to find a kind of fractal however, which I named "Enola Rail Yards". The Enola rail yards are an actual place on Route 15 near Harrisburg, and the high point of the trip to and from Old Fractal Central. Every time I pass the yards, I glance over at the hundreds of parked locomotives, thankful that the trip is half finished. Today's image is an actual scene in its parent fractal, which is basically an oversized Mandelbrot set. The scene is located near a split-apart minibrot on the infinitely-divided main stem of the parent. Since I put almost no effort into the image, I gave it no rating. The calculation time is a blazingly brief 56 seconds. And finally, the already-calculated GIF image is or soon will be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The sun shone, the breeze blew, and the temperature reached 59F 15C here at Fractal Central on Monday. The fractal cats spent most of the day at the window, watching the non-fractal cats pass by. My day was hectic. Hopefully tomorrow will be calmer. The next FOTD will be posted in 24 hours. Until then, take care, and don't establish your depreciation. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Enola_Rail_Yards { ; time=0:00:56.44-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5a passes=1 center-mag=-18.40062430333887/+0.0023747496544122/\ 1020924/1/165/0 params=2.003/10/1000/0 float=y maxiter=750 inside=0 logmap=71 periodicity=10 colors=000_0TZ0SY0QX0PX0MW4JV6CU76V69Y6C`5Ed5Hg4Jj\ 4Mm4OqXcuyrrunpqjmnfkjbhg_fcWc`SaXOZULXQHUNDSJ9QG6\ QHCQIHQJMQKRQLWQM`QNeQOjTRiWUhZWgaZfdaegcdjfcmibok\ bjj`fi_ahZYgXTfWPeVLeUJdUzdUzdUzvDzzFzrHwqIzoKzmLz\ lNzjOFhQEgREeTFnTEmUEmUElUElUElUEkUEkUEkUEjUEjUEjU\ EiUEiUEiUEhUEhUEhUEgUEgUEgUEfUEfUEfUEeUEeUEeUEdUEd\ UPV6OW7OW8NW9NXANXAMXBMYCMYDLYELZEKZFKZGK_HJ_IJ_IJ\ `JI`KI`LIaMHaMHaNGbOGbPGbQFcQg6qhBohFniJmiNliRkjVj\ jZijbhkfgkjfknehmdelcEcWbkb_jaXi`Vi_ShZPgYMfXJeWGd\ Vfv0ct3`r6Zq9WoBTmERlHOjKLhMJgPGeSi1VAdtBdsBdrBdqB\ dpBdoBdnBdmCdlCdkCdjCdiCdhCdgCdfDdfDdeDddDdcDdbDda\ Dd`Ed_EdZEdYEdXEdWEdVEdUb83`B5ZD7YF9WHAVJCTLESNFQP\ HORJNTKLVMKXOIZPH`RFbTQVbPWaPWaOWaOX`OX`NX`NY_MY_M\ Y_MZ_LZZLZZK_ZK_YK_YJ`YJ`YJ`XIaXIaXHaWHbWHbWGbWGcV\ FcVFcVFdUEdUEdUb3W_8VXCVUGVRKVPPUMTUJXUG`U4Hk5Ki6M\ g7Of8Qd9SbAVaBX_CZYfKWfGW } frm:DivideBrot5a { ; Jim Muth z=0, c=pixel, a=real(p1)-2, d=real(p2)+16 b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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FOTD 06-10-08 (Kaleidoscope Color [6.5])
by Jim Muth 05 Oct '08

05 Oct '08

FOTD -- October 06, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: The minibrot at the center of today's image looks like an ordinary quadratic one. But do not be deceived by appearances. It is actually a minibrot of order 1.95, basically indistinguish- able from a quadratic minibrot. The parent fractal appears to be an oversized Mandelbrot set, but some minor differences along the negative X-axis spoil its perfection. Today's image lies in one of these differences. The image is located in an almost totally swallowed up scepter, its remains barely peeking out from a discontinuity. I named it "Kaleidoscope Color" when I remembered how, as a child, I spent hours gazing into one of those toy kaleidoscopes, watching the broken bits of colored glass create ever-changing 6-sided patterns. I rated the image at a 6.5, giving myself a half-point bonus for the work I put into the coloring. Had I put a little more work into the colors, I might have been able to rate the image at a 7. The calculation time of 1-1/2 minutes is within reason. Viewing the completed image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> is also quite reasonable. The trip back to Old Fractal Central on Saturday was uneventful. But curiously enough, even though I moved away 2-1/2 years ago and only one of the old fractal cats is still alive, it still seems like I'm returning home from a vacation trip. The Saturday weather at New Fractal Central was miserable -- cloudy with light rain and a temperature of 54F 12C, while at Old Fractal Central it was sunny and 72F 22C. Sunday here at New Fractal Central was mostly sunny and quite pleasant, with a temperature of 64F 18C. The one remaining old fractal cat, Thomas, slept through the fine weather on Saturday. The two new fractal cats, Nicholas and Cassandra, stood watch in the window most of Sunday, making sure no unwanted cats intruded into the yard. I simply took both days as easy as possible, which is not too easy on a day with a 300-mile round trip included. The next FOTD, undoubtedly glorious, will be posted in an incredibly brief 24 hours. Until then, take care, but leave a little room for fun. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Kaleidoscope_Color { ; time=0:01:30.08-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=dividebrot5a center-mag=-139.6825641679953/+1.069306308971118/\ 892255.3/1/63.5/0 params=1.95/100/1000000/0 float=y maxiter=1500 inside=0 logmap=149 periodicity=10 colors=0007Kl8Pm9UnAZnBcoBhoCmpDrpEvqEyqPnd_cTjTGu\ I4qJ7nK9kKChLEdLHaMJZMMWNOTNQVQTWSVXUYYW_ZYa`_daaf\ bchcekdgmeiocflaci``fZYcXV`WSYUPVSMSRJPPGMNDJMAGK7\ DI4AH27P5AX8DcBFkEIz_UzbNzZMvUMnTLjVLfYLb`KZbKVeJR\ hJNjJKeKHaLEXLBTM8PN5KN2GO0CO2EM4GK6IJ8KHAMFCOEEQC\ GSAIU9KW7MX6OW7PV7QU8RT8SS9TR9UQAVQASP9PO9MN9JP9GU\ 9DY9A`97c99f8Ai8ml7mo7rq7wr6ws6ws6rt5mu5hu5mvBrvGm\ vMcvRUvXKvaGvgGvlCwd9wX6wP3wH6uG8tGArFDqFFoEHnEKlD\ MkDOjCRhCTgBVeBYdA_bAaa9c`9ZTCVLERDGN6IL9KKBLJEMIG\ NHIOGLPFNQDPRCSSBUTAWU9ZV8`W7bX8`W9ZWAYVBWVCUUDTUE\ RTFQTGOSHMSILRJJRJIRKITMIVNIXOIZQI`RIbTIdUIfVIhZJc\ aKZeLVhMQlNLoOHnPJzPKlQzkQNjQPiRzhRSgRzfSVeSWdTYcT\ ZbT`aUa`Uc`UdZWeXYeV_fUafScgQdgPfhNhhLjhKliImiGojF\ qjDskBukAvktyinzeizbdzZ_zWVzTQzPLzMGzJBzF6zC1z94zD\ 6zH8zLAzOCzSEzWHzZJzbLzfNziPzmRzqTztOzqJzmEzj9zf4z\ c6z`8zY9zVBzSDzPEzMBzm9zl } frm:DivideBrot5a { ; Jim Muth z=0, c=pixel, a=real(p1)-2, d=real(p2)+16 b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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Re: [Fractint] system specs
by JackOfTradeZ＠comcast.net 03 Oct '08

03 Oct '08

. Phil, I don't know if this will help you, but here it is: AMD Athlon(tm) 64 X2 Dual Core Processor 4600+, MMX, 3DNow (2 CPUs), ~2.4GHz x86 Family 15 Model 75 Stepping 2 AMDA64X246AM265W Memory: DDR2 2048 Meg, 803.6 MHz Phoenix - Award WorkstationBIOS v6.00PG Alienware MoBo: MB-FCNFORCE590SLI Graphics: NVIDIA GeForce 8600 GTS, 256 Meg RAM Windows XP Professional (5.1, Build 2600) Service Pack 2 (2600.xpsp_sp2_gdr.050301-1519) DirectX 9.0c (4.09.0000.0904) It is over a year old, and it wasn't the highest high-end even when I bought it. But she sure cruises! You can see it here: http://www.fractal-animation.net/machinez.html For Dave's comment, yes - the G-card seems to be the main issue. I have upgraded my P3-733 / Win98SE system twice over the years; each new card performed worse with fractint (but better with games). The most recent was unusable in a win shell. The default image would draw but using any keys caused a lock-up. I finally put back in the original Hercules card (1999) and now fractint is cool again, but games suck. This is also the case with WinXP and current systems. There seems to be no rhyme or reason to it, at least that I can see. Some graphics cards work, some don't. Luck of the draw I guess. Cheers JoTz .

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FOTD 03-10-08 (Broken Fives [5.5])
by Jim Muth 02 Oct '08

02 Oct '08

FOTD -- October 03, 2008 (Rating 5.5) Fractal visionaries and enthusiasts: A bit of a work rush combined with further anxiety from FL left little time for a fractal search on Thursday. But by moving faster than light I did manage to find one marginally worthy of being declared FOTD for October 3. Today's little quasigem lies in a tiny filament extending from a high-order bud on the northeastern shore line of the large minibrot on the split main filament of its parent fractal. This parent fractal closely resembles the Mandeloid of the formula 2^(2.003)+C. The scene lies quite deep in the parent fractal, which makes the mathtolerance entry necessary. I named the image "Broken Fives". The five broken elements surrounding the tiny order-2.5 minibrot at the center inspired the name. The rating of a 5.5 shows that the image barely qualifies for FOTD status. The calculation time of 2 minutes shows that little time will have been wasted if the result proves not worth the effort. But almost all effort may be eliminated by hurrying to the FOTD web site to view the completed image there. The FOTD web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A fine brisk early autumn day prevailed here at Fractal Central on Thursday. The dark, scudding clouds, brisk winds and temperature of 59F 15C seemed just about right for early October in central Pennsylvania. The fractal cats, born 150 miles south in Baltimore, agreed. My day was notably uneventful. The next FOTD will be posted in 24 hours. Until then, take care, and may right win out. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Broken_Fives { ; time=0:02:04.07-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5a passes=1 center-mag=-43.75477306138761/+0.2402984335648201/\ 8.26821e+011/1/135/0 params=2.5/25/10000/0 float=y maxiter=2400 inside=0 logmap=219 periodicity=10 mathtolerance=0.05/1 colors=00025L24J23G13D12A11801500284I73G63E52C42A4\ 29317215103001LIuJGpIFlGEhFCdDB`CAXA9T000zzzxwxuuu\ soookkkgcc_XURPKIGA98OIaOGZSFWWDTdCQmBNu9KuKHuKEu5\ B548325112WYATU9QR8NO7KL6HI5EF4BC3000mw1jt0gpCbjAZ\ e9U`8QV7MQ6HL4DF38A2451G5zE4mC3cA3U82O61I41C206zz3\ zz2zz2zz2zz1zz1I91D70940420CDvCCwBBwA9wAuz9nz9my8j\ y7gy7dz6az6Zz5Uw57t5Aq5Dn5Gk4Jh4Me4Pc4S`4VY3YV3`S3\ cP3fM3iK5632eI2bH2_G2XE2UD1RC1OA1L91I81F60C5094062\ 031jVp`OeSIVICL96A81A70960850750640530420320210100\ 0duCZmAUf9P_7KT6FL4AE357144I33G33F33D22C22B2291181\ 16115004002001etpbpl_liYifVebSb_QZXNWTLSQIONFLJDHG\ AED7A9576233y3nr2hk2bd2YY1SR1MK1Hz0zz0zzyzzrzzlzzf\ zz`zzVzzOzzIzzCzz6zzHzzEzzCzz9zz7zz4zz2zz1zz0zz0Nz\ 0Bz7Wz5Pz4Jz2Cz16znxzjszfozcjz_fzWbzTYzPUzLQzILzEH\ zADz78z34zEiz7NzbozZizVdzR_zNVzJQzFKzBFz7Az35z`NzR\ HzIBz95z9az8Zz7Wz7Tz6Rz5O } frm:DivideBrot5a { ; Jim Muth z=0, c=pixel, a=real(p1)-2, d=real(p2)+16 b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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FOTD 02-10-08 (The Brot That Was Not [8])
by Jim Muth 01 Oct '08

01 Oct '08

FOTD -- October 02, 2008 (Rating 8) Fractal visionaries and enthusiasts: Today's image is named "The Brot That Was Not". I gave it this name because, when the parent fractal is rendered in the usual manner, there is no minibrot at all at this particular location on the X-axis. Nothing is there but the flat disks that fill the image. The minibrot doesn't appear until the scene is rendered with the inside set to 'atan'. Another reason for the name is that the minibrot is not quite all there. A sizable chunk has been taken out of the area on the negative X-axis beyond Scepter Valley. I spotted the elusive midget when I noticed a certain symmetry at this point in the parent fractal, which divides the M-set by (Z^(-0.1)+0.1). Actually, I'm not sure what the formula does. It makes little sense to me. But it creates some very interest- ing fractals, so who cares about exactly what is going on. The rating of an honorable 8 is not to be sneezed at. The ephemeral minibrot takes up almost the entire frame. The mass of bubbles fizzing around it almost reminds me of a glass of ginger ale. And the calculation time of a mere 19 seconds has hardly been exceeded for brevity. The ultimate in conveni- ence is to view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With a temperature of 61F 16C, Wednesday was too chilly and too cloudy to be anywhere close to perfect here at Fractal Central. The brief but heavy shower that passed over in mid-afternoon did not help things. The fractal cats weathered the rain by ignor- ing it. My day was acceptable. The next FOTD will be ready in 24 hours. Until then, take care, and let your fractal guide you to enlightenment. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= TheBrotThatWasNot { ; time=0:00:19.93-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5a passes=1 center-mag=-0.06\ 6769/0/8.541667 params=-0.1/0.1/-14/0 inside=atan maxiter=1600 float=y symmetry=xaxis periodicity=10 colors=0000EN0GR0KS0NSOQPSTRWWTZ_VacYdg_fkagmcfnee\ ngdmhcljbkkajlaij`gh`dg_ae_ZcZWbZT`ZQZZOYZLW_IU_FT\ _DR`APa7Ob4Mb2Ld4Me6Nf7Oh9PiAQjCRkDSmFTnGUoIUpJVrL\ WsMXtOYuPZsR_rS`mUahUbcUcZUdUUcPUaKU_FUYAYW5aU1dS1\ hQ1kO5jM9iPDiWGhbKhiOgpRgvShtSirTjpTknUklUljVmhVnf\ WodWobXp`XqZYrXYrWWpWUoWTnWRmWPlWOkWMjWKiWJhWHfWGe\ WEdWCcWBbW9aW7`W6_W4ZW3YW9_VE`VKaUPbUVdU_eTefTjgTj\ fRjfQjfPjfOjfMjeLjeKjeJjeHjeGjeFjdEjdDjdBjdAjd9jc8\ jc6jc5jc4jc3jc2ga3e_4cY5`W6ZU7XS8VQ9SOAQMBOKCMIDJG\ EHEFFCGDBGHEJKGLOINRKPVMRYOTaQWdSYhU_kWaoYcr_enZbj\ Y`fYYbXWZXTVWRRVONVMJUJFUHBTE8TC9RF9QH9OJ9NL9LN9KP\ 9JR9HT9GVAEXADZAB`AAbA9dA7fA6hA4jA3lA2nD5lF7jI9hKB\ gMEePGcRIbTK`WNZYPX_RWbTUdWSfYRi_PkaNmcMldPkeRkfTj\ gVjhXiiZhj`hkbgldgmgfnifokepmdqodrqcssctubuwbvyUhp\ LWhCJ_36S7BUAGVELWHPYLUZOZ_RcaVgbYlcaqedvfgwgiwhkw\ imwjowkqwlswmuwnwwoxwpywq } frm:DivideBrot5a { ; Jim Muth z=0, c=pixel, a=real(p1)-2, d=real(p2)+16 b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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FOTD 01-10-08 (Empty Vastness [6])
by Jim Muth 30 Sep '08

30 Sep '08

FOTD -- October 01, 2008 (Rating 6) Fractal visionaries and enthusiasts: There's not much time for a discussion today, once again due to FL's lingering fears of an impending apocalyptic economic armageddon. At least that's what I call the media hysteria that has FL so upset. And I would not be surprised if a fractal pattern were found in the irregular cycles of the economy that are causing so much excitement. A fractal pattern certainly does exist in today's image. In fact, that's all the image is. It shows a minibrot in the debris on the northeast shore line of the main bay of the Mandeloid fractal that results when the Z^(0.1) Mandeloid begins to morph into something unknown. The name "Empty Vastness" came about when I realized that the image evaporates as the bailout radius, defined by the setting of real(p2), is increased. The rating of a 6 might be a bit conservative, considering the serendipitous coloring. The calculation time of under 50 seconds is true on a P4-2000mhz machine booted with DOS 6.22 and running Fractint from a virtual RAM drive. The easiest way to see the image however is to surf over to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view it there. The morning fog broke to cloudy skies by 10am Tuesday here at Fractal Central. A brief peek of sun in the early afternoon could hardly take the damp chill from the 68F 20C air. The rain that was forecast never arrived. The fractal cats chased away one wandering cat by merely growling and bristling their tails. My day was acceptable. The next FOTD will be posted within 24 hours. Until that time of enlightenment arrives, take care, and look to fractals for relief. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Empty_Vastness { ; time=0:00:49.50-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5a passes=1 center-mag=+0.042146324246646/+0.031112006466792/\ 3.843e+008/1/115/0 params=-1.1/0.1/-14.6/0 float=y maxiter=1600 inside=253 logmap=54 periodicity=10 colors=000SHQNGLJGHHILGKOEMSDOVBQZASa8Ue7WhDT`IRUN\ PMSNFOSDKXBHa9De7Aj56o33s1Dt7MuDWvIdwOmxTABLOFEaJ7\ oN0qK9rHIsERuCZv9gw6px4xqAsjGndMiYSdSY_CiHGbIJXJ16\ y2SgCZfLdfUjfXeeZ`e`WebSeeNdgIdiDdk9dnA`qBYtCVvDSj\ OZ_YddRahLZlFWgIbbKhYNnTPtORzLQqIQiGQaDQTAQL8QDa2J\ d8RfEYiKekQlmWscSeUOSKKEBG1AJ1AM19O19R19T1aK2ZYCWk\ LTxUPnVMdWJWXGMYDDZQLcaSgn_lzfpmit`kwPmzQfyR`xRUwS\ OvSHuTBtT5sP8tLAuIDvEFwAIx7KyETmKaaQjQWsEVrLUqSTpZ\ OiaKbcFWfBQhILYPGNWBCb71UL9MZHElPJdNNXMRPKVHJ244F8\ FRCQcG`oKjpaDYbf``jc_mfZphYsjXtlWtmVtoUtpUtr`ltgdv\ mYxtQzzJowKetLWqLMnMCkM9`b7Rr8Vp9Zn9bmAfkBjiBnhCrf\ CueOtZ_sSjsLsfNsfNsgNsgNsgNsgNrgNrhNrhNrhNrhNjsJrh\ NriNqiMqiMqiMqiMqjMqjMqjMpjMpjMpjMpkMpkMpkMpkMXJkZ\ JlaJldJlfImiImlImnImkKjiMggOdePacRZaTW_VTYWRWYOU_L\ SaIQbFOdCMf9Kg7XB_UAUR9NP8HM7AK74LACLDKMGSMJ_NMgNP\ oNSvINqEImAEiCKnmmzGVvH_z } frm:DivideBrot5a { ; Jim Muth z=0, c=pixel, a=real(p1)-2, d=real(p2)+16 b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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FOTD 30-09-08 (Five Into Six [N.R.])
by Jim Muth 29 Sep '08

29 Sep '08

FOTD -- September 30, 2008 (No Rating) Fractal visionaries and enthusiasts: Today's discussion will be non-existent, since I spent all afternoon trying to calm FL's financial fears. ("If we try to give 'everything' to everyone," I finally told her, "sooner or later we will run out of 'everything'.") Today's image shows an order-6 minibrot that lies in the East Valley of a fractal caught in the act of morphing from the Z^6 Mandeloid into the classic Mandelbrot set. Actually, despite its haste, the image is a better-than-expected example of an East Valley type spiral. I named it "Five Into Six" because the Mandeloids of order 6 have only 5 lobes. I gave it no rating because I put almost no effort into it. The calculation time of 6-3/4 minutes is a bit slow, but well within reason. The finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The mostly cloudy but dry skies and temperature of 68F 20C seemed quite pleasant compared to the torrential rains of the past several days. The fractal cats agreed as they chased away with loud cat curses a yellow-orange cat that took up short- term residence in the back yard. My day was more exciting than it needed to be. Tomorrow could be a repeat. The next FOTD will be posted in 24 hours. Until then, take care, and remember that things will never get so bad that they couldn't get worse. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Five_Into_Six { ; time=0:06:47.71-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5a center-mag=+0.674118582480173/-0.00027770635321115\ /1.060848e+012/1/-3.25/0 params=6/2/525/0 float=y maxiter=6400 inside=0 logmap=-1152 periodicity=10 mathtolerance=0.05/1 colors=000HMnGMnGMnFMnFMmEMmEMmDMmCMmCMlBMlBMlAMl9\ Ml9Mk8Mk8Mk7Mk7Mk9NiANhCNfDNeFNcGNbIO`JO_LOZMOXOOW\ POURPTSPRUPQVPPXPNYPM_PK`QJbQHcQGeQEfQDhQCiRAkR9lR\ 7nRAoRFqRKrRPpSUnTZlUcjZhhcmjhrqmxqvzzzzttzhluXctN\ RvMLhLJYKASJB5IC6HD6GE7zm5FE7GI9HLBIPCJTEKWGL_IOVK\ MbJKiIJpINnKQlMTjOWhPZfRadTbdldbUhgDeaBcW9`Q7XJgZL\ 6_NB`OFaPKbQOcSTdTXeUafVedSdbQcaOc_MbYKaXIaJUS6dIC\ XGIPFOHEUADOJJJRPD_V8g`Di_IkZNlYRnXWoW`qViwZdrV`nS\ XjOTfLPaHLYEHUA3U3DQ7MMAVIEqHEcFHQEJDDLFCKGCKHCKJC\ JKCJLCJG3HMCJSKKYSLc_NigOtxSnoPhgNb_LXSJRKHLCFG4DK\ 7HNALRDOUGSYJW`MZdPbgSeiYgkciphomiukkzinzgqzdtzbwz\ `zzdzzZzzTzzNzzHzzBzz5zz0zzHzzYzznz0nzzkzhizRdz6gz\ 9izClzFnzIqzLszOvzRwzSxzTxzTyzTyzTzzTzzTzzTrzQjzOb\ zLWzJOzGGzE8zB1z98zEFzIMzMSzQSzSRzURzWQzZQz`PzbPzd\ Yzbezanz`vz_szVqzQozLlzGjzBhz7szXtzWuzWuzWvzVvzVwz\ VwzUxzUxzUyzTyzTzzTzzTJzI } frm:DivideBrot5a { ; Jim Muth z=0, c=pixel, a=real(p1)-2, d=real(p2)+16 b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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FOTD 29-09-08 (The Great Waves [?])
by Jim Muth 28 Sep '08

28 Sep '08

FOTD -- September 29, 2008 (Rating ?) Fractal visionaries and enthusiasts: There is not much to be said about today's image, which is a variation of the three most recent images. It's all been said previously. Today I applied the 'zmag' inside fill to the same scene and came up with an image that reminds me of rough surf at the beach. When I named the image "The Great Waves", perhaps I was thinking of the famous Japanese tsunami print. In some ways the image seems good; in other ways it seems too much of a repeat. And the colors are too jumbled also. With such conflicting opinions I could not decide on a rating. I let it go with a question mark. The calculation time of just over 4 minutes will pass in a near instant when the image begins to unfold. And downloading the finished image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> is even faster. Heavy rain fell all Sunday morning here at Fractal Central, giving a two-day total of about 6 inches or 15cm, while the temperature hung around a very humid 70F 21C. I noticed a puddle of water leaking into the basement laundry room when I checked, but one puddle can't hope to compete with the floods that plagued old Fractal Central. I must call my sister back at old FC in Baltimore, to see how the old basement made out. Very heavy rain fell there also. The fractal cats ignored the rain and stretched out on their favorite rugs. When the last shower ended at 5pm, a brilliant double rainbow appeared in the east, ending the day in a blaze of glory and making up for all the rain. Except for the rain, my day went without incident. The FOTD was good enough to avoid disappointment. The next FOTD, hopefully an improved one, will be posted in 24 hours. Until then, take care, and when the aliens visited earth, the fractals they found here must have scared them off. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Great_Waves { ; time=0:04:10.55-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5a passes=1 center-mag=-0.601964001333459/+0.012730655785964/\ 96540.18/1/157.7/0 params=-1.1/0.5/1000/0 float=y maxiter=650 inside=zmag periodicity=10 colors=000OOHMOGKNFHNEFNDDMCBMB8MA6L94L82L84K95K96\ K97K98K99K9AJ9BJ9CJ9DJ9EJ9FJ9GJ9HI9II9JI9KI9LI9MI9\ NI9LHDKGHIGKHFOFFSEEVDEZBDbACe8Ci7Bm5Bp4At3Aw5Cv7E\ v8FvAHvBJvDKvFMvGOvIPvJRvLTvNUvOWvQYvRZvT`vVbuWcuY\ euZgu`hubjucluemufouhqujruktumvunwupyuqzumwsjuqfso\ cqn`olXmjUkhRigSheTgcTfaUe_VeZVdXWcVXbTXaRYaQZ`OZ_\ M_ZK`ZJ`YHaXFbWDbVBcVAdU8dT6eS4cR1eS3fS5hS7iT8kTAl\ TCnTEoUFqUHrUJtULuVMwVOxVQyVRwTQvSPtROsQNqONpNMnML\ mLKkJKjIJiHIgGHfFGdDGcCFaBE`ADZ8DY7CW6BV5AU4AS69Q8\ 9O99NB9LC9JE8IG8GH8EJ8DK8IL7MM6QN5VO4ZP3bP2cN3dM4e\ L5fK6gJ7hI7iH8jG9jEAkDBlCCmBCnADo9Ep8Fq7Gu0Bq6GnCL\ jIQgOVcU_fUh`ZdWb`QgYLkUFpQBuMAtNAsNArO9qO9qP9pP8o\ Q8nQ8nQ7mR7lR7kS6jS6jT6iT5hU5gU3gT5gU6gV7gV8gW9gWA\ gXBgXDgYEgZFgZGg_Hg_Ig`GhaJg`Lf_NfZQeYSdXUdXXcWZcV\ `bUcaTeaSg`Sj`Rl_QnZPqZOsYNvZMuYNtXNsWNrVOqUOqTOpS\ PoRPnQPmPQmOQlNQkMRTPJRPI } frm:DivideBrot5a { ; Jim Muth z=0, c=pixel, a=real(p1)-2, d=real(p2)+16 b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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Re: [Fractint] Fractint Status
by JackOfTradeZ＠comcast.net 27 Sep '08

27 Sep '08

. My understanding is that Vista is totally incompatible with fractint. Forget it. Windows XP however, is ok (sometimes). I have 2 WinXP systems, one is a screamer with fractint, the other is a pig. Go figure. I think it is the CPU (athlon better than intel) and graphics card, also the mobo chipset that makes the difference. Win9X is totally ok, you just want a good P2 or P3 system with at least 256K memory and a good graphics card. .

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FOTD 28-09-08 (Rambling Rat's Nest [7])
by Jim Muth 27 Sep '08

27 Sep '08

FOTD -- September 28, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's fractured image is an excursion into yesterday's image, which itself is an excursion into the image of Sep 18. I named today's image "Fractured Rat's Nest". That's what the angular jumble of fractal debris reminds me of. I rated it at a 7 because of the surprisingly complex pattern themes scattered through it. The fractal action in today's image was achieved by applying the 'atan' inside fill to the original scene, which is a blank screen when rendered in the normal way. Most of the other inside fills do nothing with this image, but the 'zmag' fill works as well as the 'atan'. The FOTD for tomorrow will be a further zoom into today's scene, rendered with the 'zmag' option. The calculation time of 4-1/4 minutes is not as fast as some images, but still within reason. The ultimate in logical reason may be achieved by surfing to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Frequent heavy showers made Saturday a day that left much to be desired here at Fractal Central. But all was not lost, for the rains washed out the planned all-day antiquing trip, which gave me ample time to explore in the world of fractals, a world that could be almost as real as the 'real' world. When the tempera- ture reached 68F 20C, it felt as muggy as midsummer, and the fractal duo went into stretch-out mode. The next FOTD will be posted in 24 hours, give or take a couple. Until then, take care, and the answers lie in the fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Rambling_Rats_Nest { ; time=0:04:17.76-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5a passes=1 center-mag=-0.601958270319895/+0.0127190633904491/\ 173000/1/-64.8/0 params=-1.1/0.5/1000/0 float=y maxiter=650 inside=atan periodicity=10 colors=000SCiNKYIRMN941LH5QF9UDumxpyofrdXkVWg8ee6n\ d5pcLqc`rcofbkVagLaLBXJ2SICXJM`KVdLaWJhNHoEFv5Dvq2\ tnIskXe_cSPjEDq12xNJbh_HSUBYZFNYDoBvWNZGb8E_A5IC9Q\ BWm5Ri7Me8HaAL2eHIQjA8UMAFzHr3GYJDvOPs`Wh_QYZLNYGT\ eYPcSLaMH_GT54NF7IP9`Y1TY5LY8btdUlVLdLOgpLdeIbWF_L\ `vqPiWE9ceqhkBqUNWRnRNiNKeJGaF2ysnq2Wg7nnXXySNkJqp\ LPlQJdI`gOVdKPbHJ_E4ej9aT`RqTUbLWPbq_WlTQgNJbHPLxJ\ S_NrkJkZGdNVDxPKgJRRubU8QAATBCWB7IrdLFVQDMUCNemIaU\ ciaQcOqBmJSjHUZFWN3a78_9600893AH6CQ9IFvFPZDaFD_DDZ\ CRtXNnRKhMGbGSpchRnYU`NWO26i8KShnnYh`NbOhWY`XSTXML\ YGMwNJpKHjHFcEkTibV`UWSLXJD8tDHdDQQMu3Jm6Ge9kzO_pJ\ OfFwAh_MSmDIiO6`R8TT9LWA8kqAfbCaPIcRF`JAlJBgGCbDOb\ cI_PlBL`JHPREo1JWIFHk`FdOTVsLXXRwMMnIHeEOCoINVhEP5\ 1u8CeBNQcDmVK`MROxUrlVg`WXPXM6F1i7o7dA9bBA`BCZB6c9\ 8aAA`ACZBOi8_`FS_DKZCCC8DI9DNADTBFhYEbMJNBHQBGTBEW\ BzzcsmURZKwcU9zU5rTgTk0hz } frm:DivideBrot5a { ; Jim Muth z=0, c=pixel, a=real(p1)-2, d=real(p2)+16 b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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Fractint's status
by Bob Lester 27 Sep '08

27 Sep '08

Greetings all! I've just subscribed to the list and am wondering what Fractint's status is as far as Windows Vista goes. I've watched the program's webpage over the years and there doesn't seem to have been much movement from V 20.0 for quite a while. I used earlier versions of Fractint quite a bit back in the day, when DOS was still a major player. I've not tried using the program at all under 'recent' (i.e., Win95/98, 2000, XP and now Vista). Is there a version that will work under Vista? I would really like to start using the software again! Thanks!! Bob Lester

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FOTD 27-09-08 (All in the Details [7])
by Jim Muth 26 Sep '08

26 Sep '08

FOTD -- September 27, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's image is a shallow dive into the FOTD image for Sep 18 -- "Beyond the Unknown" . I have changed the colors, rotated the frame, and increased the magnitude. The result is an image that in my opinion rates a 7. I named the image "All in the Details". I can give no logical reason for choosing such a name; I simply liked it. Like its September 18 parent, today's image consists totally of 'inside' stuff made visible by the 'atan' inside fill option, an option that usually creates so much chaos that I rarely use it. This option works quite well in today's image however. The calculation time of just over 4-1/4 minutes gives ample time to ponder the mysteries of the fractal universe while the image is rendering. Those who prefer to avoid the pondering may view the finished image instantly on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds and light drizzle made Friday unpleasant here at Fractal Central. The fractal cats slept through a good part of it, so they were not bothered. In my department, things went reasonably well, which is as good as can be expected. If I can avoid another antiquing expedition on Saturday, the next FOTD will be posted in 24 hours. If not, the FOTD may not appear for 36 hours. Until next time, take care, and don't worry yourself with the unknown until you have mastered the well-known. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= All_in_the_Details { ; time=0:04:16.29-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5a passes=1 center-mag=-0.60223402872641/+0.012787950234423/\ 2462.961/1/85/0 params=-1.1/0.5/1000/0 float=y maxiter=650 inside=atan periodicity=10 colors=000wn`vq`us`tv`sx`nq_ij_dc__X_VQZQJZLCZH5ZL\ A_OE`RJaVNbYSc`WcfMhlCmr3qn9pjFpfLpbRpZXpWbpRf_MjK\ Sp`Yupczz`zzYzzVzzrzzpzznzzlzzjzzhzzfzzezzczzazz_z\ zYzzWzzUzz7zzAzzCzzFzzHzzKzzMzzPzzRzzbzz`zz_zzYzzX\ zzVzzUzz8zzCzzFzzJzzMzzQzz5zz8zzBzzEzzHzzKzzNzz7F0\ 8E09E0AD0CC0DC0EB0EA5GAAIBKKBWOCcP0cRDsUUz006000PP\ rOTo1P_000cczbZutZzuQzuHwv8sv0po6mhCkaHigPdmW`sbXz\ zzI6pHBrGFtFJuERmDYeCdYOWS`NLmEEz47x47u37r27p27m17\ j080tVUs`xrfqpXinNgoMepLbrJ`sIYuGWvFTxDTpEUhGV_HVS\ JWJKXBMY2OO2NE2L31JyjBvoIstQpzYMh6z_nx`nubnsdopfom\ hokjphlpenqhcilT`j`ZghXepVbyTbtTanTahT`bT_YT_STZMT\ YGSabPfzLjwPnsTroYnnXjlVfjTahRYfQUdOQbML`KX_MiYOvW\ RrWNmWJhWEdWA_W6VX1ZZ9caHgcQlfYpheuknueiuZduSZtMUt\ FOt8Js1Do6GkCKgIOcOR_UVV_ZYdWaiSenPisLmyHltKkoOijR\ heVg`ZeWadRebMicRldXoefvfmzccq`Rl8OZ9IUBBQHA7O99V7\ B`6Cg5Es3GuBElJCfMAmZ8zmY } frm:DivideBrot5a { ; Jim Muth z=0, c=pixel, a=real(p1)-2, d=real(p2)+16 b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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FOTD 26-09-08 (Lost in the Circle [No Rating])
by Jim Muth 25 Sep '08

25 Sep '08

FOTD -- September 26, 2009 (No Rating) Fractal visionaries and enthusiasts: Today's not-quite-super image lies in the parent fractal that comes about when Z is combined with 10 parts of Z^(-7) and (C) is added. This parent fractal resembles a circle that is trying to morph into a Mandelbrot set. Off the screen to the west of the morphing circle lies a huge scalloped blob, with smaller blobs between it and the circle, all of this connected by a spider-web network. Today's scene, filled with blobs, lies in this network. I named the image "Lost in the Circle". I must have had a good reason for chosing this name. I gave it no rating because I neglected to give it the coloring work it deserves. The calculation time of 22 seconds needs no excuses. The calculation moves faster than light and as a result finishes before it starts. It will take slightly longer than this to go to the FOTD web site and view the image there. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The following O.T. diversion is strictly 'in my opinion'. I began the day Thursday reading in SciAm magazine that the 'big bang' may be out, replaced by the 'big bounce'. When I mentioned it to FL, she made some casual comment about reality. I have forgotten the innocent comment, but the rambling line of thought it brought about is still going strong. Big Bang or Big Bounce? How do we even know what exists at the present time, much less what existed 13.7 billion years ago? And what of all the other strange stuff? What does existence mean? Does the supernatural exist or is it an impossible dream? Are fractals real or are they supernatural? The answer appears to depend on the definition of the word 'supernatural'. My view of the word 'supernatural', as well as the similar word 'paranormal', is that both words are merely wrong classifica- tions. Something truly supernatural or paranormal is impossible. Everything that exists must in some way be natural or normal. The difficulty arises because we have such a limited grasp of the full extent of the natural (normal) world. I strongly believe in the existence of many of the so-called supernatural or paranormal phenomena such as psychokinesis and ghosts haunting buildings, and (gasp) even conscious spirits of the dead. But I do not consider these things supernatural; I consider them to be fully natural things not yet understood and incorporated into the natural world. By contrast, I am sometimes called an Atheist because I doubt the existence of the familiar god-in-the-sky of conventional religion. To me, this god is as much a mental construct as are the various interpretations of the quantum phenomena. Yet I do believe in a universal creative power. If one wishes to call this power something more 'scientific' such as the energy of the vacuum, so be it. But to be considered the God of the universe, this power must be conscious. Actually, the problem is our limited concept of the extent of the natural world. Things that are considered supernatural in one century are well understood and considered perfectly natural in the broadened concept of the next century. And we will always have skeptics to guard us from excessive broadening. I'll only briefly mention the aliens from outer space who are supposed to be visiting us. Here I turn skeptic. An alien in a space ship is something I must see with my outer senses before I can take the claims seriously. Thickening clouds marred the sky here at Fractal Central on Thursday, but the temperature of 70F 21C was close to perfect. The fractal cats watched proudly from their window shelf all morning, satisfied that the seven stray cats that were hanging around yesterday have moved on for good. (I am not so sure they are gone for good however.) My day was moderately busy and very thoughtful. The FOTD turned out moderately good. The next FOTD, hopefully better, will be posted in about 24 hours. Until then, take care, and heed the skeptics. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Lost_in_the_Circle { ; time=0:00:22.39-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident center-mag=-0.651456440912045/+0.1830358557352468/\ 91605.68/1/-64/0 params=1/1/10/-7/0/0/0/0 float=y maxiter=1000 inside=0 logmap=21 periodicity=10 colors=00000AJGLJ7AM9RPBNRDJUFGXHCXJ8WL4SN0hwseugf\ oefidfcbfYafS_gMZhHYiESiCNiAIi7Di58i33k67m9BnCFoFJ\ pHMoNKnTIiZHf`ccaye_ugZqiYmkXimWeXRTGNG0J3AI8JHCiN\ 5dOD_PLVPSRQ_MQfHRnDRuHQnLQgPQaTPVXPO_PIbOHeNHhMHk\ LHnKGqJGtIGwHGmCLd8QW4VN0ZM0aL0cK0eJ0gDFd7Ub1h`6fY\ BdWGbTL`RQZOVXM_VJcUHcXDcZAc`7h`El`Kq`Qu`WrZRpXNmV\ IkTEaQGTOHJMIAKJUXamitnfuocupaupZuqXurUurSuoWrlZoi\ alfdjchg`kdYnaVq_WoVWmRWlNXjJXhFXgBZbN_ZY`VhaRsZWr\ W_qUdpRhoPlnToiXqd`s_duWZs`TqdNohHnlMpfRq`VsW_tQcv\ LhwFlxAitGgpMdmSbiY_ecYbiVZoTWtWVrZUqaTodSngRljQkl\ PjoGdq8Zs0T_PSGmSBB1QL6dVBrdFffIWgKLiMAjOfLI`RLVWO\ Q`RKfUEkX9pZTd_kT_fQkbNwcTtdZqecnfikgnhhteiyblwdou\ fqshntdltaiuZguWevTbvQ`wNZwKcdFhMAm45iBEfIMcPU`WaY\ biViqSpycsdovKzx0yt3xp6wl9viCueFtaIsYLsVNqXRoZUm`X\ ka`iccgefffiggNgh0jj7mkDpmKsnQvpXxqbffWPWQJZJDaD7c\ 7VtiQkjMbjHUjDMjLkhIimJ_h } 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 25-09-08 (A Flawed Jewel [No Rating])
by Jim Muth 24 Sep '08

24 Sep '08

FOTD -- September 25, 2008 (No Rating) Fractal visionaries and enthusiasts: Between reassuring FL that the end is not yet nigh, pondering the fourth dimension, and finishing an unexpectedly large pile of work, I had less time to devote to the FOTD on Wednesday than I would have liked. But all is not lost. FL is reassured for at least a day that the end is not yet here, and the work is behind me. As for the fourth dimension -- that continues to puzzle me. Some things supposedly possible in 4-D space are logically impossible. I read recently in a book of four-dimensional geometry that when a hypersphere is subject to double rotation and the two rota- tions are equal, then all points of the hypersphere except the single point at the center move in a circle. The puzzle is what happens to the points at the centers of rotation of the circles. Are these points moving in circles also? The description of double rotation, says that they must be. But if they are, then the points circling them are being carried along, and not moving in perfect circles at all. As I said above, it's logically impossible. But one thing certain is that the fourth dimension is fascinating. It's too bad that, even though my mind is capable of pondering 4-D, I'll never get to see it -- at least not in this world. I will get to see more fractals however. In fact, today's image is a grossly overblown sample of one. I named it "A Flawed Jewel" because I feel it has potential, but due to the lack of time I was unable to bring out its full luster. As it is, the colors are far too gaudy, so much so that I dared not give the image a rating. Most of the gaudiness was achieved by rendering the scene with the outside set to 'real' and the inside set to 'fmod' with a proximity of 0.75. A good part of the image consists of this glorified inside stuff. The little minibrot at the center suffers from an insufficient maxiter, a flaw that is easily remedied at the cost of a little slowdown by raising the maxiter to 3600. With the maxiter at 1800, the image calculates in 2-1/3 minutes. A maxiter of 3600 adds about one minute. All such problems may be eliminated however by surfing out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoying the already-calculated GIF image posted there. After the early morning fog cleared off, perfect early autumn weather prevailed here at Fractal Central on Wednesday. Total sun and a temperature of 75F 19C can hardly be surpassed. The fractal cats' thrill came in the afternoon, when seven, yes seven, half-grown cats appeared in the yard next door. A half hour later the seven cats were gone and the fractal cats had settled to sleep. As stated earlier, my day was quite busy. Tomorrow will likely be slower. The next FOTD will appear in 24 hours. Until then, take care, and though the country is a clown show, don't lose the faith. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Flawed_Jewel { ; time=0:02:20.52-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-1.801058963211113/+5.410777958127436/\ 3.52828e+010/1/4/0 params=-0.88/-1/0.176/-5/0/-95/\ 0/0 float=y maxiter=1800 inside=fmod proximity=0.75 outside=real periodicity=10 mathtolerance=0.05/1 colors=0005g`DbXKZTRVQP`VNf_LldJriIwmJvlKvlLulMulN\ tlNtlmJ7IXdHS`GNYFJUEERD9ND5KH7PL9UPBYSCbWEg_GkcIp\ fJtcKsaLr_MqYNqWOpUPoSPoZWYeaHkg0ce6WdBObHGaM8`RBP\ XEDaEF`DG`CH_CJ_BKZBLZAKZ9KZ8KZ8KZ7JZ6JZ6JZ5JZ4IZ4\ IZ3IZ2IZ2HZ1HZ0HZ0HZj`DdYI_UMVQRPNWKJ`FGdGPYHXRIdK\ 4WX7ZYAaZDd_Gf`JiaMlbPncSldVjdYhd`fdcdefbei`el_ehY\ YdWRaUKTPTLKaDGiQP0VN2_M4dK6iJ8nHAsGCxFEuJCsMApP8n\ T7kW5iZ3ga2i_3kY3mW3oU3qS4sQ4uO4wM4rW3nd2jm1fv0`o0\ Vh0Qa0KV0EO09H0DF5GDAJBFM9KP8OT6QW5SaBQfHOkMMpSKuY\ IzbGxYFwUFvPEtLEsGDrCD`XEKpE49V9BUECTJDTOESTFSYGRa\ HRPZgDpxChtC`qCTnCLkCDhC5ezXwvVtsTroRplPniNleLjbJh\ _IfVJgRJgNJhIKhEKiAKiIgWGYIEO4DO3CO2CO1AUA8ZI6cR4h\ Z2mfHncWnajn_kockpfkqjkrmlsplttluwluzeouZipSckMZgi\ TsjTtkTulSqlRnlRklQhmPdmPamOZmOWA43FB8KHCONGPL`OMT\ OOKNQCNR4PNIQKVSGhTDub35XN4Rf4My4XyFgyPcqQ`jQXcRUX\ RQQSNJSKCSwpCw2miDiWNfIYc } 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 24-09-08 (Not a True FOTD [No Rating])
by Jim Muth 23 Sep '08

23 Sep '08

FOTD -- September 24, 2008 (No Rating) Fractal visionaries and enthusiasts: On Tuesday for some reason, FL fell into a state of near panic over the economy, (probably from watching too much doom-and- gloom TV), and by the time I got things settled down, it was too late for a real FOTD. But I did not want to miss the FOTD, so I decided to post an image that was intended to be a passing scene on the route to the real FOTD. I named it "Not a True FOTD" and gave it no rating. How could I rate an image that consists of merely two grossly mis-shapen minibrots? Actually the distortion is all the image has to offer. The main minibrot is so twisted that its buds are almost impossible to identify. The East Valley is obvious enough, but the Seahorse Valley lies on the upper left side of the main bay, where the period-2 bud is located. The really prominent valley sets off the southern period-3 bud, which is grossly distorted by the presence of a spurious hole. The large bud to the right of East Valley is actually the southern period-4 bud. All this being said, the image calculates in a blessedly brief 1-1/2 minutes. And the trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the completed image is also blessedly easy. One-hundred-percent wall-to-wall sunshine prevailed here at Fractal Central on Tuesday. When the temperature rose from 50F 10C at sunrise to 72F 22C at 4:15pm, the fractal cats voiced their approval by calling for their afternoon treat. My day was kept busy by discussing economics, a topic about which I have far too little knowledge. But then, I see by watching the news that I'm not alone in my ignorance. At any rate, the next FOTD will be posted in 24 hours -- that is unless the stock market crashes on Wednesday, when the FOTD could be delayed indefinitely while I try again to ease FL's anxieties. Until next time, take care, and if money is metaphysical, then it is nothing. Why then do we complain when we have too little of nothing? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Not_a_True_FOTD { ; time=0:01:28.49-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=t center-mag=-2.04951/7.75484/3.212379/1/127.5/0 params=1/-11/0.1/2/0/525/0/0 float=y maxiter=1800 inside=0 periodicity=10 colors=000myXlxWlwWlvWluWrbHncHjdHfeHefGdeHceHbdHa\ dH`dH_cHZcHYcHXbHWbHVbHUaHTaHS`HRZHQYHQWHPVHPVHOUH\ OUHNUHMTHMTHLTHLSHKSHISFKTHMWIOZKQaLSdMUfOWhPYjQ_l\ SanTaqSbpTcoUcnVdmVdlWekXejXfiYfhZgg_gf_he`idaicaj\ bbjack`dk_dlZelYfmXfmWgnVhoUioTipSjpRkqQkqPlrOmrNn\ sMnsLotKptJpsLorMnqNmpOloPknQjmRilShkTgjUfiVehWdgY\ dfZce_bd`aca`bb_acZ`dY_eXZfWYgVXhUWjUVkTUlSTmRSnQR\ oPQpOPqNOrMNsLMtKLuJGwGIvIKvJLuKNuMPtNQtOStQUsRVsS\ XrUYrV_qWaqYbqZdp_fpagobiocjpejodjndjmdjldjldjkdjj\ djidjhdjhdjgdjfdjedjedjddjcdjbdjadjadj`dj_djZdjYdj\ YdjXdjWdjVdjVdjUdjTdjSdjRdjRdjQdjPdjOdjNdjNdjMdjLd\ jKdkIcjKdiLeiMehNfhPggQggRhfShfTieVjeWjdXkdYkcZlb`\ mbamabnacn`eo`fp_gp_hqZiqZkrYlsYmsXntXotPnfImTBlF1\ i03j14k16k27l28l3Am3Bm4Cn4Eo5Fo5Gp6Ip6Jq7Kq7Mr8Ns8\ Os9Qt9RtASuAUuBVvBWvBSpAOjALdAHZADTAANA6HAsAy3BA8G\ DDLFHQHMVJQ_LVdO_iQcnShsU } 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=========================================

2 1

FOTD 23-09-08 (Safe at Home [7.5])
by Jim Muth 22 Sep '08

22 Sep '08

FOTD -- September 23, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: The fourth dimension is all around us, but because we look in the wrong direction, we can't see it. Then we protest that there are no more directions out there for us to look in. And this explains the difficulty. Instead of looking out there, we must look within, into our minds, which is where the fourth dimension, whatever it is, intersects our three-dimensional space. After years of looking within, I have created a mental four- dimensional hyper-planet, which I sometimes explore when sleep eludes me. Exploring this planet one 3-D section at a time is a far more efficient way of falling asleep than counting sheep. Sometimes, while traveling around the equator of my hyperplanet, I can almost form an image of the whole hypersphere. As I progress westward, I can see the polar great circle, which is the axis of rotation, appearing to turn on itself, all points of it always 90 degrees from wherever I may wander on the equator. At the same time, the equator can be the axis of rotation of the polar circle, resulting in the strange motion known as double rotation, a motion that can exist only in spaces of four or more dimensions. I am not sure what would be the apparent motion of the heavenly bodies as seen from the surface of a 4-D planet in a state of double rotation, but I suspect it might resemble a 3-D helix. One thing totally certain is that today's image has a minibrot at the center, and lies in the fractal that results when the formula Z^(1.9)+C. is iterated 8.7 turns up the logarithmic ladder with no function applied. When I named the image "Safe at Home", I might have been thinking of the Orioles baseball team, which I still listen to on the radio. I was definitely thinking of the coloring when I rated the otherwise humdrum image at a 7.5. The calculation time of 1-2/3 minutes will give the eager fractalist little time to think of anything else. And as always, the finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Persistent clouds blocked the sun here at Fractal Central on Monday, but the temperature of 70F 21C was near ideal. The fractal cats must have agreed, for they spent an unusually long time on their shelf in the side window, watching for any stray cats that might wander by. My day was rather good. The work was out of the way just after lunch, and the fractal is at least adequate. The next FOTD will be posted in 24 hours. Until then, take care, and live life in the hyper-reality of 4-D. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Safe_at_Home { ; time=0:01:39.33-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.6619148328728458/-0.66194260281007/\ 2.045298e+010/1/-100/0 params=1.9/0/8.7/0 float=y maxiter=2200 inside=0 logmap=147 periodicity=10 colors=0000300400500600700800901A02B03C04D05E06F07\ G08H09I0AJ0BK9CLEDMIENLFOOHRRIUUKXZL_cNahOdmQgrRjv\ TmzUpzWszXpzQmzKezDWz7Sz6Qz6Nv6Kr6Gm6Eh5Bc58Z56U53\ P51L83JB4IE5HH6GK8FM9EPADSBCVDBYEA`F9mG8rI9vJ9zP9z\ U9zZ9zP9zQ9wR9mNEcIIUDMTDQTIUTNYSSYSSUSSURSURSURKU\ PKUNKUMKUKKUJKUHKUFKUEKUCSUBRUFSUJTUNUURUUVVTZWTbX\ SfXRjYQnZPqZPnXTkVXiT_fRccPgaNjZLnWJrUHuSJqQLmONiN\ OfLQbJSZHUVGVSHXQIYOIZMJ`KKaJKbHLcFMeDMfBNgAOh8Oj6\ Pk4Ql2Qm1Pj2Oh2Ne2Mc2M`2LZ2KX2JU3IS3IP3HNzGKzFIzFG\ zBCz79z46z3Gz2Qz1_zkNz_TzOZzCdza3zJPzIFziQzVXzGcz`\ qzc7zRKzEXzcYzShzyUzd_zLdztezffzTgzFhzc5zKQzVozLmz\ BkzY`zTezUYzVQzWIzXBz`CzdDzhDzbCzYCzSCzNCzMGzMKzMO\ zl_z`bzJgzPdzDgz2jz1izAGzZ0zINzjXzvmztlzfkzTjzFizE\ IzAPz7Wz4bzGHzCPz8Wz4bzr9zdJzSSzE`zMAzBSzd_zVbzLdz\ BgzyWzOMzISzCYz6cz5Uz8Cz4TzLhz15z1QzKkzFjzAjz5izpn\ zLazEdz7gz5`z3ezkjzmlzpoz } 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=========================================

1 0

FOTD 22-09-08 (Almost an Elephant [?.5])
by Jim Muth 21 Sep '08

21 Sep '08

FOTD -- September 22, 2008 (Rating ?.5) Fractal visionaries and enthusiasts: Today's image lies in the pseudo-East Valley of the parent fractal that results when the formula Z^(1.9)+C is iterated 66 levels up the logarithmic ladder with no function applied. (I'm not sure how the various functions make the mathematics any more accurate, but they sure do add to the variety of fractals.) I could not decide on a rating for today's image, so I finally let it go with a question mark plus 1/2 point for the effort I put into smoothing the palette of only 256 colors. Sometimes I look at the FOTD fractals I create and feel like I'm living in the past. I'm still enthusiastic about the type of fractals that were being created in the late 1980's. Then I feel like a total anachronism, a lone scientist in a makeshift laboratory, with wires clumsily hooked up to batteries, search- ing for the most efficient filament to put in an incandescent light bulb, while the rest of the world has moved on to far more efficient light-emitting-diodes. But what the heck -- finding fractals uses so little energy that it may actually help us out of the latest what's-up crisis. I named today's image "Almost an Elephant" because it is located in the trunk of an East-Valley elephant that is only 90-percent there. The calculation time of 1-3/4 minutes is brief by any standard. And the trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the completed image is ultimate convenience. Sunday here at Fractal Central began with fog, but with a strong sun, the fog cleared off by 10:00am, leading to a most pleasant day, with tons of sun and a perfect temperature of 77F 25C. The fractal cats were distracted for a few minutes by the crows that gathered in the yard to finish off a bag of cheesy corn curls, then the duo settled for a nap on their shelf in the sun. My day was average, which is all that need be said. The next FOTD will appear in 24 hours. Until then, take care, and be fractally frugal with our limited resources. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Almost_an_Elephant { ; time=0:01:44.40-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.0534895390843374/+0.239156045629176/\ 1.700906e+007/1/52.5/0 params=1.9/0/66/0 float=y maxiter=1800 inside=0 logmap=125 periodicity=10 colors=000ugstgrsgqrgpqgoogomgokgoifoffndenaenZenX\ dnUdnSdnQelPekNfjMfiLghJggIgfHheFhdEicDibBjaAj`9j_\ Bk`DlaFmbGncIodKodLmcOkbRh`TeYWbWZ_U`XRcUPfRMhOKkL\ InGFqDDs9As68p36m68i9AeCBcFD_IEWMGSOHORGKUGIYFH`FL\ dFOgESkEVoEZrDauDdvDetEeqEenEekEehFeeFebFe_FeXGeUG\ eRGeOGeLHeIHeFHeCHdFLdHPcKTcMXbO`bRdaThaVl`Yp`_t`a\ xPTsELnGNmHOlIQkKRjLTjMUiNWhPXgQZfR_fSaeUbdVdcWebX\ fbi3p06sGOiSGcTLbUQaVVaW_`ZWCYYHX_MXaRWcWzf6teCoeH\ jeMedR`dWbCnaGl`Kj_NhZRgYVeXYcWaa1EG8KLEPPKVTQ_Xfv\ PnwSiqOdkK`fGanZavpPYaDAOEITEPXEW`EceEjiEqmExqTqmf\ jitcfUgP4k8CjEJiKRhQYgWdfabe`ae``e`Zd`Yd`UabXd`VcQ\ WdTWdWWdZCI`MU`ioxgmtekqcjmahj_gfY`cIWHKXKMYMOZPP_\ RR`UTaWVbZYeYXhZXkZXn_Xq_Wt_Ww`Wz`YzIXzMXzQWzUWzYz\ z6zzAzzEzzIzzMzzQzzUzzYzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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=========================================

1 0

FOTD 21-09-08 (Divided We Prevail [8.5])
by Jim Muth 20 Sep '08

20 Sep '08

FOTD -- September 21, 2008 (Rating 8.5) Fractal visionaries and enthusiasts: I somehow got involved in another 'antiquing' expedition on Saturday, this one to a tiny town named Richfield. And I must reluctantly admit that I am actually starting to enjoy these weekly trips to examine the stuff someone else no longer wanted. We got back to FC by 5pm, which left barely enough time to do the FOTD. As for that FOTD, it turned out surprisingly good. The parent fractal is the Mandeloid that appears when the formula Z^(1.9)+C is iterated 22 levels up the logarithmic ladder when no function is applied. Today's scene is located in a wedge-like valley leading to a large bud, where the fractal is divided to an unusual degree. Due to the fortuitous coloring, the image is one of the better ones I have yet found in the exponent range between 1 and 2. The rating of 8.5 includes the 1/2 point for my coloring effort. The name "Divided We Prevail" hints at the discontinuities that fill the frame and actually create the patterns. The calculation time of 2-1/2 minutes is about what would be expected for such an image. This is about the same time that is required to surf over to the FOTD web site and view the finished image there. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Thick cirrus clouds occasionally dimmed the sun here at Fractal Central on Saturday, but the temperature of 73F 23C was as perfect as could be hoped for. The fractal cats must have agreed, for while we were out, they spent the afternoon in the window, wishing they could go out with us. My day was spent doing my duty, which isn't all that bad. The next FOTD will be posted in 24 hours or so. Until then, take care, and don't let the fourth dimension abstractions leave you all abstracted. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Divided_We_Prevail { ; time=0:02:24.41-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.547729219193736/-0.6087350590135784/\ 228263.9 params=1.9/0/22/0 float=y maxiter=2400 inside=0 logmap=267 periodicity=10 colors=000C6HC7HC8HD9HDAIDBJDCKHDKLCKPBJT9IW8H_7Fc\ 5Eg4Ck3An28rILuXYrX`oXcmXejXhhXkeXmcXp`XsZXub`vffv\ jjvnrwwwwzzzwwwurstrqtrptrnsqlsqksqirqgrqfqpdqpbqp\ app_ppYppXllWihVfdUc`T`XSYTRVPQSLPPHOMDNJ9MHBLGDLF\ ELEGLDHKCJKAKK9MK8NJ7PJ6QJ5SJ4TJ6SL8SMASNCSPESQGSR\ ISSKSUMSVOSWQSYSSZUS_WS`UT_ST_QU_OUZMVZKVZIWYGWYEW\ YCXXASX8UX6cW4mW2cW0ZW4TM7NDNJTbFgiEjpDmwDpsMnpVml\ clilkfujcrk`plZnlWlmTjmRhnOfnMdoJapG_pEYqBWq8Ur6Sr\ 3Qs1Os9RpHTmPWjXYgd`dlbasdZUkK4r5QqCkpIiqKhqMgrNer\ PdrQcsSbsT`sV_tWZtYYtZKqR7oK9nLBnMDnOFmPGmQImRKlSU\ lUUlVckWckXckYmkZmlYmlYzlKzmKzmKmeYznXznXcnXdoXeoX\ foXgmZhl_ij`jickghkfmkerkcvkbzk`zl_zmZzjazgczeezcg\ zbivbgscfpcdmccjcagc`dcZacYZcXWcVTcUQcSNcRKcPHcOEc\ NBcMAcM9cM9hL8hL7mL7mK6rK6vK5zJ4zJ4zJ3zK2zP2zU1zZ1\ zc0zc0zc0zc0zc0zc0zc4zc8zcCzcGzcJzcLzcMzcOzcPzcRzc\ zzczzczzczzczzczzczzczzcz } 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 20-09-08 (Another Minibrot [6.5])
by Jim Muth 19 Sep '08

19 Sep '08

FOTD -- September 20, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Let's face it, today's image is just another minibrot, so that's what I named it. True, the minibrot is a bit fancier than some, but it's still only a simple humdrum minibrot in a world of infinite fractal possibilities. The little fellow has paid the price for being so common-place by having his rating cut from 7 to 6.5. The parent fractal is a fairly typical oversized north-south string of large bays, with a prominent 'fan' opening east from the origin. It was created by mixing various portions of Z^(-1.45) and Z^(-5.5) than adding (1/C). Today's image is located in a tiny cut-off goldfish-shaped feature near the eastern edge of the parent fractal's fan. The calculation time of 2-1/2 minutes is fast enough to prevent boredom, yet slow enough to let the anticipation build. Of course, all this anxiety may be avoided by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Another perfect end-of-summer day shone forth here at Fractal Central on Friday. The cloudless skies, brilliant sun and temperature of 72F 22C were just what the fractal cats wanted. As for humans, we could use a bit more rain, but all-in-all, things have been going quite benignly here for the past several months. Unfortunately, the same cannot be said for other parts of the country. The fractal cats were more interested in the feline financial situation than receiving the weather they had wanted. My work day was as expected. I see no reason why tomorrow should not be a repeat or even better. The next FOTD will be posted in 24 hours. Until then, take care, and where does the money go when the economy goes sour and everyone loses money? If it simply vanishes into nothingness, then the world of high finances is based on a wispy metaphysical ideal, which if true, could explain some of the mystery of economics. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Another_Minibrot { ; time=0:02:27.96-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.984466593566174/+0.0997746718087592/\ 1.326004e+008/1/12.5/0 params=-4.5/-1.45/-0.5/\ -5.5/0/0/0/0 float=y maxiter=1250 inside=0 logmap=158 periodicity=10 colors=000PIGPHIPGKPFMPEOPDQPCSPAUP5WP2YP4_O6aN7cE\ 9e6Bg0Cu6AgC9jI8dO7_T5UZ4Pd3Jj2Eo19k4Bg6Dd8E`AGXCI\ UEJQHLNJMJLOFNQCPR8RT5TU8XXA__CbbEeeHihJlkLonNpqPn\ nRkkTfhVdeXZbZZ_`RYbNidJSfFPhBMj7Jl3Gn0Eoa5pc8qeAz\ gCzhEziHzjJzkLzlNzmPncQkbShaTe`UbZW_YXXXZUW_RV`OTb\ LScIReFQfCPgHLdMIaRFZVCW_9Td6Qi3Nm0Kc9SUH_LQgBcz2m\ z5mz8czBWlEThHPeKMbNJZQGWTDTSCSRCSRCSQCSQCRPCRPCRO\ CRNCQNCQMCQMCQLCPLCPKCPKCPIGOGJOFMODQOBTOAWOHSTOOY\ VLaaHfgEjfGkmHzmIzmJzmKzbLzbMzaNz`Oz`PzaNoaMobKnbJ\ nbIncGmcFmcEmdEidEeeEaeEZeEVfERfENfEKmBOt8Sz5W_PM9\ hDBdFCaHEYJFVKGRMIOOJKQKHRMDTNAVO7WVgbYf_`eXbdUecS\ hbPjaMm`Jp_HrZEuYBxX8zW6m4pg9haEaWJVQNNKSGEX99`28a\ 47a56a66a85b94bA4bC3bD2cE2cG1cH0cI0cJ4dL8dMCeNFeOJ\ fPNfQRgRUgSYhTahUdiVfiYijakjdnkgplksmnunqvoowpmwqk\ xrjxshytfyuervbkw`exZZyWTzUMzSGzQJzRLzRNzSPzSRzSTz\ TVzTXzTZzU`zUbzVdzVIzPKzO } 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 19-09-08 (Living Minibrot [7])
by Jim Muth 18 Sep '08

18 Sep '08

FOTD -- September 19, 2008 (Rating 7) Fractal visionaries and enthusiasts: A quick glance at today's parameter file will reveal a 'biomorph' entry. I'm not sure what this feature was originally intended to do. My guess is that the idea came from an old, now forgotten article in 'Scientific American' magazine, which showed how life likely develops along fractal patterns. The parent fractal almost isn't. Instead of appearing as a screen filled with interesting intricacies, it is little more than an almost impossible to find dot far off to the southwest of the opening screen, which is a disappointing blank. But in this dot lies a tiny Mandelbrot set surrounded by far tinier dots with far tinier M-sets at their centers. Today's image is one of these miniscule sub-Mandelbrot sets. The 'biomorph' feature supplies the cusps that fill the image. The name "Living Minibrot" implies that earth life might have developed along fractal patterns. The rating of a 7 seems about right for a moderately impressive image that calculates in a F.T.L. 32 seconds. The image, as always, is or soon will be posted for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Thursday began foggy here at Fractal Central, but the sun soon broke through, leading to a near-perfect day with blue skies, light winds and a temperature of 72F 22C. The fractal cats were more interested in the cats prowling around outside. My day is best described as rather good. The work went well and the fractal of the day is at least acceptable. The next fractal of the day (or is it the fractal of tomorrow?) will be posted in 24 hours. Until then, take care, and keep your cool. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Living_Minibrot { ; time=0:00:32.17-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-34.95007187798075/-26.2115596616193/\ 6.3263e+008/1/96.75/0 params=0.001/12/12/2/0/0/0/0 float=y maxiter=500 inside=255 logmap=19 biomorph=51 periodicity=10 colors=000GBYB4KUMOWUUZ`_`gecnlA22z_Iz8ztKloXhiidj\ hckfagUyOXDLfDOKBMG8KD6H93ZNMgOVzPzzQlLRNFVXAZf4cq\ UIHRCMa6Re0WRVESbGXLDcJDjHDqEELYPGh`ZOOgPZqQjEfmCZ\ ploRIVC9bA0k8YPBTUFXaH_hJcpMQNPRMaSMmTLzMcGHtJUXRY\ fdaqr_KJiHPsEVROFTQHVSJYKFfHHoEJxALH_G7lJqC1Va8_p2\ VHSe3wOJBMF9KA7XKNcGYjChr8sKLIEJN8HS2FXQnaBxAUIFYC\ Ha7Jf1LIKT9Gh0CxVIJ`CQf6Xl0cSbjYC9f14QPJQSQRVXvIN_\ VMibVsjdfEGw5KLxRvsEOTFLZIIdKFjNTc0oy9UMOZKZbIigGu\ SOBVP9YQ7MKNIGYEDh99sOKHMHLKEPIBUMWIHeOCoU5b3F_O3l\ _W2f_QUcoJRCXS0pVOJ`QPeSVkUaLC9F14RUDTaDVhDXpEYMIe\ KNmJSvHYfSVwXmLODFPC9QC3RBmLNTPOWSZZVibYu`dRlwdQSJ\ QYPQcVQi`NROKVZHZiNWIKeOHoUDy_XXJdfQlpXPHAOA7M33ab\ WmroMQLHUUDXa8`jRMOTKZVIiXGtZHLhBUJPWBRoUTEY_FafGf\ mHVVG_cJdkMjtPOJALE7JA4G51U`RZoeLINGDYB8g63rQU8Pa2\ aWCmeBHdAaUBma8o9HLL`GIxDAEOYOMhZKtjcYCrhA`PTkShwV\ xiwpcOY3`TWX`gOFyQILHNszz } 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] CHAOS
by JackOfTradeZ＠comcast.net 18 Sep '08

18 Sep '08

. ""Its a "normal" chaos, just like the financial situation in the US. Like a Lorenz fractal with 3 attractors: 1) Money, 2) Global Warming, 3) Idiocy in Politics. (...). "" I humbly beg to differ. The psychology of greed and money, as well as the perpetual idiocy in politics, is very orderly and predictable. Nothing chaotic there, no sensitivity to initial parameters. Gobal climate change is another thing .... Cheers JoTz .

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Re: [Fractint] Houston report
by Timothy Wegner 18 Sep '08

18 Sep '08

David wrote: > Good news for you guys, here's hoping things get back to normal, but I > wonder ... New Orleans still has a long way to go! The short answer is Houston has a huge number of trees down and power out over most of the city. Power is being restored fairly slowly. However Houston will recover fine. The coastal areas such as Galveston have been devastated like the worst areas in New Orleans and will take years to recover. My workplace (NASA) is apparently little damaged but has no power or water, so I am out until at least Monday. Very possibly won't have my own power back until then, but I walked over to the University of Houston campus to send this. UH has power and is open. Tim

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FOTD 18-09-08 (Beyond the Unknown [8])
by Jim Muth 17 Sep '08

17 Sep '08

FOTD -- September 18, 2008 (Rating 8) Fractal visionaries and enthusiasts: Today's image is a complete reversal of yesterday's. Though today's image is a blow-up of a small part of the lower left corner of yesterday's, it has none of the hellish malevolence. Instead of the fiery devilish effect, we have a peaceful almost heavenly effect, consisting almost entirely of various shades of blue. I can see no saints or angels in the scene, but who knows what we might find if we were to dig deep enough. Today's image is so different mostly because I evaporated the scene by raising the bailout radius to 1000 and rendered the resulting 'inside' stuff with the inside set to 'atan'. The result is an image that could almost have been taken through the space telescope. It is filled with stars and wispy fractal nebulae, with a few spirals thrown in to remind us that this is the virtual world of numbers, not the presumedly real world of the outer universe. I named the image "Beyond the Unknown". After all, this rather accurately describes most fractals. The rating of an 8 may seem liberal to some fractalists; to me it seems just about right. The calculation time of 4-1/4 minutes actually grows longer if any of the short-cut algorithms such as passes=g or passes=t are used. I guess the algorithms use too much time figuring what to do next and too little time calculating. But all these minor problems may be bypassed by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A foggy morning gave way to a sunny afternoon here at Fractal Central on Wednesday. The temperature of 75F 24C was just what the fractal cats ordered. In my department things were notably un-notable. Just to keep things un-notable, the next FOTD will be posted in 24 hours. Until then, take care, and walk with N. Lightenment, whoever or whatever he is. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Beyond_the_Unknown { ; time=0:04:14.80-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5a passes=1 center-mag=-0.60128109/+0.01548312/232.74/1/-137.5\ /0 params=-1.1/0.5/1000/0 float=y maxiter=650 inside=atan periodicity=10 colors=000bZutZzuQzuHwv8sv0po6mhCkaHigPdmW`sbXzzzI\ 6pHBrGFtFJuERmDYeCdYBlQAsI000IraRjzWkt_kldlehlYllR\ niQogPpdOqbNtgOhlKXpGLuCAy9EvCHsEKqHNnJQkMTiOWfRZc\ TaaWdZYgW`jUbpcYumUZciDUxGVsJWoMXkPYgSZcVZZY_V``Rc\ aNfbJibFffSdjcano_rzYnvXkqVglUdgTabRYYQVTPSOS9rQFm\ OKiMQdKV`I_WGeSEjNCoJEoNFoQHoTIoWJoZPlRUiJRdPO_VLW\ `IRfFNlCXe9fZ6pS4yL8sICnGFiEJdCM_AHYKDWU9Uc5Sl9LpC\ FtF8xI2zG4vF6qD8lCAgACb9EYGBbM9fS7jZ5nd3rj1ve0wa0w\ Y0wOJs6VHBSIGQIKOIPMITKIYIIaGIc4ygXgjyRbsSVnSOiSGd\ T8_T1VTMZVebXyeYxhZxk_wn`vq`us`tv`sx`nq_ij_dc__X_V\ QZQJZLCZH5ZLA_OE`RJaVNbYSc`WcfMhlCmr3qn9pjFpfLpbRp\ ZXpWbpRf_MjKSp`Yupczz`zzYzzVzzrzzpzznzzlzzjzzhzzfz\ zezzczzazz_zzYzzWzzUzz7zzAzzCzzFzzHzzKzzMzzPzzRzzb\ zz`zz_zzYzzXzzVzzUzz8zzCzzFzzJzzMzzQzz5zz8zzBzzEzz\ HzzKzzNzz7F08E09E0AD0CC0DC0EB0EA5GAAIBKKBWOCcP0cRD\ sUUz006000PPrOTo1P_000ccz } frm:DivideBrot5a { ; Jim Muth z=0, c=pixel, a=real(p1)-2, d=real(p2)+16 b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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Re: [Fractint] Houston report
by Timothy Wegner 16 Sep '08

16 Sep '08

Noel wrote: >Glad to hear that you and your family survived the storm without too much damage. Actually no damage of any kind for us personally. In my neighborhood it was a matter of where the trees fell - a few folks will have some repairs ranging from minor to major. But as you folks must be only too aware from news coverage, Galveston and many coastal places are all but wiped out. The surging tides do most of the damage in situations like this. In Houston, for the most part, we are just waiting for power to be restored. As of this morning about 75% of the greater Houston area was still without poweI'm writing this from Milby High School where my wife teaches. Power and air are on, and we just feasted from some left overs that would have otherwise spoiled in the freezer. I've got the laptops, cell phones, and mp3 players all charged up. However the school district will not reopen until Monday. My workplace, the United Space Alliance, did well despite being closer to the coast than we are. I'll be back at work Thursday at the soonest. Paul commented about Braes Bayou. We are indeed close but quite a bit higher. During Allison the bayou came over McGregor. This time not quite as high, but nowhere near us. Recently the Bayou was widened, which probably saved some friends. The lowest house along the bayou flooded last time but this time the water came right up to their steps. Tim

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Re: [Fractint] good news
by JackOfTradeZ＠comcast.net 16 Sep '08

16 Sep '08

. Glad you all OK Tim, I knew or thought some fractint people were in Houston but couldn't remember. "My workplace, the United Space Alliance, did well despite being closer to the coast than we are." What, I say WHAT is the "United Space Alliance" ?! Is that for real? Sounds like something from Star Trek!!! JoTz .

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FOTD 17-09-08 (The Dark One Rises [7])
by Jim Muth 16 Sep '08

16 Sep '08

FOTD -- September 17, 2008 (Rating 7) Fractal visionaries and enthusiasts: I never took the existence of the evil one very seriously, that is until behind me I heard FL exclaim, 'Oh my!', and saw the dark one himself leering from the screen. The scowling face is more noticeable at some distance from the screen. The prince of darkness, complete with his army of imps, came into being when I divided Z^2 by (Z^(-1.1)+0.5) or something like that, and set the bailout radius to a stingy 3. The resulting parent fractal is something I'm not going to try to describe, though it contains a Mandelbrot set stretched in the vertical direction, with two large semi-main buds attached to the single period-2 main bud. Today's scene, which is rota- ted 90 degrees, is located on the X-axis just west of the M-set. I named the image "The Dark One Rises". And the only place he could be rising from is the fiery pit. I rated the image at a 7, not because I admire the evil one, but because the image is a fractal, and a 7 is what I think such a fractal is worth. The calculation time of 1-1/3 minutes is brief, but not too brief for the duke of darkness to work his mischief. But all calculation may be avoided by going to the FOTD web site and viewing the finished image there. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tenacious clouds prevented the temperature of 68F 20C from being perfect here at Fractal Central on Tuesday. The fractal cats were having a good day until Cassie caught wind of a stray cat that had wandered onto the front porch. When Nicholas saw her bristled and growling in the window, he joined her, and together they chased the intruder away. I rewarded their bravery with an extra treat of tuna. They no longer get cheddar cheese, which their doctor said is not too good for cats. As for my day, it was close to average. And tomorrow promises to be the same. Until next time, take care, and at least I did not rate today's image at a 6.66. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Dark_One_Rises { ; time=0:01:22.54-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5a passes=1 periodicity=10 center-mag=-0.587139/0/68.88/1/90/0 params=-1.1/\ 0.5/-13/0 float=y maxiter=1800 inside=0 logmap=yes colors=000KF9LE9KEALDALCALCAMBANAANAAMBIMBQOCYPCeR\ DmSDuRHrQLoPPlOTiNXfM`cLd`KhYJlVIoTMjVQeXUaZYX``Sb\ dOdhJflEhoAipBfqBcrBasBZtCWuCUvCRwCOxCM`_dEzwCzzAm\ e8_X6KO4FG70I9NKulFzhGteHwaIsZJuVKsSLuOMrLNtHMrIOp\ JPoJQmKRkKSjLThLUfMVeNWcNXaOY`OZZP_UNaYP`aQ_eR_iTZ\ mUZqVYuWYtYWs_UraSqcQpdOofMohKnjImlGlmEkoCjqAis8it\ 6ft5dt5at5_t4Yt4Vt4Tt4Rt3Ot3Mt3Kt2Ht2Ft2Dt2Fr4Gq6H\ o8InAKmCLkEMjGNhIPgKQfMRdOScQVeTTbRS`PQZNPXLOUJMSH\ LQFJODILBHJ9FH7EF5DD4EIDFNM7SQFRUNQYVPa`KfaPebTdbX\ cc`bcdadh`dl_biZagZ`dZ_bYZ`YYYYXWXWTXVRXUPWTMWSKWR\ IWSKXTLYTNZUO_UP_TPZZbRYaS7ke7ke6hg6zz6zz5zz5zz5zz\ 4zz4zz4zzAzzFzzLzzQzzVzzgzztzzrzzpzznzzlzzkzzizzgz\ zezzczzbzz`zzZzzXzzVzzUzzlzzizzfzzczz`zzYzzVzzrzzp\ zznzzlzzjzzhzzfzzezzczzazz_zzYzzWzzUzz7zzAzzCzzFzz\ HzzKzzMzzPzzRzzbzz`zz_zzYzzXzzVzzUzz8zzCzzFzzJzzMz\ zQzz5zz8zzBzzEzzHzzKzzNzz } frm:DivideBrot5a { ; Jim Muth z=0, c=pixel, a=real(p1)-2, d=real(p2)+16 b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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Houston report
by Timothy Wegner 16 Sep '08

16 Sep '08

Some of you know I live in Houston. You probably know more about what's going on here than I do, but just to let everyone know my wife and I are fine. Many trees down in the neighborhood, but we have no damage. We are all cooperating getting each other back on their feet. My wife has power at school, so I decided to shoot off this message via dialup on the last few watt-minutes of battery, then shee can charge up. I'm guessing we will be without power at least several more days. The upside is a blessed cool front rolled in after the hurricane, so life is pleasant without power, and will be for at least a few more days. Tim Wegner

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FOTD 16-09-08 (Field of Fractals [5.5])
by Jim Muth 15 Sep '08

15 Sep '08

FOTD -- September 16, 2008 (Rating 5.5) Fractal visionaries and enthusiasts: The parent fractal of today's image is a routine Mandelbrot set that has been rotated about 180 degrees. But this M-set is anything but routine. To start, its formula is Z^(2.001)+C, and to finish, it has been calculated at a level 1.6 turns up the logarithmic hyper-ladder. Mandeloid fractals with fractional exponents of Z are usually intricately divided along the negative X-axis. In today's parent, the East Valley lies near the negative X-axis, so the East Valley area is where all the dividing takes place. The result is an image that bears no resemblance whatever to what one would expect in a scene from East Valley. In fact, the image bears no resemblance to anything in the classic M-set. It is something entirely new, almost like a fantastic flower garden. I named the image "Field of Fractals" and rated it a 5.5. I'm not totally satisfied with the coloring, so I couldn't rate it any higher. The calculation time of the included parameter file is 4-2/3 minutes, which is within reason. The image may also be seen and hopefully enjoyed on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> After a breezy Sunday night, Monday was near perfect here at Fractal Central. The mostly sunny skies and temperature of 81F 27C were just what the doctor ordered. Extra treats were just what the fractal cats ordered, and they gave us no peace until we delivered the goods. Otherwise, my day was uneventful. The next FOTD will be posted in 24 hours. Until then, take care, and if the ultimate reality lies within, where does within lie? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Field_of_Fractals { ; time=0:04:39.87-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-0.2908010563418544/+0.001787407398163/\ 2.0987e+007/1/-46.25/0 params=2.001/0/1.6/0 float=y maxiter=4200 inside=0 logmap=350 periodicity=10 colors=000QccQcbRbaRa`R`_R`ZR_YRZXRZXSYWSXVSWUSWTS\ VSSURSUQTTPTSOTRNTRMTQLTPKTPJUOIUNHUMGUMFULEUKDTJC\ UKDULDUMDUNEUOEUPEUQEURFUSFUTFUUFUVGUWGUXGUYGUZHU_\ HU_HU`HUaIUbIUcIUdIUeJUfJUgJUhJUiKUjKUkKUlKUmLUnLU\ oLTrKUpLUoLUmLUlLUjLUiMUgMUfMUdMUcMUaMU`NUZNUYNUWN\ UVNUTNUSOUQOUPOUNOUMOUKOZJPdHPjGPoEPrDPoBQkCPgDPeD\ OcEObEOaFN`GN_GNZHMYHMXIMWJLVJLUKLTKKSLKRMKQMJONJM\ NJKOIIPIGPIEQHCQHARH9SG8SG7TG6TF5UF3TE5UF6VF7WF8WF\ 9XFAYGBZGCZGD_GE`GFaHGaHHbHIcHJdHKdHLeIMfINfIPgIQh\ IRiJSiJTjJUkJVlJWlJXmKYnKZoK_oK`pKaqLbrLcrLdsLetLb\ yUdwcevmfttgszhqzipzjnzkmzlkzmjznhvogrpemqdhwbcxf`\ ydZzc_za`z`azZbwYcvVdtRetRftRgvQgrQhsQitQiuPjvPkwP\ kxPlyOmyOmyOnyPoxQoxRpxSqxTqxUrxVsxWsxXtxYuxZux_vx\ `wxawxbxxcyydzxeywfyvgyvizukztmztmzsmzrmzrmzqmzpmz\ pmzomznmznmzmmzlmzlmzkmzjmzjmzimzhmzhmzgmzfmzfmzem\ zdmzdmzPmzQmzQmzQmzQmzQmz } 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 14,15-09-08 (Eight Heptagons [No Rating])
by Jim Muth 14 Sep '08

14 Sep '08

FOTD -- September 14, 15, 2005 (No Rating) Fractal visionaries and enthusiasts: NEW FORMULA ALERT! The DivideBrot5a formula is a new one. And today's FOTD is good for two days. It's hard to be a fractal visionary when you're looking at the stuff someone else threw out, or a lot of wannabe-country stuff such as feel-good slogans, teddy bears and scented candles. (I think they call this stuff 'primitives'.) Maybe I'm insensi- tive, but to keep FL happy on Saturday, we went down to an old factory in Duncanon, where they once made Lightning Guider sleds, to look at the stuff there. (I'm ashamed to admit that some of the stuff actually brought back pleasant old memories.) But regardless of how I felt about the expedition, when we got back to FC, it was after dark, and I had no time to do the FOTD for Sep 14. All is not lost however. The FOTD for September 14 is combined with the FOTD for the 15th, and is here now in its full glory. (No claims are made as to the amount of glory.) It's a scene in the fractal that results when Z^2 is divided by something like (Z^(-0.75)+1) with the bailout radius set to a chokingly small value of 2. Look at it and like it, or look and laugh, the image is very fast, calculating in 49 seconds. I named it "Eight Heptagons" for obvious reasons. I gave it no rating however, but if I had rated it, I would probably have given it a 5. The easiest way to see the image is to give Paul a chance to post it, and then to view it on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Saturday here at Fractal Central was a partly cloudy and plea- sant day with light rain in the evening. Sunday was unusually warm, with a temperature of 88F 31C, which would have been warm even in July. The fractal cats slept through most of the in- action. Once I survived the antiquing expedition, (It really was not as tortuous as I put on.), the rest of the week-end was easy. The next FOTD will be posted in 24 hours, and it just might be pretty good. Until next time, take care, and reality is all around you. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Eight_Heptagons { ; time=0:00:48.94-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5a mathtolerance=0.05/1 center-mag=+0.1439816637241745/-1.048371371384964/\ 5.851476e+010/1/-50/0 params=-0.75/1/-14/0 float=y maxiter=1500 inside=0 logmap=176 periodicity=10 colors=000UHKUMKUKKULKbPNTKOUNPhZQcUQZUOUQN9GMB1L9\ 5O89Q6DT5HV6IP7JJ8KD9L8MZHZlPjzXhsVfmUdgTcaSaWR_QQ\ YKPXEORLPLSQGZQISRKLRMESO7SP1SO8XNE`MLdLRhKYmJcqIj\ uHpyMqpQrgVs_ZtRcuJgvAkv2feHaQWYAidKdjT`qaXwjTphSi\ fSbdSXbSQ`RJZRCXR6VRRUMjUI_ZGPcFFhEDbNCYWBSdANm9Iu\ 11KLEScR_PYPLUZHRgDNp9Ky7Us5cn3mi1vdgrgfibe`YeSTdJ\ OdBKcNEbZ9bi4Xg3Re2Lc1Fa09_0BcADfJEiSGl`HoiFlfDjcC\ h`AfY9dWEgZIj`NlcRoeWrg_tjdwlhyneujbqf_mbYi_VeWSaS\ PYONVLPWPRXTTYWUZ_W_cY`f_aj`amYemWimUlmSpmQsmZnnfi\ oodpw_qggoSonRgoQ`oPToOMoNFo8ES9KTAQUY_XX`_Tb`Pc`M\ e`IfaFhaBia8ja6iZ5iX4hV3hS2gQ1gO6bRAYUETXJO_NJbREe\ VAhYFd`K`cPXfTUiYQlbMogIrkFslIsmLsnNsoQspSsqVsrXrd\ PrSIqFBq24p79oBDnFImJMmNQfUZ_`fTgnMnvZQ2UdEQsPOtMM\ uKLvIJwGIxEGyCFzAIzELzHOzKRzNUzQXzT_zWazZZzaWzdTzg\ QziNzlKzoHzrEztFzoGzkHzfIzbJzZQz`XzbozyjztfzobzjZz\ eVzaPzbJzbDzb7zb1zbHzWMza } frm:DivideBrot5a { ; Jim Muth z=0, c=pixel, a=real(p1)-2, d=real(p2)+16 b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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FOTD 13-09-08 (Colorful Menagerie [5])
by Jim Muth 12 Sep '08

12 Sep '08

FOTD -- September 13, 2008 (Rating 5) Fractal visionaries and enthusiasts: What results when Z is subtracted from Z^3? A fractal that resembles a bloated honeybee mooning a sunflower, which, if it existed, would be located just beyond the right edge of the frame. In the center of this fractal, four very thin valleys form a spidery letter 'X'. Today's scene is located rather deep in the valley forming the northwest arm of this 'X'. I could rate the image no higher than a 5 because it doesn't appear to be worth the excessive calculation time of 24 minutes caused by the unusually large iteration count of the elements. The lowest count in the entire image appears in the upper left and lower right corners. It is over 2700. I did not use the logmap with this image however, since it squeezes the colors too close to the central minibrot. I named the image "Colorful_Menagerie" because I didn't want to mention the bee mooning the unseen sunflower. This leaves only one problem to be settled -- that of the too-long calculation time. But this frustrating wait may be avoided by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the image in finished form there. An all day rain and temperature of 68F 20C made conditions less than ideal here at Fractal Central on Friday. The two fractal cats ignored the weather as they took it easy, while my day was spent doing a lot of nothing. The next FOTD will be posted in 24 hours. Until then, take care, and look for the right light. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Colorful_Menagerie { ; time=0:23:59.03-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident center-mag=-0.07911857351156/+0.078788632004786/\ 4.032995e+009/1/-102.5/0 params=1/3/-1/1/0/0/0/0 float=y maxiter=250000 inside=0 periodicity=10 colors=000mQ_kS_iU_gW_eY_c__aa_`c_lNmx7zy8yy9xy9wy\ AvyAuyBtzCszCrzDqzDpzEozEnoFjdGfVGcbOViWMqcDxj4uk5\ sl6ql7nm8lm9jnAhoBeoCcpDapE_qFXrGVrHTsIRsIQoHPlHOi\ HNeGMbGL_GKXFJTFIQFHNEGKEFGEEDDDADD7DGBFIEGLHHNKIQ\ OJSRKVUMXXN_`OacPdfQfiRgkPhlOinMjoLkqJlrImtGnuFovE\ puHpuKquMquPruRrtUstXstZttattcrsZprVoqQmqMkpIjoDhn\ 9gn5jmElmNnlWpldohaoeZnaXnZUmVSmSPlONlLKkHHkEFjACj\ 7Ai37i05f16d26b36`46Z56W66U76S86Q96OA6MB6PACR9IU8O\ W7TY6Z`5db4jd3of6ng8nhBniDnjGnkInlKnnNmoPmpSmqUmrX\ msZmt`mLVoWUjfTeqTasggtulotgksbgrYbqTZpPVoKQnFMmAI\ l6Im8Im9InBInCIoEIoFIpHIpIIpKIqLIqNIrOIrQIsRIsTIsU\ MlZPebS_fUXcVVaWTZXRXYPUZNS_KP`INaGKbEIcCFdADfEFgH\ GhLHjOIkRJlVKmYLo`MpdNqgOrjPbWaNHm83y4Tg1qQ5oO8nMC\ lKFkIJjGMhEQgCTfAVc9W`8YY7ZV6`T6aQ5cN4dK3fI3gF2iC1\ j90k70RPU6fv8biA_XBXKAZJ9_J8aI7bI6dI6eH5gH4hH3jG2k\ G2lG4hIxE_vG_tI_rK_pM_nO_ } 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 12-09-08 (The Low One Dances [7])
by Jim Muth 11 Sep '08

11 Sep '08

FOTD -- September 12, 2008 (Rating 7) Fractal visionaries and enthusiasts: I named today's image "The Low One Dances" for both mathematical and poetic reasons. To begin, the exponent of Z in today's formula is 1.067, certainly on the low side, and hardly an exponent expected to produce an interesting fractal. And the torpedo-shaped minibrot in today's image certainly has every reason to be dancing in triumph. The parent fractal is shaped somewhat like a letter 'A' lying on its right side, with today's tiny minibrot located near the egde of a debris field, some distance southwest of the main open area. The rating of a 7 indicates a typical FOTD of average quality. Due to the very large maxiter of 150,000, the calculation time is a rather slow 16 minutes, leaving it to the individual fractalist to decide whether to run the included parameter file or go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and see the completed image there. Typical late-summer weather prevailed here at Fractal Central on Thursday. The thin clouds and temperature of 72F 22C were typical of this time of year. The fractal cats were more concerned with squirrels gathering nuts in the yard than the central Pennsylvania weather. In my department things progressed smoothly. FL's flowers have pretty much recovered from the beating they took in the storm on Tuesday morning. If all goes well, and I see no reason why it should not, the next FOTD will be posted in 24 hours, give or take a few. Until that enlightening moment arrives, take care, and the answers to all questions are written in the fractals. All we need is someone to decipher the fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Low_One_Dances { ; time=0:16:34.92-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=t center-mag=-7.525986636550791/-3.471416076886081/\ 4.64746e+010/1/52.5/0 params=1.067/0/0/1500 float=y maxiter=150000 inside=255 logmap=424 periodicity=10 mathtolerance=0.05/1 colors=000PPEQQFSRFTRGVSGWSHYTHZUI`UIaVJcVJdWKeXKf\ XLgYLhZLiYNjXPkWRlWSmVUnUWnUXoTZpS`qRbrRcsQetPgtPh\ rLlqHopDroAujBmeBf`B_WBTRBMMBFIB8ME9QHAUKBYNCaQDeT\ EiWFmZGqaHudIxgJteIpcIlaIi`IeZIaXHYWHVUHRSHNRHJPGG\ NGCMG9ZH8KG4IGtIBhHCYHDNHECHFGRzFQyFQwFQvEQuEPtEPs\ DPrDPqDPpCOoCOnCOmBOlBNkBNjANiANhANg9Nf9Oe9Pd8Qc8R\ b8Qa7Q`7Q_7QZ6PY6OX6OW5NV5NU5MT4LS4LR4LQ3KP3JO3JN2\ JM2JL2HK1HJ1HI1HHnvrgpmakhWfcQaZJWUDRP7MKBB8AC9AC9\ AChUC99Ch9DhUDAUDh8DhUDhUDBUEB7EB7EZ6EZ6EZ6EZUFD5F\ Z5FZUFD4FE4FZ4GE3GZUGE3GZ3GF2GZ2HF2HG1HG1HH1HHmmJm\ nKmoKmpKmqKmrKmsPmtUmuZmvcmwhmxmmymmzmmzmczmUzmUzm\ czmczmczmczmczmczmhzmmzmmzmrzrvzvzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzcmw } 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 11-09-08 (Age of Iteration [6.5])
by Jim Muth 10 Sep '08

10 Sep '08

FOTD -- September 11, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: The complex logarithm is multi-valued. To take advantage of this, the MandelbrotBC (Branch-Cut) formulas are supposed to make visible all the fractals that result from the infinity of values that may be given to the 'k' part of the logarithm. This situation exists because the formula for the complex logarithm is: (1/2)ln(x^2+y^2)+i(atan(y/x)+2kpi) where the value of 'k' may be given any value from plus-to-minus infinity. I am not sure if any of the MandelbrotBC formulas calculate the different values of 'k' correctly, or even if a correct way actually exists. In fact, I'm not even sure of where to look to find a correct way. The correct way, if one exists, would probably fall in the field of 'complex variables' or something like that, but information on 'complex variables' is not easy to find. One thing I am sure of however is that the MandelbrotBC formulas, with the various functions applied, make some incredible fractals, so who cares if the images are mathematically correct. Today's image lies in the Z^(1-2/3)+C Mandeloid as it appears 83 levels up the logarithmic ladder, with the 'floor' function in effect. At this level, the Mandeloid somewhat resembles a distorted Mandelbrot set standing on its nose. The scene is located deep in the chaos on the western shoreline of the large period-2 bud, which is actually shaped rather like a nose. The minibrot at the center of today's image suffers from an insufficient maxiter, but its surrounding pattern is unusually well-defined for a minibrot in this range. All things considered, I rated the image at a 6-1/2, not quite as high as I would have liked, but high enough to make the calculation worth the 4-1/2 minutes required. The name "Age of Iteration" has no significant meaning. I simply pulled it out of the air. Finally, if all else fails, the completed GIF image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> In comparison to Tuesday, Wednesday's weather began peacefully here at Fractal Central, with singing birds and wisps of fog hanging over the river. When the fog cleared away, we were left with a day of mostly clear skies and a temperature of 72F 22C. The fractal cats purred approval, then meowed for breakfast. After such a hectic week, Wednesday, which actually was about average, seemed unusually slow. But psychological time ignored, the next FOTD will be posted in 24 hours. Until then, take care, and when it comes, recognize it for what it is. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Age_of_Iteration { ; time=0:04:30.82-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=floor passes=1 center-mag=-0.2811119334670882/-0.991563627943696/\ 5.35274e+011/1/10/0 params=1.6666666666667/0/83/0 float=y maxiter=2000 inside=0 logmap=428 periodicity=10 mathtolerance=0.05/1 colors=000LTdKUbIV_HWYFXVEYTDZQBZOAZL8ZJ7ZG5ZE4_B3\ `96a88`8B_8D_8F_8I_8KZ7NZ7PY7RY7UX7WW7ZV6`V6bV6eV6\ gV6iV6`PFTKOKFXCAe12p45n68l8AkADiCFhEIfGKeINcKQaMS\ `OVZQXYS_WUaVWdTXeTYfSHdR1bQ3_P5YP7WP9UOBSODQOFONG\ LNIJNKHMMFMODMQBLS9LS4JT7LUANVDPWFUWIZXLcYOhZQmZTr\ _Wv`Yza`zbczbfzchzdkzemzbozeqzgsziszlsznrzpqzsozum\ zwkzrizmgvifrdem`ehWecRdZNdUIdPEdKFcFFcAGc5Gc6GU7H\ c8HU9HcAIUBIUCJUDJUEJUFKUGKbHKbILbJLbKMbLMbMMbNNbO\ NbPNbPPcOQdNSeNTfMVgLWhLYiKZjK`kJalIcmIdnHeoGgpGhq\ FjrFksEmtDnuDpvCqwBsxBtyAuzAswCrtEqrGpoHomJnjLqkJm\ hMjePfbSc`V`YYXV`UTcQQfNNiMLmKLkJLiILhHLfGGdFGcEBa\ DB`CBZBBXABW90U8UzUUzzUzzUzzUzdKzaKzZJzWIzTIvPHrMG\ mJFhGFeDEdAEb70_90XA0UB0UD0UEQYFSXHUVIWUJYSL_QMaPN\ cNPeLQgKRiISkHTmHUnHVoHXpHYqHZrH_sH`tHauHbvHcwHdxH\ byIczJmzKqzKvzLzzMzzMzzNzzOzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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 10-09-08 (Alien Visitation [7])
by Jim Muth 09 Sep '08

09 Sep '08

FOTD -- September 10, 2008 (Rating 7) Fractal visionaries and enthusiasts: Curiously enough, the parent fractal of today's image, which has perfect XY-axis symmetry, rather resembles a flying saucer bearing alien visitors from outer space. This explains why I named the image "Alien Visitation". I have no idea why the parent fractal should have this symmetry at the unlikely height of 71 floors up the logarithmic ladder, and then only when no function is applied. But I suspect that, like the 'cosxx' function of Fractint, using no function with the MandelbrotBC3 formula creates a serendipitous mistake. I also suspect that the fractals that result with this formula appear in a circular repeating series rather than an infinite line of always-new images. Today's scene is located very near the X-axis at the eastern edge of the main bay of its parent. Due to the Y-axis symmetry, a similar scene exists at the western edge of the bay. Most of the action in today's image consists of the 'fmod' inside fill. The rating of a 7 is conservative enough to be honest and liberal enough to be interesting. The calculation time of 7 minutes is a bit on the slow side, but fast enough so that no one will have an attack of acute impatience. The finished image will be, or may already be, posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tuesday started with a bang here at Fractal Central as a very strong thunder-storm moved in, with flooding rain, crashing thunder and roaring wind. The fractal cats weathered the storm under the bed; FL weathered the storm in the rear window, watching the flowers in her garden being flattened. I weathered the storm in the front window, enjoying the show. The rest of the day featured cloudy skies and a threat of more rain, which never developed, and a temperature of 75F 19C. With the big rush job just about wrapped up, things are return- ing to normal here at F.C. Though I had little time to write today's fractal discussion, the discussion for tomorrow's FOTD should be more elaborate. That next FOTD will be posted in 24 hours. Until then, take care, and I'm undecided whether to vote for a 'rock' star or a beauty queen. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Alien_Visitation { ; time=0:07:02.02-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+1.112397863899667/+0.005607924256098/\ 6713.695/1/46.5/0 params=1.6666666666667/0/71/0 float=y maxiter=1000 inside=fmod periodicity=10 colors=000aM`bPZbSXcWVcZUdaSdeQehOekNXRXP7eQ8dQ8dQ\ 8dQ9dQ9dQ9dQAdQAdQAdQAdMBaIB_EBYBBW7BU3BS0BQ6HTCMV\ IRXOWZU`c_fhekmkqrqwvzzzqwvlqrgkmbfhYaeTYcOTbJOaEJ\ `9E_5AZN0SJ7TGETDLTARU7YU4dU1jUqJFpKEoKDnKCnKBmKBl\ KAkK9kK8jK7iK7hK6hK5gK4fK3fK3HhwIfuIdtIbsI`rIZqIXp\ IVnITmIRlIPkINjILiIJhHGbHDXHBRH8LH5FN3KP6NR8PRASRD\ UQGWPJYOM_NPaMScLVeLYgK`iJckIfmHioGlqFosFqtFruFrvF\ rxFszFsvFsrFsmFthFtcFtZFtUNpQVmO_kVahXaeZab_a_a`Xb\ `Ud`Re`Og`MhZNfXOeVPdUPcSQaQR`OS_NSZLTXJUWHVVGVUEW\ SCXRAYQ9YPFSrEUqDWpCYoB_nAam9clAGD9HE9HE9HE9HE9HF9\ HF9HF9IF9IF9IG9IG9IG9IG9IG9JH9JH9JH9JH9JH9JI9JI9KI\ 9KI9KI9KJ9KJ9KJ9KJ9LJ9LK9LK9LK9LK9LK9LL9ML9ML9ML9M\ LejGbj9_j2_c6_YA_RE_LI_EM_8Q_2TW6TS9TODTKGTHJTMOQR\ TOVYM_UTdQ_iMfnImrFtlJqfNn`QkVUhPXeJ`bEc`JYWNTRRNN\ WII_CDc79gD9kJ9nO9rU9v_9yd9x`MxYYwViwSu_TsDUqj8GXN\ NJaU5p_7lY8iWAeVKrzGhpCdp } 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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Brief FOTD break
by Jim Muth 04 Sep '08

04 Sep '08

Fractal fans: Due to a huge design job that came in Wednesday morning, there will be no FOTD for September 4 to 9. If all goes well, the next FOTD will appear on September 11. Until then, be brave. Jim Muth

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FOTD 03-09-08 (Original Symmetry [4])
by Jim Muth 02 Sep '08

02 Sep '08

FOTD -- September 03, 2008 (Rating 4) Fractal visionaries and enthusiasts: A fractal with a rating of a 4 leaves much to be desired, but it's still better than the 3-rated image that passed for yesterday's FOTD. The parent fractal was created by the formula Z^(1.666667)+C as it appears at ground level of the logarithmic ladder when no function is applied. The most notable thing about the parent is its origin symmetry -- a most unusual thing to appear in a Mandeloid. Even more interesting is the fact that many of its minibrots have a similar symmetry. Today's image shows one of these almost- symmetrical minibrots. I named the image "Original Symmetry" because of this symmetry. The rather average calculation time of 3-1/4 minutes should cause little discomfort. But if a problem should arise, the completed GIF image is or soon will be available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The third consecutive perfect day passed uneventfully here at Fractal Central on Tuesday. The temperature of 86F 30C was a bit on the warm side, but the unusually dry air kept it quite comfortable. The fractal cats, who might have seen the last of the manx, spent most of the day chasing each other up and down the hallway and getting into various other trouble. My day was appropriately busy with non-fractal things. The next FOTD will appear in 24 hours. Until then take care, and if elected president, I will give everything to everybody. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Original_Symmetry { ; time=0:03:14.60-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-0.193684837028058/+0.6447822429058375/\ 7293.786/1/90/0 params=1.6666667/0/0/0 float=y maxiter=3600 inside=0 periodicity=10 colors=000R`dSZcUWbWUaYR`_P_`NZfdhkvrlwolwllwilwgl\ wdlwamxZmxXmxUmxRmxOmxMV8NTDLSIJRNHQSGOXENaCMfALk9\ KfEJaJJXOISSIOXHJaGEeG9jF4oF0sK6jPBaUHTYMKWPMVSNUV\ OSYPR`QQcRPeSNhUMkVLnWJqXItYHwZGy_LhXQSUVBRXFQYIPZ\ LP_PO`SNaVNcZMdaLedLfhKgkJhnJilMikPijSiiUihXig_ieb\ iddicgibjiami`oeXeaUWZQMVNCSK3_KLeIFlG8rE2KigG`ZCT\ Q8LH5D9AJ9FO9JU9OZ9Tc9Xi9an9es9ci8a`7_S6YI5W94U03r\ OpkLidIbYFXRCQK9JD6D636okLgdI`YFTRCMK9ED6763xNKkIG\ _DCO98C44uuLkkHaaETTAJJ7993uCpf9bT6QE3D`eyTXlMP`EG\ O78CaMAUH8MD6F847426KA3A5_9vV7nR6gM5_I4TD3M92E417n\ _zn0RP0DHoMEgIC`F9TC7M94E6273J30F20C20910610300FpD\ DiBBb99X87Q65J43D3161BiIwTWUEGMVlHObDIT8CJ469DOiAK\ a8GU6CN48F2471nE0eB0Y90P70H408266yZ4cN2QB1DI2qE1fA\ 1W70L30ADonAdc7VU5KK2AAxfihWYULNFABJuaCaP6JCNyvIlj\ D`Z9ON4CB60g50_40T30M20E107yfEp_CgUAZO8QI6HC4862Lz\ 9O3FKdPGojImiJjhLhgNefPce } 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 02-08-08 (Purely a Filler [3])
by Jim Muth 01 Sep '08

01 Sep '08

FOTD -- September 02, 2008 (Rating 3) Fractal visionaries and enthusiasts: Rarely do I post a FOTD fractal that rates as low as a 3, but today I have done it. My sister stopped in unexpectedly Monday afternoon, and I spent the rest of the day talking with her. But when FOTD post time came I was caught with no fractal ready. In a near panic ;-) I hastily entered two numbers into the DivideJulibrot formula and used the first thing that appeared. The image consists totally of inside stuff made visible by the 'fmod' inside fill. The interesting part of the image lies in the holes, which surprisingly have a unifying theme. Even though they are of different sizes, most of them vaguely resemble the letter Z. I named the image "Purely a Filler", which is what it is. The image can be seen by running the included parameter file or by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. The weather was perfect and the fractal cats were happy on Monday. The next FOTD will be posted in 24 hours. Until then, take care, and try not to get into too much of a rush. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Purely_a_Filler { ; time=0:03:16.85-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot passes=1 maxiter=1500 center-mag=-1.84216/1.27087/11.85244/1/-1.5/0 params=0/0/0/0/0/0/0/0/0.333/3.333 float=y inside=fmod proximity=1.25 periodicity=10 colors=0000Sb6S`ES_MSZUSXaSWgRYhSWhSViSUiSSiSRjSQj\ SOkSNmTMoTLqTJsTIuTHwTFxTEzTDzUCzUAzU9zU8zU6zU5zU4\ qC6pL4pU3pb1pk0ps0no3lk7kgBicFg_JfWMdSQbOUaKY_Ga_C\ fZDdZEcYFbYGaYH`XI_XJZXKYWLXWMWWNUVOTVPSVQRURQUSPU\ TOTUNTVMRWNSVMTVLUUKVUJWUIXTHXTHYTGZSF_SE`SDaRCaRC\ bQBcQAdQ9eP8fP7fP7gO6hO5iO4jN3kN2lM0kN2kO4kP6kQ8kQ\ AjRCjSEjTGjTIjUKiVMiWOiWQiXSiYUhZWhZYh__h`ahacgaeg\ bggcigdkgdmhenhenienieoieojeojfpkfpkfpkfqlfqlfqmgr\ mgrmgrngsngsngsjdkfadbZYZXRVUJRRCNO5JL0KM0KM0KM2KN\ 4KN6KN8KNAKOCKOEKOGKPIKPKKPMKPOKQQKQSKQUJPWKQVLQUM\ RTNRSOSRPSQQTPRTOSUNSUNTVMUVLVWKWWJXXIYXHZYG_YF`ZE\ d`Db_E`ZEZYFXXFWXFUWGSVGQUHOTHNTHLSIJRIHQJFPJEPJCO\ KANK8ML6LL5LL8KWBKfDKqCLpCLoBMnBMmAMlANk9Nk9Nj8Oi8\ Oh7Og7Pf6Pf6Pe5Qd5Qc4Qb4Ra3R`3R`2S_2SZ1SY1TX0TW0RY\ 0TW2UV5WU7XT9ZSC_RDd_Dd_Dc_Db_Db_Ea_E`_E__E__EZ_EY\ _EX_EX_EW_EV_EU_EU_ET_ES_ } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 01-09-08 (Land of Loopiness [7])
by Jim Muth 01 Sep '08

01 Sep '08

FOTD -- September 01, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal lies in the same area of the same parent as the images of the past 2 days. And like those two images, it con- sists of an intricate network of filaments. The cubic minibrot at the center of today's image is well beyond resolution, though the mixture of quadratic and cubic effects surrounding it is apparent. I named the image "Land of Loopiness" because so many of the filaments form closed loops. Then I rated it at a 7. The calculation time of 1-1/3 minutes is brief enough to keep every- one happy. And of course, the finished image is or soon will be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunday morning, when FL asked if I felt like going to visit a new antique emporium that just opened about 75 miles away, I reluctantly said yes. This is why the FOTD for September 1 is so late. I guess I can't see what is so fascinating with the 'junque' other people have the sense to throw away, but it makes FL happy if I am there with her, looking bored, so I just can't say no to her. Luckily, or unluckily, we found nothing worth picking up. With maximum sunshine, low humidity, and a temperature of 82F 28C, Sunday was a near perfect day here at Fractal Central. The fractal cats celebrated the fine weather as well as the apparent departure of the manx cat by giving themselves a thorough grooming. (And that's no tall tail!) Like some ovens, cats are self-cleaning. My day was fair enough, despite somehow being drawn into the antiquing expedition. The next FOTD, with a new theme, will be posted within 8 hours. Until then, take care, and the question is not, "why is there something instead of nothing", it is "why is it impossible for absolutely nothing to exist". Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Land_of_Loopiness { ; time=0:01:22.56-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot passes=1 periodicity=10 center-mag=-3.94470157911456/+0.00001549964882567/\ 8.2e+012/1 params=0/0/0/0/0/0/0/0/3/3 maxiter=1800 float=y inside=0 logmap=154 mathtolerance=0.05/1 colors=0007VN8WO9XPBYQCZRD`TEaUFbVHcWIdXJeYKfZLg_N\ iaOjbPkcQldRmeTnfUogVqiWrjXskZtl_um`vnawobxpZskWog\ TkcQg_NcWJZRGVNDRJANF5GA6IB7JB7KC8LC8MC9ND9ODAQEBR\ EBSECTFCUFDVGDWGEXGFZHF_HG`IGaIHbIHcJIdJIeJPbMW_Ob\ zR`z_ezWizTzzPzzMzzJzzHzzGzzEzzDzzBzzAzz8zz7zz5XQ4\ VT2TV1SW4SW6SW9SWBSWERWGRWJRWLRXORXQRXTQXVQXYQX_QX\ bQXdPZeQXfRVfRTgSSgTQhTOhUNiVLiVJjWHjXGkXEkYClVDqX\ CnYBl_Bi`AgaAdc9bd8_f8Yg7Vh7Tj6Qk5Om5Ln4Jo4Gq3Er2B\ t29u16v14r57o89lCBiFDeIFbMH_PJXSLUWNQZPNaRKeTHhVDm\ WEkXFjXGiXHhXIgXJfXKeXKdXLcXMbYNaYO`YP_YQZYQYYRXYS\ WYTVYUUYVTZWSZWRZXQZYPZZOZ_NZ`MZaLZT2QYBVaKZeTbxjw\ i`fVRQJDAHH9FK9DO9BR9AU98Y86`84d82g81j83iB4iE6iH7h\ K8hNAhQBhTDgWEgZFgaHgdIfgKfjLfmMfpJfsHfuKgsMhrOiqR\ jpTkoVlnQmeLnYGoPCpHBqGBrGBrGBsGBtGBtGBuGBvGBvGBwG\ BxGBxGByGBzGBzGHxNNvUSt`Yrgbpngojlofqncvn_znXqiShd\ N__JRVEIQAPMEWJHbGLiCOp9S } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 31-08-08 (Orderly Disorder [6.5])
by Jim Muth 30 Aug '08

30 Aug '08

FOTD -- August 31, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image comes from the same general area of the same parent fractal as yesterday's image. It's actually a very rich area, especially since the minibrots that fill the area are almost all cubic ones surrounded by unusually extensive patterns with both cubic and quadratic characteristics. I named the image "Orderly Disorder". That's what fractals are. Then I rated it at a 6.5, which includes a questionable 1/2 point for my coloring efforts. The included parameter file calculates in just under 1 minute, that is after the file is set up to run. This is about the same time required to hop over to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoy the completed image there. The clouds hung around on Saturday here at Fractal Central, but it stayed dry, and the temperature of 75F 24C was not at all bad. The fractal cats were much more relaxed, which means that the intruder cat was not in the area. My day was peaceful enough, and if all goes well, tomorrow will be the same. I'll be taking a brief trip back to Old Fractal Central tomorrow, so the next FOTD fractal image might be late. But the image is assured. I already have it in cold storage, ready to go. Until then, take care, and be with fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Orderly_Disorder { ; time=0:00:58.35-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot passes=1 float=y center-mag=-3.944756829565295/+0.000377496511276/\ 1.105404e+007/1/-115/0 params=0/0/0/0/0/0/0/0/3/3 maxiter=750 inside=0 logmap=91 periodicity=10 colors=000TcnRcoSeoTfoUgoVioWjoXkoYmoZno_oo`qoarob\ socuodvoewofxohwpjwqlvrnvspvsruttuuvtvxtwztwvorskm\ pfimbdjZ`gUWdQSaMNZHJWDET9APG8LM6HT5DZ39e16k0Bl4Fl\ 8JmBNmFRnIWnM_oQcoTgpXkp_ngToZNoRHoIBqA5nE4lI4jM4j\ Q4kT4iX4g`4dd4bh4`k4Zo4Xs4Vw4Tz4Wx6Yw7_v9btAdsCfrD\ ipFpoGrnIuqJwpLyoMziNuaMtULsMKrEJq6Jo8HnAGlCFkEEiG\ DhICfKBeMAdO9XNNQM_JLlCKyBJvBIsBHpAHmAGjAFg9Fd9Ea9\ DZ9DWDGXGJYJMYNPZQSZTV_WY`_``bcaefahibllcoocrrdutd\ opbjlaei__eZVbXQZWKWUFSTAPSCQRESRGUQHVQJXPLYPN_OPa\ ORbNTdNUeNHkf4qzCmxKjwSgv_ctg`soYrlWnjVkhUhfTddSaa\ QZ_PWYOSWNPUMMSLJTMKTMKTMKUMKUMKUNKVNKVNKVNKVPKXQJ\ ZTI`WHbZGd`GfcFhfEjiDlkDilGgmJenMcoOapR_qUYrWWsZUt\ aSudQvfOwiMxlKynPzkTzhXze`z`dzWhzRkzNgzMdzLazLZzKW\ zKTzJUzIZzIczHhzHmzGrzGvzKzzOzzSzzWzz_zzczzgzzazzX\ zzRzzMzzGzzBzzDzzEzzFzzGzzHzzIzzJzzLzzMzzNzzOzzPzz\ QzzRzzTzzUzzWzzXzzZzzkzzm } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 30-08-08 (A Cubic Conundrum [7.5])
by Jim Muth 30 Aug '08

30 Aug '08

FOTD -- Aubust 30, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image shows an unusually rich cubic minibrot, which I named "A Cubic Conundrum". The parent fractal is an oversized Mandelbrot set, just starting to morph into a cubic Mandeloid. Today's scene is located in an extra valley pushing into the second bud along the negative X-axis. The generating formula divides the Z^2 Mandelbtot set by (-Z+3), or something like that. At least I think I've got it right this time. Bur regardless of how it happened, the image, which rates a 7.5, is well worth the 1-1/2 minutes it takes to run the included parameter file. And even this small task may be avoided by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Friday turned out to be a strange day here at Fractal Central. The temperature of 70F 21C was fair enough, and the overcast skies were not too bad, but it was too wet to be a dry day and too dry to be a rainy day. The occasional showers of mist kept it undecided. The fractal cats were not undecided however. They definitely want that intruding manx tomcat out of the area for good. My day was definitely not filled with loitering. The work was somewhat heavy, and the leisure, somewhat limited. But the fractal is acceptable, and that's what matters, at least as far as the FOTD goes. The next fractal will be posted in 14 hours. Until then, take care, and what is that heavy feeling in the air? . . . I just realized that Fractal Central is filled with a million tons of dark matter and energy. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Cubic_Conundrum { ; time=0:01:31.56-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot passes=1 center-mag=-3.945176537568527/+0.00000000678488286\ /5.016586e+011/1/72.5/0 params=0/0/0/0/0/0/0/0/3/3 float=y maxiter=1800 inside=0 logmap=114 periodicity=10 mathtolerance=0.05/1 colors=00000H00J10M10P10S10U40V60V90VB0WD0XG0ZI0aL\ 0cN0eM0iQ0kR0mT0nU0nV0nT0lR0jP2iN4gL6fJ8dHAcECaBE`\ 8GZ5IY2IW0KV9Uezcezmfzsfzzgzz0zz0zz06zhBzdFzaKwZOu\ WztTzzzzzzzzzzzzzzzzzFzzEzwDzwCzwBbwzawz`wz_wzZwzY\ wzWvzVvzUvzTvzSvzRuzQuzPuzOuzNuzMuzNrzOoTPlTQjTQgT\ RdTSbTT_UUXUUUUVSUWPUXMUXKUXKUZNS_QQaSObVMdYKe_Igb\ GheEjgCkjAll9jj8ii8hh7gg7ff6de6cd5bc5ab4`a4_`4aZ5b\ Y5dX5eW5gU5hT5iS6kR6lP6nO6oN6pM6qL9qLBrLDrLFsLHsLJ\ tLLtLNuKPuKRvKTvKVwKXwKZxK`xKbtIdqHenFgkEhgDidBkaA\ lZ9mW7oS6pP5qM3sJ2tG1uH2qH3mH4iH5fH6bz7Zz8Wz9SzAOI\ zLzzHIzDzzAHzBGzBzzBFzBzzBEzCzzCCzCCbCBdCAgDAjD9mD\ 8pD8sDMv9Zx6lz3yz0qz7jzEbzKWzRPzYzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzVzwVzwWzxWzxXzxXzxY\ zyYzyZzyZzybzyezyizylzypzyszywzyzzyrzvkztczrXzpQzn\ PziPzdOz_OzVNzQNzLMzGMzBLz6Lz2Mz7MzBMzGNzKNzPNzTOz\ YOzaOzeZziizl9zN9zQ9zUAzY } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 29-08-08 (The Underdog Wins [4])
by Jim Muth 28 Aug '08

28 Aug '08

FOTD -- August 29, 2008 (Rating 4) Fractal visionaries and enthusiasts: Everyone is for the underdog, even though the underdog rarely wins. In today's image however, the underdog actually wins. It wins by default more or less. Due to an unexpected rush job, I had no time to explore for a new fractal, so I grabbed an old image that has been lying in the 'maybe' file for months. It is obvious why this image never made it beyond the 'possible FOTD' stage. It has little to show. This is the kind of scene I usually immediately pass over on the way to the final FOTD, but with today's lack of time, it is where I stopped. I'm not going to deceive myself into thinking the image is worth more than a 4. In fact, even the rating of a 4 might be a bit generous. The only thing of note in the image is a minibrot in the upper left corner shaped rather like a peanut. The rest of the scene is a mish-mash of broken-up fractal stuff, some of it arranged into curious patterns, but ultimately dis-satisfying. The parent fractal looks much like the minibrot in today's image; the scene is found in the east branch of a valley leading to the northern period-2 bud. I named the image "The Underdog Wins". In a way, due to the rush, this underdog image actually did win its way into FOTD immortality. The calculation time of 5 minutes is longer than I would have preferred for an image such as today's, but relief is at hand on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the already-calculated image is posted for immediate satisfaction. The weather was far from perfect here at Fractal Central on Thursday, as the remains of the dissipated tropical storm Fay arrived. Heavy clouds prevailed all day but only a few light sprinkles fell from them, while the temperature hovered around 70C 21C. The fractal cats spent a good part of the day watching for the manx tomcat who is trying to establish his territory in the small field beyond the back yard. The intruder cat never appeared and the fractal duo eventually grew bored watching the rain. My day was unexpectedly busy, which explains the 'filler' fractal. The next FOTD will be posted in 24 hours. Until then, take care, and don't mix the concrete with the abstract. It can lead only to confusion. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Underdog_Wins { ; time=0:05:06.93-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident center-mag=+0.598635449/+0.490200106/2010 params=1.7/0/66/0 float=y maxiter=50000 inside=0 logmap=75 periodicity=10 colors=000cZAbXBbVCaSD`QE_OFZMGYKHXIIWGJWEKXFMYFNZ\ FP_FQ`FRaFTaFUbFVcFXdFYeFZfF`gFagFbeJddNfbQhaUj_Xl\ Z`nX0hW0cV0ZK0NO1OPHKRJFTLAVOFYSK_XPabUdgZflchqhjv\ mjuljuljukjukjujjtjjtijtijthjthjsikrjlqklplmomnomo\ nnomoplpqkqqjrrjrsisthttguUW1UX2UY3VZ4V`5Wb6Wd7Xe8\ Xg8Xi9YkAYlBZnCZpD_qD_qE_rF`rG`rHaqIaqIaqJbqKbpLcp\ McpMdpNdoOdoPeoQeoRfnRfnSWPfMHnC9uDAvEAvFAgGChGCiH\ DjIDkJElJEmKFnLFoMGpNHqNHrOIsPItQJuQJvRKvSKvTLvTLv\ UMvVMvWNvXOvXOvYPvZPv_Qv_Qw`RwaRwbSwvewbSwcTwdUweU\ wfVwfVwgWwhWwiXwiXwjYwkYwlZwlZwm_wn`wo`wpawpawqbwr\ bwscwscwtdwudwvewAZzF_zJ`zO`zSazXbz`bzeczidzndzrez\ `WzbXzdYzfZzh_zj`zk`zmazobzqczsdzueztRzuSzuTzuUzuV\ zHbzFazC`zA_z8ZzAfzCnzDuzHqzKmzNizQezTazWYzZUzaQzd\ MzfPzgRziTzjWzlYzm_zobzpdzrfzsizukzvmzxpzyrzztzvsz\ srzprzmqzjqzkozknzllzlkzmizmhznfznezndzmezlfzkgzkh\ zjizijzikzhhzgfzfdzebzd`z } 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 28-08-08 (Pantominia Coregia [5])
by Jim Muth 27 Aug '08

27 Aug '08

FOTD -- August 28, 2008 (Rating 5) Fractal visionaries and enthusiasts: Today's fractal is a quick one, and it shows. The rating of a 5 shows that the image leaves much to be desired. The name "Pantominia Coregia" means nothing at all. I dreamed it up because it sounds kind of like something scientific. The chief advantage of the image is its fireball calculation time of under 15 seconds. It doesn't get much shorter than that. The formula divides Z^2 by (Z^(3)+6) and produces a near- Mandelbrot set, with today's scene located in the northeastern suburbs of the large minibrot on the main spike. When this is done, we see a quintic minibrot surrounded by smaller similar minibrots. There is nothing artistically notable about the image, it is merely interesting to observe. And observe the image is what you'll do if you run the included parameter file or zip over to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and peruse the image already calculated and posted there. Despite a thin layer of cirrus clouds that hung over Fractal Central all day Wednesday, the day, with its temperature of 81F 27C, was near perfect. At least the fractal cats must have thought so, for they spent half the afternoon on their shelf by the window, wishing they could go outside, where that tough manx tomcat is lurking and ready for a fight. Needless to say, the duo had no chance to go out and engage the usurper. My day was too busy to be called perfect. Maybe tomorrow will be better. The next FOTD will be posted in 24 hours. Until then, take care, and keep searching for a photon at rest. If you find one, you'll rewrite the physics books. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Pantominia_Coregia { ; time=0:00:14.72-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot center-mag=-10.48325696865905/+0.09877741090398924\ /3.971914e+010/1/-50/0 params=0/0/0/0/0/0/0/0/5/6 float=y maxiter=316 inside=0 logmap=59 periodicity=10 mathtolerance=0.05/1 colors=000A7LA6MA5OA4PA3R52SADZFNeKXlPfszzzkjBkjBk\ jBeiCZeCQaDIYDATE3PEEWOPbY_igipqUfpFXo0Oo4Ve7aXBhO\ EnFzmKzmzzmzzlZKlcLlhPefTZeXSd`MbdFah8`l2_a3hR4qG5\ yH6qI6iI6bcXmxvxkrv_nt`go`ajaWeaQ`aKXdQRgVMj`HmeBp\ k6sp1ll6ehA_dET`IMXMGUQK_LNeHQkDTq9Wv5RoFMhOIaYzVf\ zOozSgzW_z_SzcLzgFzjAzm5zp0zo7zoEznLznSzmZzmeXzl6z\ 0Uz2pz3hzFazRVzaTzZzzXzzUzzSzzPzzNzzMzzLzzKEzJBzI9\ zH6zG4zG5zL5zP5zT5zX5z`LzT_zLSzMLzNDzO6zODzMKzKRzI\ YzHMzLKz1Jz9JzGJzOIzVIzbIziIzpGzjEzdCzZDz`DzbDzdIz\ bMzaRz_VzZ_zYczWhzVlzUZzdWzfUzhRzjPzkMzmKzoIzpMziP\ zbSzWWzPZzIazBdz5SzXFzxTzwezwrzwSzh1zVCz_NzdYzihzn\ rzsgzVmzWrzXwzXwz_wzawzdwzfwziwzkwzmgzlTzkNzcHzWBz\ O5zGCzEIzDOzCUzB_zARzIIzPNzRRzTVzVZzXczZgz`kzbozcn\ zhnzlnzpnztnzxSzV5z1AzCFzNKzYPzgOzdNzbMz`LzZKzWJzU\ IzSIzQez`ezVezQezKezEez8ez3gz2iz2jz2lz2nz2oz2qz2rz\ 2_z4Hz6Fz4Ez3Dz2mzGgzIazJ } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 27-08-08 (Something from Nothing [6.5])
by Jim Muth 26 Aug '08

26 Aug '08

FOTD -- August 27, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Today's 6.5 rated image truly gets "Something from Nothing", which is what I named it. To begin, it consists totally of 'inside' stuff, but due to some quirk in the 'fmod' routine, the inside stuff inside the minibrot is more 'inside' than the inside stuff outside the minibrot. Yes, I know it makes no sense, but that's the way it is. (Changing the 'logmap' to 1 eliminates this quirk.) The generating formula divides Z^2 by (Z^(-2.1)+4). The immediate result of this operation is a blank screen, which can be resurrected from the dead by the 'fmod' feature. I really cannot say much more about the image, for I really have no idea what's going on with it. But with its smooth coloring, it's an interesting fractal to study. The calculation time of 1-1/3 minutes should cause no one any grief. The pre-calculated image is or soon will be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> An absolutely perfect day prevailed here at Fractal Central on Tuesday. Perfection is defined by crystal blue skies, a few puffy clouds for decoration, low humidity, gentle winds, and a temperature of 79F 26C. The fractal cats must have agreed, for they spent much of the day in the window, watching for Max the Manx cat, who is prowling the area, establishing his dominance. My day was busy, which is about all that can be said. The next FOTD, one with more substance, will be posted in 24 hours. Until then, take care, and what does a massless photon become when it sits at rest? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= SomethinFromNothin { ; time=0:01:21.46-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot center-mag=+0.2602484/\ +1.367610189/9214.697/1/92.5/0 params=0/0/0/0/0/0/\ 0/0/-0.1/4 float=y maxiter=1500 inside=fmod proximity=0.25 periodicity=10 colors=000fXYeWXeWXdVWhVYgUYfTYeSXdRXcQWbPWaOV`NV_\ MUZLUYKTXJTWJSVJSUJRTJRSJQRJQQJPPJPOJONJOMJNLJNKJM\ JIMIIMHILGILFIJEHKDHKCHJBHIAGJ9GI8GI7GI6GH5GH4GH3F\ G2GG1FG0GF0FF1FE2FE3EE4ED5ED6ED7EC8EC7DC6DB6DB5CB5\ CA4CA1972A83B94B94CA5CA6DB6DC7EC8ED9FD9FEAGFBGFBHG\ CHGDIHEIHEJIFJJGKJGKKHLKILLIMMJMMKNNLNNLOOMOONPPNP\ QOQQPQRQRRQRSRSTSSTSTUTTUUUVUUVVVWWWXXWXXXYYXYZYZZ\ Y__Z_`Z`a_`a_ab`bc`bcacdacebdfbdfcegcfhdfhdgiegjeh\ jfikfilgjmgjmhknhkoiloimpjmqjnrknrkoslptmptoqupqvr\ rvsrurqtqqtppsopsnormormnqmnqmmpmmpmmomlollnlknlkm\ ljlljllikliklijlhjlhilgilghkfhkfgkegkefkdfkdekdekc\ dkcckbckbbkabjaaj`aj``j``j__j__jZZjZZjYYjYYjXXjXXj\ XWiWViWViVUiVUiUTiUTiTSiTSiSRiSRiSQiRQhRPhQPhQOhPN\ hPNhOMhOMhOLhNLhNKhMKhMJgLJgLIgKJgKKgJLgJMgJNgIOgI\ PgHQgHRgGSfGTfFUfFVfFWfEXfEYfDZfD_fC`fCafBbfBcf6df\ 8ef9ffAgfBheCieDjeEkeFleG } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 26-08-08 (Ultimate Unreality [6.5])
by Jim Muth 25 Aug '08

25 Aug '08

FOTD -- August 26, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image is another ultimately unreal one, which is why I named it "Ultimate Unreality". The generating formula contains an unlikely Z^(-0.5), which, when combined with Z^2, produces a blank screen. But there is action within the blankness. Just as empty space is filled with virtual particles, the blank screen is filled with a virtual fractal, and the energy supplied by the 'fmod' inside fill brings the virtual fractal to fractal reality. In this case, the 'fmod' inside fill is the only one that works. (Since virtual particles also need energy to make them real, I suppose they are also ultimately made of numbers.) Anyway, today's image, composed totally, as it is, of inside stuff, rates a 6.5, 1/2 point of which is a reward for the 20 minutes or so I spent tweaking the colors. The calculation time of 3-1/3 minutes is fast enough to avoid impatience and slow enough to give time for anticipation. Perhaps the easiest way to view the image is to forget parameter files and visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image is or soon will be posted in finished form. The near-perfect weather here at Fractal Central on Monday was fully enjoyed by the fractal cats, who slept through most of it. I also noticed the blue skies and temperature of 82F 28C, but I was a bit too busy to enjoy it. The next FOTD, hopefully one with more reality, will be posted in 24 hours. Until then, take care, and never forget that fractals are as real as electrons. (But exactly what is the difference between an abstract electron and a concrete electron?) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Ultimate_Unreality { ; time=0:03:22.33-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot passes=1 float=y center-mag=+0.4129219397998285/+2.004990460705446/\ 2140000/1/165/0 params=0/0/0/0/0/0/0/0/-0.5/5 maxiter=1500 inside=fmod logmap=yes periodicity=10 colors=000fwAgwAhwAiwAjvAkvAlzAzyzwymtwhrvcquZrtUs\ sPtrKuqFuqAupAupAuoAuoAunAunAumAumAulAulAukAukAujA\ tjAtiAtiAshAshAsgAsgAsfAsfAseAreArdArdAqcApcApbApa\ Ap`Ao`Ao_Ao_AoZAmZAmYAmYAmXAlXAlWAlWAlVAkVAkUAkUAj\ UAjTAjTAjTAjSAiSAhSAhRAhRAgRAgQAgQAgQAfPAfPAfPAfOA\ eOAeOAeNAeNAdNAdMAdMAdMAcLAcLAcLAcKAbKAbKAbKAbKAaK\ AaKAaKAaJA`JA`JA`JA`JA_IA_IA_IA_IAZIAZIAZHAZHAYHAY\ HAYHAYGAXGAXGAXGAXGAY82XB5XE8XGAXJDXLFXOIWRKWTNWWP\ WYSW`UWbXVeZVhaVjcVmfVohVrkVtmUqjTnhTkeShcReaRbZQ_\ XQYVPVSOSQOPNNMLMJJMGGLDELBCMCDMDEMDFMEBMECNFDNFDN\ GENFFNGGOGHOGIOGIOGJOGKOGKPGKPGKPHLPIMPINQJOQJPQKQ\ QKRQLSQLTRMUSMVTNWUOXVOYXPZWPYWQWVQUUPUTOUTXhTYiTY\ jTZkTZkU_lU_mU`nU`oUapRavSatTarUapVanWalXajYaiZag_\ ae_ac`aaaa_baYcaXdaVeaTfaRgaPgaNhaLiaKjaIkaGlaEmaC\ naAoa8pb6oa7oa7oa7oa8oa8na8na9na9na9naAmaAmaAmaAm`\ Bm`Bl`Bl`Cl`Cl`Cl`Dk`DbwI } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 25-08-08 (Pseudo-Fractal [6.5])
by Jim Muth 24 Aug '08

24 Aug '08

FOTD -- August 25, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: The parent fractal of today's image divides Z^2 by Z^(-97)+100. Unfortunately, this parent fractal does not exist. It has been totally evaporated by the extreme escape radius built into the formula. With the 'inside' set to the standard numb, the parent fractal is nothing more than a blank black screen. But salvation is at hand, for the active inside fills can often return life to dead images such as the parent of today's scene. In today's case, the 'bof60' fill works quite well. I'm not sure that what results from all this trickery is really a fractal, though it most certainly is a picture. And the picture is more interesting than might be expected from a bland all-inside image. There is a main bay at the bottom, with an imaginary shore line strung with buds. Scattered fields of debris fill the imaginary 'outside' areas, while a most interesting object lies on the left side of the frame. This 'object' is better seen than des- cribed. In fact, it is nearly impossible to describe it. I named the image "Pseudo-Fractal" since I'm not sure that it is really a true fractal. I rated it at a 6.5 to reward myself 1/2 point for my semi-skilled coloring. The calculation time of 3-1/3 minutes is not as short as I would have preferred, but I think the image is worth it. At any rate, the finished image is posted for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A pleasantly warm day prevailed here at Fractal Central on Sunday. The warm sun and temperature of 88F 31C were ideal for outdoor activities of all kinds. The fractal cats limited them- selves to indoor activities however. My day was pleasant also, and F.L.'s new oriental lamp actually looks kind of comforting glowing a soft amber on the living room table. The next FOTD will appear in 24 hours. Until then, take care, and if a thing isn't real, what is it? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Pseudo-Fractal { ; time=0:03:20.18-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot passes=1 center-mag=+1.032172008373736/+0.0316130942554965/\ 2352.071/1/95/0 params=0/0/0/0/0/0/0/0/-99/100 float=y maxiter=750 inside=bof60 periodicity=10 colors=000zzUuxUowUkuUesUcpUamU_jUYhUWfUUdUSbUQ`WO\ ZYMX_NUaOScQQfROhSMjTKlUInVGp_HndHmhHkmHjqHhvHgzHf\ vGdrGcnFbkFagF`cE__EZXDXTDWPDVLCUICTEBSABR7BQ7ET7G\ W7IY7K`7Mc7Pe7Rh7Tk7Vn7Xq7ZtJgwpzzhwzZtzRowQltPirO\ fpOdnNbnM_lLXiLUfKSdJPbJMaIJ_HEZHCXNBU000_gcagabg_\ dgZegXggWhgUigTheSgdSgcSfbSeaSe_SdZScYRcXRbWRaURaT\ R`SR_RR_QRZTPYWNYYLX`JWbHWeFVgEVjCUlATo8Tq6St4Sv3T\ s6Uq8VoAWlDWjFXhHYeKZcMZaORXZZJOe6Di7Hl8Kp9OsARwBV\ zCYxAav8dt6hr4kp2oo0rg9i_I`SQSKZJCfAAbB9_B7XB6UB5R\ BXSUxSksQjoPjkOjgNjcMjAnP8tM7yK8uN9rQAoTBlWCiZDfaE\ cdF`gE_PD_7NTHXMQfG_p9hz3qq8shCt`Gug2Nf7MfBLeFKeKJ\ dOIdSHdWGWRPNMYYUVhaSshQE6PK9NPBMUDKZFJcHHhJGmLFgH\ KbDPY9UT5ZO2bK7YHBTDFOAKJ6OE3S90W5P`YRYaTVeVTiXQmY\ OqPPeGQU8RJ9NI9JH9GH9CG98F95FGFCMOASY8Yf6co4dj5ee5\ f`5gW5hR5iM5jH5kD5UHIDLUBF_AAe95kFBbKGUQLMVQD_V5`U\ E`UM`UV`Ub`UjWYcS`YOcSKfM } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 24-08-08 (Seven from Eight [6.5])
by Jim Muth 24 Aug '08

24 Aug '08

FOTD -- August 24, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Today's FOTD is very late because on Saturday I somehow got involved in another of FL's antiquing expeditions. But all was not lost. We found an oriental-style lamp for $15, which FL claims is worth over $250. To me it looks like an old lamp, but who knows . . . Today's image came about when I divided Z^2 by (Z^(6)+3). The parent fractal resembles a Mandelbrot set starting to morph into the Z^8 Mandeloid. Today's scene is located in some island debris that has appeared in the northwest interior of the large period-2 bud. The image is extremely fast, taking only 24 seconds to run on the fast machine. The name "Seven from Eight" refers to the fact that, though the central minibrot has only 7 lobes, the surround- ing pattern is a series of powers of 8. The rating of a 6.5 could be a little liberal for such a hasty image, but the image is still better than average for one of order-8. The finished image will be available on the FOTD web site as soon as Paul can calculate and post it. The FOTD web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather was near perfect here at Fractal Central on Friday. Need anything more be said. The fractal cats enjoyed the great conditions to the best of their ability. My day was busier than expected, yet still within reason. Expect the next FOTD in about 6 hours. But do not be too disappointed if it does not make it. Until next time, take care, and look for those extra iterations. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seven_from_Eight { ; time=0:00:24.58-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot center-mag=-3.653068462538817/+0.2509654289884953/\ 1.06659e+010/1/-85/0 params=0/0/0/0/0/0/0/0/8/3 float=y maxiter=750 inside=0 logmap=47 periodicity=10 mathtolerance=0.05/1 colors=000GACKAFOAISALWAN_AVcAbgAjkArnGygWo`ccWmUh\ xKztAqp8mjBhfDcbGZ_IUYKPVLKRMGOMKHNOBOS6OXjZayiWjn\ QXsRTpRPnRLlRHiRDgR9eR5cX9XbDQhHJnLCsO5nS5jW5fZ5bb\ 5Ze5aZGdSRgMajFlm9vbFZTLBPLQLLdOOgRQiTSlWUnZXq`Zsc\ `vebxCAyIFtNJpTNkYRgbVcnXEj_LgaRdcXaebZghWinaglgej\ mcisagy_frahlbifck`elVfnPgoOirOluNmxNozMpmLp`KpOJZ\ YIIgI1pM9iPHbTPWWXQ_dJblCes6dtBcuFbvJawO`xS_zWZzUY\ zSXzQWzOVzMUzKTzITzGTzSTzcTzoMzmGzlAzj4ziHzZTzOezD\ qz2NzKmzV7zZ9zSAzLBzEszXdzOQzGSzPMzJHzDSzzMzzHzzkz\ zUzzFzzczzXzzQzzJzzmzz`zzOzzYzzSzzNzzHzz9zzAzzBzz2\ zz7zzQzzUzzazzizzgzzezzdzz`zz`zz`zz`zz`zzgzzlzzqzz\ vzz0zz4zz8zzCzzGzzQzzZzzhzzqzzbzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 23-08-08 (Web of the Spirits [7])
by Jim Muth 22 Aug '08

22 Aug '08

FOTD -- August 23, 2008 (Rating 7) Fractal visionaries and enthusiasts: Another rushed day will make necessary an abbreviated discussion. Fractals are sometimes filled with spider webs, but never have I seen a fractal as web-filled as today's image. To create the parent fractal I returned to one of the earlier versions of the DivideBrot series, the number 4, which has the means to change the escape radius. The parent fractal is better seen than described. All I can say about it is that a minibrot lies near its center, and today's scene is located near the tip of but not exactly on the main spike of the minibrot, which is infinitely divided, making the image kind of a railyard scene. I named the image "Web of the Spirits" because this name sounds better than something like 'web of the spider', and spirits are as mysterious and every bit as real as fractals. I rated it at a 7 because it is pretty good, whatever the word 'pretty' means. The magnitude of an almost off-the-scale 3*(10^13) makes the mathtolerance entry decidedly necessary. But the calculation time of an incredibly brief 32 seconds makes up for the diffi- cult magnitude. And the already-calculated image is or soon will be posted to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> More near-perfect conditions prevailed here at Fractal Central on Friday. The fractal cats again seemed unconcerned. And once again, my day was too busy to allow a full appreciation of the brilliant sun and comfortable temperature of 84F 29C. The next FOTD will be posted in 24 hours. Until then, take care, and walk with the spirit of fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Web_of_the_Spirits { ; time=0:00:32.72-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot4 passes=1 center-mag=-0.064\ 00318711939516/+0.00009960571606727/3.390477e+013/\ 1/-100/0 params=-1.5/0.032/-95.9/0 float=y maxiter=350 inside=0 outside=real logmap=64 periodicity=10 mathtolerance=0.05/1 colors=000SwWPwUMwSJxQGxOExMNmIVcEbUBo08rJDuaIxtMt\ iMpZMlOMbLKTIJKGIJQHIZGHhFGqElzzKr0zzzOdVQY_TRcWKc\ ZDc`6_ZPxXhoVdgTa_RYSPVKNRCLO4JmDzZLmcUmhaFziGXBKU\ CmRDzPDcMEzKEhHFbFFjPRqYbxfn4mvAorGqnMsjSufYwbcxZg\ ybkyeoziszlvzoizoYzoLzo9zoCslEmjHfgJ`eMUbOO`p7eTZd\ 6zcHxbRwaau`kt_usZon`ijacfbYbcSYdMUeGQfBMg41hODngP\ sz`xxWpvSitObrKWpGPnCIl8Bj44bB9VIDNPIFVMXNDmG4nF7o\ F9oFCpFEqFGqFJrFLrFNqEPpERoETnEVmDXlDZkD`jDbkFXkGS\ kHNlIHlJClK7mJ6nU6oU6oU5pU5qc5qc5mc9jcCgmGdmJamNZm\ Q_wU`wYawa_wWYzRzzLzzGzzzzzzzzzzzzzzzFzECzG9zI6zK4\ zMLzJOzPQzUSz_UzdWziYzo_ztazyJz_1zB9zCHzCPzDXzDWzE\ VzFUzFTzGSzHRzHQzIQzI`zGkzFuzEuzEtzFtzFszGszGrzHrz\ HqzIqzIpzJpzJozKozKnzLnzLmzMmzMlzNlzNkzOkzOjzPjzPi\ zQizQhzRhzRgzSgzSfzTfzTezUezUdzVdzVczWczWbzXbzXazY\ azYxzYxzYxzYxzYxzYyz3tz9pzElzKhzPdzV_z_WzeSzjOzpKz\ uGzzJzoLzeNzWPzMQzPYzWVzZ } frm:DivideBrot4 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1), d=real(p2)+100: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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FOTD 22-08-08 (One From Many [6])
by Jim Muth 21 Aug '08

21 Aug '08

FOTD -- August 22, 2008 (Rating 6) Fractal visionaries and enthusiasts: A big rush left little time for fractals on Wednesday, but I did manage to find one in a hurry. The little order-6 minibrot in today's image mixes both quadratic and order-6 elements. It is located on the northeast shore line of the main bud of its parent fractal, which exactly resembles an oversized Mandelbrot set. Since I found the scene almost automatically, I could rate it no higher than a 6. The name "One From Many" had some relevance when I thought of it, but now I can see little meaning in it. The calculation time of 2-1/4 minutes is speedy enough for such a routine fractal. And the already-calculated image has been or soon will be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Another perfect day went un-noticed by the fractal cats on Thursday, while I noticed the perfection but had no time to enjoy it. The next FOTD will be posted in 24 hours. Until then, take care, and wait with anticipation. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= One_from_Many { ; time=0:02:15.66-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot passes=1 float=y center-mag=-23.3599216711707/+3.587124300227662/\ 5.186719e+009/1/-158.75/0 params=0/0/0/0/0/0/0/0/6\ /30 maxiter=2200 inside=0 logmap=239 periodicity=10 colors=000h5Ag5Ae5Ac5A`5AY8AVBASEAPHAKKAGNABQ87S6C\ T9GUCKVEOWHTXKXYM`YPdZRi_Um`XqaZubaybctaao`_j_YfZW\ aZVXYTTXROWPJVNFVMIXLLZLN`LQbLSdLVfLXhL_jLakLgmQln\ Vro_wpdunfsmgqkiojjmhlkgmifngdpecqcasa`t`_u_aq_cnZ\ djZfgZgcYi`YkXXlUXnQXoNWqJWsGVtCVv9Vw6Tl8Rb9PTBNJC\ L9DSIBYRAc_9ih8oq7uy6ozEizLczSYzZTzeUqgViiWakWUmhb\ iukfVTNSWMPZLN`KKcJIeIFhHDjGAmF8oFDiKIdOM_TRVXVQa_\ LecGiWJbOMXHPRGSPGUOFXNFZMFaLEcKEfJEhHDkGDmFDpECrD\ CuCCwBFtCHqCJnDLlDNiEPfERdFTaFWZFYXG_UGaRHcPHeMIgJ\ IiHIkJHlKHmLHnNGrOGvPGzNJzLLtJNnIPiGReEUdDWbBY`9__\ 8aaFbcLbeRbgXbibbkhbmnbotbpzbmrajjagbadV`aN`_G`_G_\ _F__F__F__F__FZ_EZ_EZ_EZZEYZEYZEYZDYZDXZDXZDXZDXr5\ _x4Xs9YoDYkHZgLZcPZ_T_WX_S``Od`Kh`Xjdilhumkpngkocf\ p_aqWXrSSsONtKIuGDvC8w84x46y87zB8zFAzIBzMCzPDzTFzW\ Gz_HzbIzeHzfHzfHzfHzfHzfHzfGzgGzgGzgGzgGzgGzgJzdMz\ bPz`RzZUzXXzV_zTazRdzPhzd } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 21-08-08 (A Trunk-Full [7])
by Jim Muth 20 Aug '08

20 Aug '08

FOTD -- August 21, 2008 (Rating 7) Fractal visionaries and enthusiasts: The following paragraph is science, not philosophy. Physicists are searching for the 'Higgs particle', which is the particle aspect of the 'Higgs field', the field that is theorized to interact with and give mass to other particles. This 'Higgs particle' is assumed to be so massive that the world's most powerful accelerators will be pushed to the limit in the effort to find it. My question of the day is this: what then gives mass to the Higgs particle? Is it self-massifying? When you stop laughing, try to think of a rational answer. While we're pondering that puzzling bit of science, let's discuss the fractal of today. Today's image is a scene in the East Valley area of the Mandeloid that results when Z^2 is divided by (Z^(-0.91)+500). The actual minibrot in the image is found deep in an elephant trunk of an elephant that itself lies deep in the trunk of an even larger elephant. I guess it's elephants all the way down. This endless nest of elephants inspired the name "A Trunk-Full". A certain lack of satisfaction held the rating to a not-too-bad 7. The calculation time of 2 minutes may be done away with by trekking to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the pre-rendered image there. Wednesday was the reference standard perfect day here at Fractal Central. All measured parameters of the atmosphere were perfect for both human and cat comfort. The temperature was 77F 25C, the humidity was 50 percent, the sky was cloudless, and the north wind blew at a mild 7 knots. However, the fractal cats paid more attention to the scraggly manx cat that appears to have moved into the neighborhood. My day was slow enough to leave lots of time for leisure, yet busy enough to avoid recession concern. The next FOTD will be posted in 24 hours. Until then, take care, and I can't help it if these silly questions keep coming. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Trunk-Full { ; time=0:02:04.45-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot center-mag=+188.3134121\ 224326/-0.9553325705714198/4e+008/1/165/0 params=0/0/0/0/0/0/0/0/1.09/500 float=y maxiter=2200 inside=0 logmap=244 periodicity=10 colors=000OIKNIKMIKLHKKGKKFKKEKKDOKCRKBUNDTPESSGSU\ HRWJRZKQ`MQbNPeOOgQOjRNlTNnUMqWMsXLuYLtWMtVNtTOtSP\ tRPtPQtORtMStLTtKTzbdztozsnzsmzrmzrlzqlxqkvpjtpjro\ ipoimnhkngimggmfemfbje5Wa7Va9UaBTaDSaFRbHQcJPcLOcN\ NcPNcRLiTLjVMkXMoZNp`Pl_QlZRiYRfXScWS`UTYTUVSUSRVP\ QVNRXISYES_AT`6Ta2bOGlATt6`z3gz5fz7ez9ezBdzDczFczH\ bzJazLazN`zP_zR_zTZzVYzXYuWWpWVkWTfWSaVRXVPSVONVNT\ WSYXWbX`gYdlZiqZmv_rz_vwZusZtoZtkYsgYscYr_XqWXqSXp\ OXpNVkMUgMTbLSZLQUKPQKOLJNHJMDIPEISEHVEHXEH_EGbFGd\ FFgFFjFFlFXaJmSNzIQyCOx7NwANvDNuHNz1Mx5Poihnkjmllm\ mnknjinfgnbeo_doWboS`pPZpLYpHWqEUqASq6Rq3mp6zp8zpB\ zpDzpGzzczzz`pNbpPcpSdpUepWZiVScVLYVJNLICBMDEQDHTD\ JXDM_DOcERfETjEWnEZqE`uFcxFezFhzFjzImzLozOnzRnzUmy\ Wmv_msblpelmhkjkkgnkdqjajjZmj_oc`qXasQbuJcwCdz6bzD\ `zJ_zPYzVWz`Vzfcz2kz4sz5zz6zz7zzDzzIzzOzzTzz`zzRzz\ IzzJzzKzzLzzMzzNzzOzzOzzP } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 20-08-08 (Blue Mandeloid [8])
by Jim Muth 19 Aug '08

19 Aug '08

FOTD -- August 20, 2008 (Rating 8) Fractal visionaries and enthusiasts: Today's image is undoubtedly the bluest of all time. But it's not really a melancholy blue, it's a dynamic artistic blue, a deep royal blue that brings out the incredible energies flowing within the number fields that make up the world of fractals. Actually, it's a slice of the Julibrot that results when Z^2 is divided by (Z^(2)+1.5). Yes, I realize that the value of real(p5) is 4, but dividing Z^2 by Z^2 creates a fractal with Z^4 attributes just as multiplying Z^2 by Z^2 creates Z^4 attri- butes. The 1.5 value of imag(p5) merely enlarges the parent fractal and moves the switchover to Z^4 stuff to a deeper level. To add to the confusion, the orientation of the image slice lies halfway between the Mandelbrot and Rectangular directions. And actually, the Mandelbrot attributes are more apparent in this halfway direction than in the straight Mandelbrot direction. (To see the straight Mandelbrot direction change the value of real(p1) from 45 to zero.) Since blue is one of my favorite colors, and there is so much of it in today's image, I rated the image at an 8. The name "Blue Mandeloid" is a bit of a misnomer however, since the image is as much a Seahorse Valley Rectangleoid as a Mandelbrot fractal. One thing not in doubt is the speed of the calculation. It takes all of 13-1/2 seconds for the included parameter file to run on a S.O.T.A. machine capable of digesting ancient DOS programs such as Fractint. The finished image, in all its deep blueness, is or soon will be posted for instant viewing enjoyment on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> There were a few more clouds than the fractal cats would have preferred here at Fractal Central on Tuesday, but there could be no complaining about the temperature of 77F 25C. The cats did not complain. With the real work finished early, my day was a bit slow. After browsing an hour or so in the philosophical section of the local library, I returned and settled down for my daily contest with the world of numbers. As today's image shows, the results of the battle were rather good. The next FOTD will be posted in 24 hours. Until then, take care, and think in higher dimensions. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Blue_Mandeloid { ; time=0:00:13.34-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot passes=t center-mag=0/-0.457742/0.9418072/0.819/90/0 params=45/0/0/90/-1.25/0/0/0/4/1.5 float=y maxiter=1500 inside=0 periodicity=10 colors=000D3AD3DD3GE3JE3ME3PF7SFBVGFYGI`HMcHQfIUiI\ XlH_oGbrFeuEhwFkxKnyPqzUtzZwzczzhxzmvzrszvpzzmzzjz\ zgzznzzpzzqzzrzzpzwozwmzwizwgzwfzwgzwfzVlzUmzTmzSm\ zRmzZgzfbznXzvSzrQznPzjOzgNzcLz_KzWJzTIzUGzVEzWCzX\ AzX8zP7zH6z95zJVzTszKczCPzDPzDOzEOzENzFNzFMzGMzGLz\ HLzHKzIKzIJzIJzHMzGPzGRzFUzEWzEZzD`zCczCfzBhzAkzAm\ zDjz9pzIBzFQzCdz6szl7zTVzVOzNZzGhzfPzcSzaUzZWzXYzU\ _zSazQczNfzLhzIjzGlzDnzBpzxJzfVzQfza5zXDzTKzPRzLYz\ HdzDkz9Yz9hz9wz9vz9uz9uz9tz9tz9sz9sz9rzSAzPFzNKzLP\ zJUzHZzFczDhzBmzx9zsDzoHzkLzfPzbTzZWzU_zQczMgzHkzD\ ozVKzTNzRPzQSzOUzNXzLZzKazIczGfzFhzDkzCmzApzSIzLVz\ Ffz49z6Lz7Wz8gz0Wz5gzn3zUTz6Yz8hzMqzKrzIrzHrzFrzDr\ zCrzArzdDzaHz_KzXNzVQzSUzQXzN_zLbzIfzGizDlzBozKFzJ\ JzINzHQzGUzFYzE`zDdzChzBkzAozLlzFoziGzdLz_QzWVzR_z\ MdzIizDnzNXzIdzDkz8uz9tz9tz9tz9sz9sz9sz9sz9rz9rz9r\ ztUzh`zEGzDBzC6zB2zC3zC3z } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 19-08-08 (Stars of Iteration [8])
by Jim Muth 18 Aug '08

18 Aug '08

FOTD -- August 19, 2008 (Rating 8) Fractal visionaries and enthusiasts: The formula for today's image adds a very small bit of Z^(-20) to Z^2 to produce a Mandelbrot set with disks of Z^(-20) stuff at the centers of all the bays and buds. The image is located on the X-axis, in the detail at the east edge of a disk almost filling the large period-2 bud of the M-set. More than anything else it resembles a surrealist's spider-web. I named the image "Stars of Iteration", which sounds a little poetic and in a way describes not only today's fractal, but all fractals. And then I rated it at an 8. I considered adding a half point for my coloring, but decided that I did not do quite enough color tweaking to merit the extra half-point. The calculation time of only 42 seconds is fast enough to cause no impatience. The finished image, which is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> is convenient enough to totally take the work out of fractals. With a temperature of 88F 31C here at Fractal Central on Monday, it was just a bit too warm to be perfect, but all else was the picture of perfection. The dynamic fractal cats, who never stop reiterating, agreed. Just after lunch they spotted an unfamil- iar manx cat in the yard next door, and with a volley of hisses and growls, sent it on its way. I did not tell them that the cat was ready to move on anyway, and their empty threats had nothing to do with its departure. Otherwise the day was uneventful. The next FOTD will be posted in 24 hours. Until then, take care, and to become famous, solve the measurement problem. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Stars_of_Iteration { ; time=0:00:42.84-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.9160783767764306/0/8.62e+008 params=1/2/1e-018/-20/0/0/0/0 float=y maxiter=1450 inside=0 logmap=153 symmetry=xaxis periodicity=10 colors=0000EC0FF0GI0HL0IO0JQ0LT0NW0PZ0Ra0Td0Vg1XiD\ _aPbV`cOldHwdAwgBwjCwmDwpEwsFwvGwyGvvFutFuqFtoFslF\ sjFrhFqeFqcFp`FoZFoWFnUFnSFoTEpTDqTCrTBsTAtT9uT8vT\ 7wT6xT5yT4yT4pO9hJEsFTSAcJ5cB1cC2cC2ZD2UC2PB2KA2FA\ 2AA3AA3AA3AA3AA3AC3AF3AI3AN5AS7FW9L`BReCWiEanGgsPz\ wUzvUzuUzuUztUztPysKwrHurHsqHsqHsmJmjLhgNcdPZaRUYT\ OVVJSXEPZ9M_4K`5Ja6Ha6Gb7Fb8Dc8Cc9Ad99dA8eB6eB5fC4\ fCm6Am9DmCGmFJmIMmKOmNRmQUcTXUW_OYaSdSWkJ_zAbzKYzU\ TzcOzmJztFzzGzzHzzHzzIzzIzzJzzKzzKkVLlYLm`MncMnfOl\ dQjcShbUg`We_YcZZbY``WbZVdXUfWShURjSQkRPceQXsQUrQQ\ qRNpRzoSznSzmTzlTzkTziQHhNLgLPfITeFXdD`cAdb7ha5cX5\ _T5VP5RL5PPAOSENWIMZMLbQKeVJiZIlbHpzGszIzzFrzCjz9c\ z6Wv4Pr3Mm3Kh2Ic2GZ1E_1Ce0Ak08q06v6CoCIhIOaOUVU_U_\ eZdkcamh_omYqrVsvzuzzwzzxzzyzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzezzNzz4zz6zz7zz8zz9zzAzzCzzDzzEzzFzzGzzIz\ zJzzezzfzzgzzhzzhzzezzbzz } 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 18-08-08 (A Quick Journey [5])
by Jim Muth 17 Aug '08

17 Aug '08

FOTD -- August 18, 2008 (Rating 5) Fractal visionaries and enthusiasts: Today's image is a minor thing worth a rating of a measly 5 points. But its calculation time of an equally measly 17 seconds means that almost no time will be wasted calculating it. The parent fractal combines just the tiniest bit of Z^(-63) with Z^2 before adding C. This parent resembles a classic Mandelbrot set obscures by scalloped disks. Today's scene is located near the X-axis in an interesting area between the two largest disks. I added a modicum of interest to the not-so-impressive scene by rendering it with the outside set to 'tdis'. Then I named the image "A Quick Journey" because I found it in less than 5 minutes. And I rated it a 5 because I found it in less than 5 minutes. The final result may be seen by running the included parameter file or by viewing the completed image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The sky was blue enough, but a few too many puffy white clouds kept Sunday from being absolutely perfect here at Fractal Central. The temperature of 84F 29C and low humidity were all that could be asked for, but those puffy clouds got in the way of the sun a bit too often. The fractal cats, unconcerned with minor cloud details, had a near perfect day anyway. My day was very good, which I would enjoy being able to say more often. The day's fractal was not quite so good, but no one ever claimed that this fractal world is perfect. The next FOTD, hope- fully a bit closer to perfection even if not quite there, will be posted in 24 hours. Until then, take care, and embrace your reality before it gets away. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Quick_Journey { ; time=0:00:17.04-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident center-mag=-0.840428912973/+0.001176307923/9345305\ /1/-115/0 params=1/2/1e-018/-63/0/0/0/0 float=y maxiter=1000 inside=0 outside=tdis periodicity=10 colors=000P8W5BS`ibYg_WeXUcURaRP_ONYLLWIKXTKYcJZnJ\ ZxGYtEYpCXlAXh8Wd6W`4VX2VT9HIG48MBERIKWPQ`WWebajig\ oolmijkchiYggSefMdRBjNHkJNlGTmCZn8do5jp`GUbGVdGWfG\ XhGYjGZlG_mG`gI_bK_YLZTNZOOYJQYERYKTXPVWUWWZYVcZVa\ QM`HE_86i`xhapgbifcbedVdeOcfHcgAZjEVlIRnMNpPbzjYri\ TjhObhKVgFNgAFf68fDGbJN_QUXW`UcUXkN_sHbrJZrLVrNRrP\ NrRJrTFrVBrX7mRDhMIcGOZBTU5ZP0cUHVZXMclE`mHZnKXoNU\ pQSqTQqVLhOH`HCTA8L3GQ7OUAK_EHeHEkLBpOAnT9mX9l`8kd\ 7ii7hm6gq6fu8isAlrCnpEqoGtmIvlMwcQwVUwNQoPMhRIaTEU\ UANW6GY39Z7F`AKbDQdGVfK`hNejQklTpmZf_cXMX_OQbQJdSC\ gU6iVAiSEiPIiMRaLZULfMLTdBFv2Dw5Cw7AwA9wC7wF6wH4wK\ 3wMPBkKLgFVdBda6nZ2xWPUdVTc`TcfTclTcrTcwTcsUaoU_kU\ YhUWcPUZLTVHRQCQL8OH4NVK_gZktmwgicVeLZhNajOelPhoRl\ qSosTruUsqTtnSukRvgRwdQxaPxZPraXldcfgk`jrVly_hoddf\ i`XnXOsTEwQ5pV4iZ4bb3Wf3Pj3In2Br24v2Bt1Ir1Pp1Wn0bl\ 0ij0pi0gd7_`ESXLKTSCPYi5_ } 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 17-08-08 (It Is Impossible [6.5])
by Jim Muth 16 Aug '08

16 Aug '08

FOTD -- August 17, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: As the title of today's image implies, the image is impossible. With the value of real(p5) set to -2, the minibrots deep in the parent fractal must be of the order -2. Minibrots of a negative order are by definition impossible however. If they did exist, they would have a number of lobes 1 less that their order, but how can a minibrot have minus-3 lobes? This is what I decided to find out in the search for today's fractal, when I set the value of real(p5) at minus-2. The first problem was that, with such a large escape radius and a negative exponent of Z, the image turned out to be all blank inside stuff -- an evaporated image. This problem was quickly solved by re- rendering the blank screen with an active inside fill. In this case I first tried the 'bof61' fill. When I did this, a ghostly arrowhead-shaped thing appeared, only vaguely resembling a Mandelbrot shape with a rudimentary East Valley. A closer search of this proto-East Valley revealed the symmetries that indicate minibrots are at the center. Zooming in on a prominent symmetry, I found today's scene, with its pseudo-minibrot at the center. The 'bof61' inside fill revealed the scene, but I found that the 'fmod' fill actually works best with this image. And what does a minibrot with minus-3 lobes look like? That question can be answered by checking today's image. I'm not sure that the thing at the center is a minibrot at all, but with its symmetrical surroundings, it sure does seem to be trying to be one. After all this mathematical excitement, I could rate the image no higher than a 6.5, 1/2 point of which is due to my coloring. The calculation time of a fireball 45 seconds will burn no one. And as always, the finished image is or soon will be available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A perfect day here at Fractal Central on Saturday pleased humans and cats alike. The warm sun, blue sky and temperature of 77F 25C were perfect for everything but skiing. I doubt that anyone in the area had planned on skiing however. The day's FOTD might be a bit hasty, but the next FOTD is due in 24 hours. I suspect it will actually be ready on time, and it might even be a pretty good one. Until then, take care and make the impossible possible. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= It_Is_Impossible { ; time=0:00:45.13-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot passes=1 periodicity=10 center-mag=+0.21857780829516740/+0.051382415163788\ 77/284576.4/1/-87.5/0 params=0/0/0/0/0/0/0/0/-2/0.5 float=y maxiter=1000 inside=fmod proximity=0.051 colors=000gaEhcEjeElgDniDokDjdLfZSaTZYMeTGlPAsrmmX\ Cn`DldDihEglFepFbtG`xHZzHXzKVyNUwPSccctVPsXOq_MpaL\ qbNrbPsbRtbTubVvcWwcYxc_UUPzcczddzdfzdhzdjzdlzdmze\ kzfjxfiughsggqhfoielicjjbhjafk`cl_alZ_mYYmX`kWciVf\ gUuuMppPlkRhfTdbV`YXXT_TPaPKcLFeF9eHBgIDhJFjKHkLJl\ MLnNNoOPpPRrQTsLXvOWuRVtUUtXTs_SsbRreQqhPqkOpnNpqM\ oPTGdPYsLooMlkMjgMgcNe_NcXN`TNZPOXLOUHOSBMOEOQHPSK\ QUNRWQSYTT_WU`ZVbaWddXfgYhjZjm_lvQHsWYnfvp`mqWerRY\ sMQtHImRHf`G_jFUsFVpIVnLVlNVjQVhSWfVWdXWb_W`aWZdMe\ NWXfOHBXL`iNzdOz_OyWOyRPxNPwIPwEQv9Qu5QuFRnPSgYTag\ UVcBgogHp`LpUPqOTqHXrA`r4ds6as7_s9YsAWtCTtDRtEPtGN\ tHLuJIuKGuMEuNC8zihVckTbmSaoR`rP_tOZvNYzN_xMYuLXrL\ VoKUlKSiJRfJPcIO`INDSkLWeT_``cWhgQpkLxoGzrBboUAmkE\ gWIbGKcHMcIOcJPcJRcKTcLUcLWcMYcN_cO`cObcPdcQecQWRQ\ MEQC2QD3PE4OF5OG6NH7NI8MJ8MK9LLALMBKNCKOEJOGJQIISK\ IUMHVOHXQHZSG`UGcWGcXFcXF } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 16-08-08 (Few Discontinuities [7])
by Jim Muth 15 Aug '08

15 Aug '08

FOTD -- August 16, 2008 (Rating 7) Fractal visionaries and enthusiasts: It is an inescapable mathematical fact that fractals with frac- tional powers of Z must have discontinuities. These discontinui- ties sometimes make interesting patterns in themselves, but just as often they spoil the perfection of the fractal in which they are found. The discontinuities cannot be avoided, but as the FOTD image for today unexpectedly shows, they can be minimized. The formula for today's image contains Z^(3.5), which demands that the image have discontinuities. The breaks are there indeed, but they are so few and so unobtrusive that they could easily be missed when the image is glanced at casually. With its one minor break on the left side, today's image is a scene in the East Valley area of its parent fractal, which is an oversized Mandelbrot set. I named it "Few Discontinuities" and rated it at a 7. The calculation time of just under 5 minutes is fast enough to hold boredom at bay, yet slow enough to allow ample time for anticipation. The image is also available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Pleasant temperatures and plenty sun made Friday an acceptable day here at Fractal Central. A sudden thunder-shower at 5pm was too brief to spoil things. The fractal cats agreed as they stretched in the returning sun. For me the day was acceptable. I could think of a few things that might have gone better, but why quibble with minutiae. The next in the apparently endless series of FOTD's will be posted in 24 hours. Until then, take care, and if life is all a dream, where will we be when we wake up? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= FewDiscontinuities { ; time=0:04:53.03-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot center-mag=+3.798906332849346/-0.0029529560051977/\ 5.019158e+007/1/20/0 params=0/0/0/0/0/0/0/0/3.5/15 float=y maxiter=15000 inside=0 periodicity=10 colors=000jbjgciddhaegZefWfeTgdQhcNibKjaHk`Fk`Lh_Q\ fZVdY_bXd`WiZVnXUsVTxTTsWRnZQj`OecNafLXhKTkIOnHKpF\ FsEBuDApFAlHAhIAdKA`M9XN9TP9PR9LS9HU9DVBFXCGZEH_FJ\ aHKbILdJMeLOgMPiOQjPSlRTmSUoTVpUWoVXnWXnXYmYZlZZl_\ _k`_ja`jbaicahdbhebgfcfgdfhdeiediedhbeh_ehYfhVfhTg\ hQghOhhLhgIhgGigDigBjg8jg6kg3kg1ke2ic3ib4i`5hZ6hY7\ gW8gU9fTAfRBePCeODeMEeKFeJGeHHeFIeEJeBGi8Dl5Ao28r5\ Ar7CsADtCFuFGvHIwKJxMLyPMzROxTQvWRtYTr`UpbWpeXogZo\ j_olaonbom_nlYmlWmkTljRkjPkiNjhKihIigGhfEgfBge9fd7\ eb3gd5ee6cf8ag9`hBZiCXjEWkFUlHSmIRnKPoLNpNLqOKrQIs\ RGtTFuUDvVBvW1xZAwbJtfRrj_mmhlolknngmkdke`h`YfVUcQ\ Q`KNYFJV9HR3GT4FV5EX6EZ7D`8Cb9BdABfBAhC9jD8lE2Nn8m\ EAe9CY5AN0DQ1GS2JU3MW4PY5R_6Ua7Xc7_f8bh9djAglBjnCm\ pDprEtuFrtEptEotEmsDlsDjsDisDgrCerCdrCbqBaqB_qB`s9\ ZqBXpCVnDUmESkFQjGPhINgJLeKKdLIcMGaNE`ODZQBYR9WS8V\ T6TU4SV1PV3RW5TW7VW8WWmak } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 15-08-08 (Little Critters [8])
by Jim Muth 14 Aug '08

14 Aug '08

FOTD -- August 15, 2008 (Rating 8) Fractal visionaries and enthusiasts: In today's fractal I divided Z^2 by (Z^(0.000001)+5), or some- thing like that, and then added C. At least, that's what I think happened when I entered the parameters. But regardless of what actually happened, the resulting parent fractal resembles an oversized Mandelbrot set, though deep inside it is different. I found today's scene on the edge of the infinitely divided main spike, in the area just east of the large minibrot. This is quite a rich area, filled with surprises, an area which until now I have largely ignored. I named the image "Little Critters" when I noticed the dark insect-like things sitting on the webs surrounding the central minibrot. Then I rated the image at an 8, which includes a small reward for my coloring. The brief calculation time of 1-1/3 minutes will make everyone but the most impatient fractalist happy. And even those impatient few will be only slightly discombobulated. To avoid all possibility of discombobulation however, the finished image may be accessed on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Too many clouds and a threat of rain kept Thursday from being perfect here at Fractal Central. But the temperature of 82F 28C was quite pleasant and the rain held off until nightfall, so the fractal cats had nothing to complain about. I had nothing to complain about either. So I'm not complaining. The next Fractal of the Day will be posted in 24 hours. Until then, take care, float like a duck and sting like a flea. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Little_Critters { ; time=0:01:20.40-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot center-mag=-10.49111003\ 76656/+0.00000459624450347/5.459246e+011/1/177.5/0 params=0/0/0/0/0/0/0/0/2.000001/5 float=y inside=0 maxiter=1800 logmap=200 periodicity=10 mathtolerance=0.05/1 colors=000K8_K9bK9dKAgKAiKEkKHmKKoKNqKQsKUsKXvJ`vG\ cxDfvAjw7nxAqyKuzUvuZwqcwlhuhmscrq_voVzmRzkUziXzfZ\ zbazZczXfzVhFSdEP`CNXBKTAHP8FL7CH69D479345222`_IZZ\ HYXGXWGWVFVUFTTESSERQDQPCPOCNNBMMBLLAKJ9JI9HH8GG8F\ F7EE7DC6BB5AA5994884773552442331221110AM38H26D1481\ 240oYOjULeRJ`OHXLFSIDNFAIC8E969644324Yz3Xz3Wz3Vz3V\ z3Uz3Tz3Tz3Sz3Rz3Rz3Qv3Ps2Po2Ok2Ng2Nd2Mc2Lb2L`2K_2\ JZ2JY2IW2HV2HU1GT1FS1EQ1EP1DO1CN1CL1BK1AJ1AI19H18F\ 08E07D06C06A059048047036024023012001W0NU0LS0KR0Jq4\ 5n45k45h45e35b35_35X35U35R25O25L25I25F25J79MCCQGFT\ LIWPL_UObYRfbUifXlk_pobstevxhuwitvisuirtiqsipriori\ nqimpiloiknijmiilihligjfgicfh`fgYffVedSecPdbMd`JdZ\ G_ULVSPRRUMQYHPbDQfEReESeETeEUeFUeFWeFYdF_dKadPcdU\ edZgdbidfkajm_noYqqWusUuuSuwQvzOwzMxzKyzIzzGzzFzzE\ zzDzzCzzBzzAzz9zz8zz7zz6zz54z49z7Ez9JzCOzETzHYzJbz\ MgzOlzRqzTuzVezRQzNlzVkzY } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 14-08-08 (Cosmic Un-Conquest [Rating Unbounded])
by Jim Muth 13 Aug '08

13 Aug '08

FOTD -- August 14, 2008 (Rating Unbounded) Fractal visionaries and enthusiasts: Since space is unbounded though not necessarily infinite, and today's image reminds me of a globular cluster in space, I decided to give today's image an unbounded rating. Regardless of what this means when applied to a fractal rating, today's image is different enough to be well worth a look. I named the image "Cosmic Un-Conquest" in sympathy with mankind, who, because he must carry a clumsy physical body with him wherever he goes, will never conquer even the solar system, much less the infinite multiverse. A temporary mind of limitless fancy trapped in a body of wet kleenex can do little more than sit here on earth, look up at the night sky and wish it were otherwise. But such is not the case with fractals, where we can venture wherever our computers and fanciful minds can take us. In today's case we journey to the land of Z^2/(Z^(-2)+11)+C, which at first appears to be a blank screen consisting totally of inside stuff. But, as the 'bof61' fill reveals, this inside stuff is active. Today's image is unusual in that it is dependent on both the screen resolution and the choice of passes. Whenever one of these is changed, a different image will result, since different dots will be chosen or passed over. Perhaps the biggest drawback in the image is its rather slow calculation time of 10 minutes. But this drawback may be turned into an advantage by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image is posted for effortless viewing. Fine midsummer weather prevailed here at Fractal Central on Wednesday, with a cat-pleasing temperature of 82F 28C and sunny skies. In my department things went pretty well also. As for the next FOTD, it will be posted in 24 hours, perhaps not as cosmic as today's but interesting nevertheless. Until then, let your mind soar where your body cannot. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Cosmic_Un-Conquest { ; time=0:10:07.25-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot passes=1 float=y center-mag=-1.1400168468679/+1.308367613934373/\ 1.048206e+007 params=0/0/0/0/0/0/0/0/-2/11 maxiter=1500 inside=bof61 logmap=yes periodicity=10 colors=000Fm4Em4Dn4Cn4Bn4Bo5Ao59p58p57p56q55q54q53\ r52r52r5Mp7eq8do9dnAcmBclCbkDbjEaiFagG`fH`eI_dJ_cK\ ZbLZaMZ`NYZOYYPXXQXWRWVSWUTVTUVRVUQWUPXTOYTNZSM_SL\ `TJ_SK`RL`RMaQNaQObPPbPQbORcOScNTdMUdMUeLVeLWeKXfK\ YfJZgJ_gI`hHahHbhGciGdiFdjFejEfkEgkDhkCilCjlBkmBlm\ AmnAnn9on9oo8poAqpzzzAsqAtqAuqAvrAwrAxsAysAyu3yt3y\ s3yrUUU3yqzpc3yo3yo4yn4ym4ym4ylkhz4yj4yj4yi5yh5yg5\ yg5yz5ye5ye5yd5yczmb6yb6ya6y`6y`6y_6yZzyY7yz7yz7yz\ 7yz7yz7yz7yz7yz8yz8yz8yz8yz8yz8yz8yz8yz00000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 0000000000000000000000000 } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=-(real(p5)-2), bb=imag(p5+0.00000000000000000001), 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 13-08-08 (Fractal in Flight [7.5])
by Jim Muth 12 Aug '08

12 Aug '08

FOTD -- August 13, 2008 (Rating 9) Fractal visionaries and enthusiasts: Today's fractal takes us into fractional powers of Z. In the image for today the exponent is 2.5. The value of 100 that I gave to imag(p5) assures that the parent fractal will be huge, and on the surface will resemble the Mandelbrot set. But deep inside the 2.5 characteristics will appear. Today's image is located on the edge of the infinitely divided main spike of the monumental parent fractal, in the area just east of the large minibrot. I named it "Fractal in Flight". I must have had a reason for choosing such a name, but the reason now totally eludes me. The rating of a 9 includes a full point for my coloring efforts. The unusual colors are the main feature of the image. There is no risk of impatience appearing when the included para- meter file is run. The calculation time of one brief minute can hardly be bettered. The image may also be seen on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A very pleasant summer day prevailed here at Fractal Central on Tuesday, with blue skies decorated with puffy clouds, and a temperature of 81F 27C. The cats, being fractal by nature, took the conditions in fragmentary bits and pieces. I took the day as it came, finishing the work on schedule with time for a pretty good fractal. The next fractal, a cosmic one, (not a comic one), will be posted in 24 hours. Until then, take care, and when you find your reality, cling to it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fractal_in_Flight { ; time=0:01:03.45-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot passes=1 logmap=92 center-mag=-170.9755598748956/+0.1185530913812762/\ 1.643467e+009/1/172.5/0 params=0/0/0/0/0/0/0/0/2.5\ /100 float=y maxiter=1725 inside=0 periodicity=10 colors=000A6IA7KA8MA9OAAQABSACUADWAFYAH_HKaPMcROeW\ MhVKcUIYTGTSEORCIPADN98L9BN9EPAHREPTITWMXYQ_gS`pZa\ zaczfez`XvSPrIGm78c00W23V45U67T79S9BRBDQCFPEIOGKNI\ MMEKLFKKFKJFKMFKOFKQHKTHMVMKXLJ_LHaLFcKDfKBhJAjJ8m\ J6oI4qI2sI1wklsjjojhljfhiddibai`YiZUhXRhVNhTJhRGgP\ CgNhgLhgJhhKhhLhhchhchhchhchhchhchhcThQVhRXhSZhSLP\ a85kBBjDGiFLhHQgJVgM_fOdeQidSncUscSreQrgOqhMqjKqlI\ pzGpzEpzCozAoz8oz6nz4nz2nz6ozApzEqqIrnMskQthTtfXuc\ `v`dwYhxVlySpzPszNotQlnTihWfbZbYa_SdXMgUGjRBlUFkXI\ kZLkaOkcRkbPgaNcaL_`JW`HS_FOZDKZBGY9CY79aX4zv0zw1z\ w2zw2zw3zw4zw4zw5zw5zw6zw7zw7zw8zw9zw9zxAzyAzzIzzQ\ zzYzzezzmzztzzdzzQzzBzzHzzMzzRzzWXzaYzfZzk_zp`zubz\ tdzsfzshzrjzrkzqmzpozpqzoszouznvznpzdjzVdzMZzCUz3S\ z6Rz8zzAzzDzzFzzHzzJzzMzzOzzQFzSEzVzzXzzZzz`zzTzzL\ zzDzzCfzBdzAaz9Zz8Xz7Uz6Sz6Qz7Oz8Nz9LzAKzBIzCHzDFz\ EEzEQz``zvZzsYzpXzmVzjUzg } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=-(real(p5)-2), bb=imag(p5+0.00000000000000000001), 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 12-08-08 (No More Perfection [No Rating])
by Jim Muth 11 Aug '08

11 Aug '08

FOTD -- August 12, 2008 (No Rating) Fractal visionaries and enthusiasts: NEW FORMULA ALERT! The DivideJulibrot formula included in today's parameter file is a new version that has been slightly changed from the earlier version. The earlier version will still work, but the version in today's parameter file is some- what faster. As for today's image, take it or leave it. For some reason I dislike perfection, probably because it leaves no room for improvement. And this afternoon when I took another look at yesterday's image, it struck me as being just a bit too perfect. A tiny rotation took care of the perfection however. A rotation of a mere 0.0005 degree from the Julia orientation wreaked total havoc on yesterday's image. (A slightly larger rotation makes the rectangle go away completely.) But the wreckage struck me as being good enough to serve as FOTD for August 11, especially since I had little time for a further fractal search. The color palette is the same as yesterday's, with only a slight change. Since yesterday's image was the real thing, I gave no rating to today's image, which is a parody of yesterday's. The name "No More Perfection" explains itself. The parameter file runs in 1-1/4 minutes, about the same time it takes to view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Monday here at Fractal Central was actually a bit too chilly for perfection, and the heavy thunder-shower in mid-afternoon made it even cooler. An afternoon temperature of 63F 17C is hardly ideal for mid-August in the northern hemisphere, but the day was salvaged in the evening by a lovely double rainbow spanning the eastern sky. The fractal cats enjoyed the few intervals with brilliant sun, and endured the periods of rain. My day was rather busy, yet pleasant enough. I expect a repeat tomorrow. The next FOTD will be posted in 24 hours. Until then, take care, and the farmers must be praying for rain. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= No_More_Perfection { ; time=0:01:14.44-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot passes=1 center-mag=-0.0000104151/+0.002511651686/798281.4 params=89.9995/0/89.9999/0/-1.7435/0/0.00019/0.073\ 88/2.003/0.0003385 float=y maxiter=3500 inside=255 logmap=136 periodicity=10 colors=000EJMILNNNOSQQXTUaWYmdftiongjj`cdUW_NOUHGE\ 2DJ7BOBATG9hF6mK9mPBmUDmZFmcHmkImhJmfKmdLmbMmcNmhO\ mcPcVQcTRcRScPTcNUcLVcJWcIacHXcHScHOmHJgHEsG5mHAgI\ FaJKWKPQLUONTKMYHMbEMgBMl6Ds7Ir8Mq9Qp9UoAZnBbmCflC\ jlzauzcpzelzghziczk_zmWzoUzqSzsRzuPzwOzxNzyLzzKzzI\ zzHzzGzzLzzPzzUzzYzzbzzfzzkzzozznzznzzmzzmzzlzzlzz\ kzzkzzjzzjzzizzizzhzzhzzgzzgzzfzzfzzYzzezzezzdzzdz\ zczzczzbzzbzzazzazz`zz`zz_zz_zzZzzZzzYzzYdzXezX9zz\ BzzCzzDzzEzzFzzGzzHzzIzzJzzKzzLzzMzzNzzOzNPzNQzORz\ PSzPTzQUzQVzRWzSXzSYzTZzT_zU`zVazVbzWzzWzzzzzFzzzz\ zGzzzzzHzzzzzHzzzzzIzzzzzIzzzzzJzzzzzJzzzzzKzzzzzL\ zzzzzLzzzzzMzzzzzMzzzzzNzzzzzNzzzgzOgzzfzPfzzfzPfz\ zfzQfzzfzQfzzfzRfzzfzRfzzfzSfzzzzTzzzzzTzzzzzUzzzz\ zUzzzzzVzzzzzVzzzzzWzzzzzXzzzezXTzzUzXUzzUzXUzzVzX\ VzzVzXVzzWzXWzzWzXWzzWzXXzzXzXXzzXzXYzzYzXYzzYzXYz\ zZzXZzzZzXZzz_zX_zz_zX_zz } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=-(real(p5)-2), bb=imag(p5+0.00000000000000000001), 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 11-08-08 (Theater of the Mind [7.5])
by Jim Muth 10 Aug '08

10 Aug '08

FOTD -- August 11, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: As I studied today's image, I fancied myself sitting in the balcony of a celestial movie theater, viewing the fractal show being projected on the screen. I named the image "Theater of the Mind" because that's exactly what it is. The rating of a 7.5 might have been a point higher if I had not used variations of this same rectangle so often in previous FOTD's. The brilliant rectangle in the center is nothing other than a variation of our old friend the rectangle that lies in a Julia set of the East Valley area of the large fractured minibrot on the infinitely divided mail spike of the Z^(2.003)+C Mandeloid. In today's variation the minute value entered into the imag(p5) parameter has shrunk the rectangle almost to the point of invisi- bility. The slightest increase in this parameter will make the rectangle go away totally. The calculation time of 1-1/3 minutes should cause the average fractalist little if any inconvenience. The exceptional fractalist may wish to take the trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the finished image there. With lots of sun and a temperature of 81F 27C, Sunday was pleasant enough here at Fractal Central -- until 6pm that is, when the clouds started gathering. No rain ever fell, but thunder rumbled ominously in the north for an hour. The fractal cats ignored the weather and concentrated instead on a fly in the kitchen window. The fly eventually disappeared. My day was uneventful, which is acceptable. The next FOTD will be posted in 24 hours. Until then, take care, and unlike everything else, fractals are forever. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Theater_Of_TheMind { ; time=0:01:21.79-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot passes=1 center-mag=-0.00001033139728697/+0.002511651686093\ /860217 params=90/0/90/0/-1.7435/0/0.00019/0.073\ 88/2.003/0.0003385 float=y maxiter=3500 inside=255 logmap=136 periodicity=10 colors=000EJMILNNNOSQQXTUaWYmdftiongjj`cdUW_NOUHGE\ 2DJ7BOBATG9hF6mK9mPBmUDmZFmcHmkImhJmfKmdLmbMmcNmhO\ mcPcVQcTRcRScPTcNUcLVcJWcIacHXcHScHOmHJgHEsG5mHAgI\ FaJKWKPQLUONTKMYHMbEMgBMl6Ds7Ir8Mq9Qp9UoAZnBbmCflC\ jlmOufSp`WlU_hOccHg_BkW2mU5nS7oR9pPBqODrNFsLHtKJuI\ LvHNvGLrLJnPIkUGgYEcbD`fBXkAUoBVnCVnDVmEVmEVlFVlGV\ kHWkIWjJWjJWiKWiLWhMXhNXgOXgOXfPXfe`YQXeRYezmdzmdz\ mczmczmbzmbzmazmazm`zm`zm_zm_zmZzmZzmYzmYdzXezX9zz\ BzzCzzDzzEzzFzzGzzHzzIzzJzzKzzLzzMzzNzzOzNPzNQzORz\ PSzPTzQUzQVzRWzSXzSYzTZzT_zU`zVazVbzWzzWzzzzzFzzzz\ zGzzzzzHzzzzzHzzzzzIzzzzzIzzzzzJzzzzzJzzzzzKzzzzzL\ zzzzzLzzzzzMzzzzzMzzzzzNzzzzzNzzzgzOgzzfzPfzzfzPfz\ zfzQfzzfzQfzzfzRfzzfzRfzzfzSfzzzzTzzzzzTzzzzzUzzzz\ zUzzzzzVzzzzzVzzzzzWzzzzzXzzzezXTzzUzXUzzUzXUzzVzX\ VzzVzXVzzWzXWzzWzXWzzWzXXzzXzXXzzXzXYzzYzXYzzYzXYz\ zZzXZzzZzXZzz_zX_zz_zX_zz } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=real(p5)-2, bb=imag(p5)+0.00000000000000000001, 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(-aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 10-08-08 (Where Trees Come From [No Rating])
by Jim Muth 10 Aug '08

10 Aug '08

FOTD -- August 10, 2008 (No Rating) Fractal visionaries and enthusiasts: Today's image is one I found automatically. I named it "Where Trees Come From" because with only a slight change of parameters, I could turn the Julia image into one of those fractal trees. But today we have no trees. We have a surreal something, vaguely resembling a slavic helmet, better seen than described. There is no way I could honestly rate such a quickie image, so I let it go unrated. The calculation time of just under 9 minutes is longer than I would have preferred. But give Paul a chance to calculate and post the image, then rush to the FOTD web site to enjoy it. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With full sun and a temperature of 79F 26C, Saturday was the picture of perfection here in the Fractal Central area. The fractal cats must have agreed, for in the late evening when we returned from the day out, we found three waste baskets over- turned and the contents scattered -- a sure sign of bored and discontented cats. With little harm done, I managed a FOTD, though a bit too late to post on time. However, the next FOTD will be posted on time in 6 hours or so. Until then, take care, and fractals are the spirits of numbers, or are numbers the spirits of fractals? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= WhereTreesComeFrom { ; time=0:08:53.54-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=dividejulibrot passes=1 center-mag=45.1158/0/0.1140451/1/90/0 params=90/0/90/0/-105.58135/0/0/0/1.5/100 float=y maxiter=3000 inside=bof61 periodicity=10 colors=000JYCIVCHTBGQAGO9FL9EI8DG7CD6B74CB6DF8EJAE\ MCFQEGUFHYHH`JIdLJhNJkOKmQKnSLpULqXMsZMt`NvbNwdMtg\ LqjKnlJloIirHftGcwGayFbwFbvEcuEcsDdrDdqDdoCenCemBf\ kBfjAgiAggAgf9he9hc8ib8ia8i`PU_eF_u0_t2`s4ar6bq7cq\ 9dpBeoCfnEgnGhmHilJjkLkkMklQmlUnlYolapmermismmtmpu\ korjnphmmglkfkhdjfcicbha`ib_icZidYjeXjeVjfUkgTkhSk\ hRkiQljOlkNlkMmlLmmKmnJmnIkkIjiHigHheHgbGf`GeZGdXF\ cUFbS8nsAmtBmtCmtDltEltGltHktIktJktKktMjtNjtOjtPit\ QitSitThtUhtVhtWht_arbWqeQjgLdjGYlASo5Lq0Fp2Hp4Io6\ Jo8KnALnCMmEOmGPmIQlKRlMSkOTkQUjSWjUXiWYiYZi__ha`h\ cagecggdfiefkfemgeohftjeqidnhckgcigbfface``e`Zd_Wc\ ZTcYQbYOaXLaWI`VF_VD_UAZT7YT5YU6XV6XV6XW6XW6XX6XY6\ XY6WZ6WZ6W_6W`7W`7Wa7Wa7Vb7Vc7Vc7Vd7Vd7Ve7Ve7VWmXV\ kYUiZUhZTf_Se_Sc`Rb`Q`aQ_aPYbOWcOXcNTdMSdMQeLUeKNf\ JVzKMfLZdLSbMzzMY_NdjNcWzzzPiSPoRQoPzzNRuLSvLRwKfz\ JPrIOoIOmHNsGMgFLeFKbEK`D } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=real(p5)-2, bb=imag(p5)+0.00000000000000000001, 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(-aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 09-08-08 (Honest Square Deal [7])
by Jim Muth 08 Aug '08

08 Aug '08

FOTD -- August 09, 2008 (Rating 7) Fractal visionaries and enthusiasts: Yesterday's image is a Julia set that closely resembles the one in which the curious rectangle is found. In today's image I searched the place where the rectangle is found in the other Julia set. I found no open rectangle, though I did find an interesting rectangular shaped area quite deep at the same place in today's parent Julia set. OK, I admit I got out the evolver and fudged the real(p3) parameter a bit, and I also made a few tweaks to yesterday's color palette, but it's all in the name of good art. Even though the main feature of the image is a rectangle, I named it "Honest Square Deal". I gave it this name because no one ever heard of a rectangular deal. When the time came to assign the rating, I thought briefly and absent-mindedly before rating the image at a 7. A rating of a 7 is like the word 'nice'. It sounds pleasant but means nothing. The one place where the image really does excel is in its calcu- lation time, which at just over one minute will make the job of running the included parameter file as pleasant as a day at one's favorite get-away spot. Those whose over-qualified computers have an incurable case of fractintphobia may see the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Friday was pleasant enough here at Fractal Central. There was lots of sunshine and a temperature of 75F 24C, and if the sudden but brief midday thunder-shower was ignored, the day was ideal for any outdoor activity. The fractal cats had a rough day however. This morning FL took Cassie to the doctor for a shot, and when Nicholas, the macho one who fears only the doctor, saw the carrying box come out, he dashed under the bed, where he hid for several hours. All went well with Cassie, who normally is the timid one, but faced the doctor heroically. My day was moderately busy, as I got the work out of the way in preparation for a planned day out on Saturday. If the FOTD for August 10 is late, it will indicate that the day out was a success. Until next time, take care, and a fractal a day will keep the doctor away, at least until you run out of fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Honest_Square_Deal { ; time=1:04:11.62-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot passes=1 center-mag=+0.0175331707901178/+1.624411711936185/\ 7.144491e+007/1/-90/0 params=90/0/90/0/-43.7613069\ 8158602/0/0/0/2.5/25 float=y maxiter=975 inside=255 logmap=108 periodicity=10 colors=000aFXeHXhJYlL`nNerPjuRnwRzyXzu_zqVvnSmjQgg\ OccMU`K5aL4bN4bQ4cT3cW3dZ3da3fc2ge2ih2ml2up1ztczzm\ zvcvq2rn2mg2hg3cm3Zr3Uu3Pu8KrDFlIHgNIbRJXTJSQJUNKR\ LKOKKKJLOHLMGLJFMIDMHCMGBNF9NE8ND7NC6QAAS9Dz8Hz7Kz\ 6Nz5Rz4Uz3Yv2`r1cm0gm0jz0nz0qz0tz0so3sk6sh9sdDs`Gs\ YJsUMrQPrMTrJWrFZrBar8dr9asA_tBXuCVuDSuEQuFNuGLuHI\ uIGuJDuKBuL8uM6uN3uN1uN6uNBuNGuNLuNQuNVuNZuLXuKVuI\ TuHRuGPuENuDLuCKuJIuPGuVFu`DufBulAuf9u`9uW8uQ8uK7u\ F7u96u46u55u55u64u64u73u73u72u82u81u91u90u90uA2uB3\ uB4uC5uD6uD7uE8uF9uFAuGBuHCuHDuKOuMZuPiuRsuNjuJauF\ UuBLu8DuE4uJ0uQ3uXAubHuiOuoUumRukOuiMugJueGucEuaBu\ _8uY6uW3uU0uT0u2duRpuPkuNguMcuK_uJVuHRuGNuEJuDEuBA\ uA6u82u70u7Su7uuIjuT`ucQunGugEu`CuWhuVhuOcuH_uAWu4\ Su5Tu6Tu7Tu8Uu9UuAUuAUuDSuFRuHPuJOuLNuSPuYRucSuiUu\ _2uU21U31U44U57U6AV7DW8HX9KYANUBQWCTYDX_E_aFbbGecH\ hcHkeIifIhhJgiJfjKelKcmLb } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=real(p5)-2, bb=imag(p5)+0.00000000000000000001, 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(-aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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Re: [Fractint] AOTD
by JackOfTradeZ＠comcast.net 08 Aug '08

08 Aug '08

. Animation of Jim Muth FOTD 8/4/08 "hex-quad" is posted: http://www.fractal-animation.net/vid/nukleus.zip 640x480, WMV, 31 Meg, 2 min 10 sec runtime. Cute. . JoTz .

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FOTD 08-08-08 (Railyard Symphony [8])
by Jim Muth 07 Aug '08

07 Aug '08

FOTD -- August 08, 2008 (Rating 8) Fractal visionaries and enthusiasts: There can be no debate about the correct format of today's date. Any way one arranges the numbers, it's correct. And in honor of the occasion, as if it needed honoring, we have a fractal. Today's fractal combines elements of Z^2+C and Z^2.5+C, and ends up looking quite like an oversized version of a Julia set of the Z^2.003 Mandeloid. In fact, today's scene is a Julia set of the East Valley of the large minibrot on the main spike of its corr- esponding Mandeloid. It closely resembles one of the Julia sets of the same area of the Z^2.003 Mandeloid, the Julia set that holds the curious rectangle where I occasionally return in search of a FOTD. I have not yet found any rectangles in today's Julia set however, but then I have hardly started to search. I named today's image "Railyard Symphony" because the tangle of filaments reminds me of the well-known (at least to rail buffs) Enola Railyards, about 65 miles down the river from F.C. I rated the image at an 8, leaving it to the individual fractalist to decide whether it's worth this rating. One thing that can not be exceeded is the brevity of the calcu- lation time, which at a faster-than-light 19 seconds, actually threatens to go backward in time. Those who would rather avoid the risk of becoming a child again, may find the image, already calculated, on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A near perfect day here at Fractal Central was compromised by a brief but heavy thunder-shower in the afternoon, which dropped the temperature from an already pleasant 81F 27C to an almost chilly 68F 20C. The fractal cats ignored the weather and spent most of the day playing hide-and-seek in the nooks and crannies of the bookshelves in the long hallway of FC. My day was pleasant enough, and with any luck at all, tomorrow will be the same. The next FOTD is due to be posted in 24 hours. Condidering the regularity of the FOTD postings, I feel it will appear on schedule. Until then, take care, walk lightly and carry a big fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Railyard_Symphony { ; time=0:00:19.01-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot center-mag=0/0/0.3133196/1/-90/ params=90/0/90/0/-43.762/0/0/0/2.5/25 float=y maxiter=1500 inside=0 periodicity=10 colors=000U71U81U94UA7UBAVCDWDHXEKYFNUGQWHTYIX_J_a\ KbbLecMhcMkeNifNhhOgiOfjPelPcmQbnQapR`qR_sSYtSXuTW\ wTVxUUyUTuTPqTMnTIjTFgTBcT8`T5aV4bX4bZ4c`3cb3dd3df\ 3eh2ej2gm2kp2ps1vv1zy1vv1pp2ej2Xc2OY3JT3EP39M3BK8D\ SDFWIHfNIjRJiPJbOJ`NKZLKXKKVJLTHLRGLOFMNDMMCMLBNK9\ NJ8NI7NH6QFASEDzDHzCKzBNzARz9Uz8Yv7`r6cm5gm4jz3nz2\ qz1tz5so8skBshEsdIs`LsYOsURrQUrMYrJ`rFcrBfr8ir9fsA\ dtBauC_uDXuEVuFSuGQuHNuILuJIuKGuLDuMBuN8uN6uNBuNGu\ NLuNQuNVuN_uNcuLauK_uIYuHWuGUuESuDQuCPuJNuPLuVKu`I\ ufGulFufEu`EuWDuQDuKCuFCu9Bu4Bu5Au5Au69u69u78u78u7\ 7u87u86u96u95u95uA7uB8uB9uCAuDBuDCuEDuFEuFFuGGuHHu\ HIuKTuMcuPnuRxuNouJfuFZuBQu8IuE9uJ1uQ8uXFubMuiTuoZ\ umWukTuiRugOueLucJuaGu_DuYBuW8uU5uT3u2iuRuuPpuNluM\ huKduJ_uHWuGSuEOuDJuBFuABu87u73u7Xu7zuIouTeucVunLu\ gJu`HuWmuVmuOhuHduA`u4Xu5Yu6Yu7Yu8Zu9ZuAZuAZuDXuFW\ uHUuJTuLSuSUuYWucXuiZu_7u } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=real(p5)-2, bb=imag(p5)+0.00000000000000000001, 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(-aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 07-08-08 (Phantom Sunrise [7])
by Jim Muth 06 Aug '08

06 Aug '08

FOTD -- August 07, 2008 (Rating 7) Fractal visionaries and enthusiasts: There is something about perfection that annoys me, so when I took another look at the FOTD for August 4, which is as close to perfection as the FOTD comes, I felt a twinge of annoyance. I felt that I must do something to spoil that image, which rates a lofty 9.5. To wreak my havoc, I rotated the view about 0.25 degree from the Julia orientation. This tiny rotation totally changes the image. Instead of circular perfection, we now have something that more closely resembles an alien sun rising above an alien horizon. I named the image "Phantom Sunrise". The change in orientation does not improve the original image, indeed, despite using virtually the same color palette, the rotation drops the rating from a 9.5 to a 7. Today's image is therefore more a mathematical curiosity than a work of fractal art. Thankfully, the image calculates in a blinding fast 25 seconds, so little time will have been wasted if the result is found disappointing. And never forget that the finished image is always available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Only two degrees kept the weather from being perfect here at Fractal Central on Wednesday. Even though the humidity was lower, the high temperature of 88F 31C was just a bit too warm for the spoiled fractal cats, who spent the day stretched under the cool air vent. Much of my day was spent meditating on the fourth dimension and the meaning of fractals. The next FOTD will be posted in 24 hours. Until then, take care, and follow in the footsteps of the great fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Phantom_Sunrise { ; time=0:00:25.02-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot passes=1 center-mag=0/0/0.891266/1/-90/0 params=90.01/0/90.24/0/-17.4231/0/0/0/16/10 float=y maxiter=1600 logmap=11 periodicity=10 sound=off colors=000SIKTHJUGKVEKWCKXAKaCQfEXkGcpIjuKqiJnzzkz\ zzzzmzy0zt0zm0yh0xc0wZ0uU4sK8pEAnCAkBAgAAb9AZAAUAA\ QBAOBCMCKLCPMKULPZKWaJbaIjdHthKumMurPxzRzzTzzXlz_`\ zdZqO_UNYTMWSLURKSQJQPJOOMZJWbFcfBci8mn4mu1zzCVXNb\ NYjDhlCbnBYoASq9Ns8Ht7CrAGpDKnFOmISkLWiN_gQcfSggcd\ hnaiyZhydgyjXqbMiWBaO0VH8TEFRCNQ9UO7`M4hL2oJ0vI0uJ\ 6uKFtLOtMWnbfhrqikojemjZkkTjlMhlGfm9dm3ch9YcESZKMV\ PGFcnJXnNRnRLnVFnZ9nY7cX5TW3JV18V00Y70`E1bK2TGHKDV\ BAhUsnNq`GoO9mA3l0LZ9bMLs9WtGRuMMuSHvYCvc7liMbo`Ut\ o_X4cR7gLAkFDoAGrMKuXNxhRzsUzzMzzEzz6zz0zz0cm1ar2`\ v3_z4WwCTtJQqRNnYKke4SV3PS2MP1KN4GV7Db8Ea8Ea9F`9F`\ AF_AG_BGZBGZ65h8Be9GbAL_BQYCWVD`SEePFjNPeLY`KgWJpS\ IeYEWbALg6Bl3FkAJjGNiMRhSVgYZfcbeifeo`hpWjqRlrLosG\ qtBsu8cf5OT29F3MI4ZK4kMDkRLkVUkZakbjkfrkjricrgXreQ\ rdKrbDr`6r_0jS4cL8XECQ7GJ0KNBGQMCUW9Xf5_p2XmCVjLSg\ UQdbObkTfiXihalgeofFZ6GR4 } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=real(p5)-2, bb=imag(p5)+0.00000000000000000001, 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(-aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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Re: [Fractint] FotD_08-08-04
by JackOfTradeZ＠comcast.net 05 Aug '08

05 Aug '08

. FotD_08-08-04 Hexidecimal Quad Totally Freakin' Awesome! (lemme see what I can do with it ...) Also - this grabbed me: ""Until then, take care, and change the change that never changes"" Great idea! How 'bout Libertarian or Constitution instead of demopublican <--> republicrat ad-infinitum ? lets have some REAL 'change we can believe in' instead of the same-old-same-old ? nahhhh ... never happen stay amazed JoTz .

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FOTD 06-08-08 (Julia to the Center [5.5])
by Jim Muth 05 Aug '08

05 Aug '08

FOTD -- August 06, 2008 (Rating 5.5) Fractal visionaries and enthusiasts: Today's quickie fractal will cause no one pain. At the same time it will set no new records for a fractal rating. The image is the center part of its parent fractal, which is a Julia set of the Mandeloid that results when Z^2 is divided by ((Z^6)+0.6). The Mandeloid is still dominated by Z^8 elements, though even with only 0.6 added, the western bay is already growing larger. Today's Julia image corresponds to the northern branch of the valley setting off this enlarging bay. A quick glance will reveal that the image is far too busy, with too many clashing colors vying for attention. It really doesn't deserve even the lowly rating of a 5.5 that I gave it. The strange imag(p3) parameter was found at random by the evolver feature of Fractint. The value is extremely critical. The name "Julia to the Center" indicates that the image is the center of a Julia set. The calculation time of 1-1/2 minutes will get the task of running the parameter file out of the way in a hurry. The joy of visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image posted there can hardly be surpassed. ;-) The perfect weather fled fast on Tuesday here at Fractal Central, where grey skies and sprinkles of rain made no one happy. It was also very humid, making the temperature of 84F 29C feel quite oppressive. The fractal cats spent most of the day contemplating fractals, while I spent most of the day contemplating and then actually doing work. The next FOTD will appear from nowhere almost by magic in 24 hours. Until then, take care, and watch for the relief. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Julia_To_TheCenter { ; time=0:01:31.58-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot passes=1 center-mag=0/0/4.464286/1/32.5/0 periodicity=0 params=90/90/90/90/-0.8682316/0.06717689238662033/\ 0/0/8/0.6 float=y maxiter=750 inside=255 logmap=-24 colors=00000X00Y00Z00_00`00a00b00c00d00e00f00g00h0\ 0h00g00e00c00b00a00`00_00Z00Yd9zf9zgBziCzkEzlEznGz\ pHzqJzsJztKzvMzxOzyMzxOzvPztPxsRvqRtpTqnTplVnkWkiW\ igYgfYdd_cc_ac`Za`X`bVZdSXdQVePUeLSgKQgGPhFNhDLjAK\ k8Ik6Im3Gm1Fo0Do0Bp0Ap08r06t04t03u01u00w00w00y00y0\ 0w00w01w03u03u04u06u08t0At0At0Br0Dr0Fr0Gr0Gp0Ip0Kp\ 0Lp0Lo0No0Po0Qm0Sm0Sm0Um0Vk0Xk0Zk0Zj0`j0aj0cj0ch0d\ h0fh0gh0ig0ig0kg0le1ne1pe1pe3qd3sd4td4sg3td4tb6v`8\ wYAuWBsVDqRFpPGoOGnKImJKmHLmGNmCPmBQm9Sm6Um4Um2Um0\ Um0Um0Uz0Um0Uz0Um0Uz0Um0Uz0Um0Uz0Um0Um0Uz0Um0Uz0Um\ 0Uz0Um0Ux0Um0Uv0Um0Uzt0s_Daz0`t0zk0Xe0XY0VP0UJ0t4N\ s7QzVNpGXnJ`lMckzfiVigYlf`pddqZ_iSVaLPUFKL8GD1C6F9\ GQ6Qc2`n0iz0sz0zz0vz0sy0pt0lq0il0fg0cd0``0XX0US0QN\ 0NK0KF0GtRD60A106003000000001404B48IBBQHGXOKcVNi`Q\ pgUlbUiYUgVUdPUaKU`HUXCUV9US4UP0UN0UK0UI0UF0UB0UA0\ U60U40UB0XI0`N0aU0dZ0gd0i } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=real(p5)-2, bb=imag(p5)+0.00000000000000000001, 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(-aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 05-08-08 (A Strange Seahorse [7.5])
by Jim Muth 05 Aug '08

05 Aug '08

FOTD -- August 05, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: Yesterday's image showed a very unusual East-Valley type Julia set. Today's shows an interesting Seahorse-Valley type Julia set. The parent fractal came about when I divided Z^2 by (Z^(10)+2.5) before adding C. This parent fractal only vaguely resembles the familiar Mandelbrot set. It has a Seahorse Valley that is almost impossible to find, but I must have come pretty close, because today's image certainly has Seahorse-Valley Julia characteristics. It also has lots of Z^12 characteristics, which are visible all through the image as a series of circular features with 12 sections each. Unfortunately, with its rating of 7.5, today's image falls short of yesterday's. But it is still worth a look, especially with a calculation time of only 29 seconds. The name "A Strange Seahorse" pretty well describes the image. As always, the already-calculated GIF image is or soon will be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> for instant, fully hedonistic ecstasy. The weather continued absolutely perfect here at Fractal Central on Monday. With the work light, FL and I took a couple hours off in the afternoon for a 3-mile walk along a nearby hillside trail. The temperature of 82F 28C made walking as enjoyable as it gets. When we returned, the fractal cats scolded us for the unaccustomed absence. The next FOTD will be posted in 24 hours. Until then, take care, and change the change that never changes. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Strange_Seahorse { ; time=0:00:29.25-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot center-mag=0/0/0.4014516/1/-30/0 periodicity=10 params=90/90/90/90/-1.98955/0.67403096/0/0/12/2.5 float=y maxiter=600 inside=0 logmap=3 colors=000ZZccchhhmmmrrrwvvzxyzwwzwtvwqrwomwnhwmfw\ mdwlbwk`wjZwjYrfVmbSi_QdWN`SKWPISLFNIDJEAEA7A75532\ 100LtheM3hL4kL4mK5pK5sJ6uJ6xI7zI7xNCwSHvWMt`RseWri\ `icb`ZddWagU_kSYnPWrNUuLSxJQvIWtIasIggFeXCdM9cOBXQ\ DQSFJTGDVIBWK9XM8YN6ZP4_R3`T1aU0`wGPqQEl_3giA_aHSV\ OLOVDH`6AWB8SG7OL6KP5GU4CZ38b26_94XG2VN6ZL9aJCeIFh\ GIkFMiYQrzSkmSdcS_WSTSSNBSJ6SF2JO8BXD6XqB`rFcsKftO\ juTmvXpvXouWntWmsVlrUkqUjpTioThnSgmRflRekQdjQdiPch\ ObgOaf101N`eN_cMZbLYaLX`KW_KVZJUYITXISWHRVHRUGQTGP\ SFORGF_HGZHIYIKXIMWJOVJQUKSTKTTMYUObVPfWRkXSoYTkVT\ hTUeRUbPV_NVXLWUJWRHWNFXKDXHBYE9YB7Z85Z53Z21T42O53\ I63D74884AC7CF9EJCFMEJNIMNLPNPSNSVNVYNZ`NacNefNhiN\ klNooNrrNunTpjZlfdgcjchWhmHmz2r`ClLMfmWKDeJbk1W_Dg\ KPr5`s4Xt4Tu3Pv3Lw2Hx2Dy19y15M0YO4_P7aQAbSEdTHeUKg\ VNhXRjYUkZXm__nacpbfqcisdltaiqZgnWelTciRagO_dLYbIW\ _FUXDSVAQS7OQ4MN2KLBQRJVW } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=real(p5)-2, bb=imag(p5)+0.00000000000000000001, 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(-aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 04-08-08 (Hexidecimal Quad [9.5])
by Jim Muth 03 Aug '08

03 Aug '08

FOTD -- August 04, 2008 (Rating 9.5) Fractal visionaries and enthusiasts: I'm starting to discover the potential of the DivideJulibrot formula. Today's image is a Julia-set of East Valley of the large minibrot on the main stem of its parent fractal. This parent fractal came about when I divided Z^2 by (Z^(16)+10). On the surface it resembles an oversized Mandelbrot set, while deep inside it takes on Z^16 characteristics. The image is a splendid blending of quadratic East Valley elements with the more circular Z^16 elements. It rates a full 9.5, 1/2 point of which is due to my marginally expert coloring efforts. I named the image "Hexidecimal Quad" in recognition of the mixture of elements of two different orders. The calculation time of a superluminal, (which is possible in the world of fractals), 23 seconds, will make running the included parameter file a pleasure. An equal pleasure may be experienced by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the already-calculated image is posted for instant ecstasy. The Sunday weather here at Fractal Central was so good that the digital thermometer read 'comfort' from sunrise to sunset. Lots of sun, low humidity and a temperature of 82F 28C in the middle of the dog days must be considered near perfection. The fractal cats were more interested in a squirrel that was in the yard all morning, gathering nesting material. I did little but take it easy most of the day, though far busier days are in sight. The next FOTD will be posted in 24 hours. Until then, take care, and forget philosophy for a day -- a lack of philosophical pondering leads to less wisdom but more peace of mind. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Hexidecimal_Quad { ; time=0:00:23.00-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot center-mag=0/0/0.891266\ /1/-90/0 params=90/90/90/90/-17.4231/0/0/0/16/10 float=y maxiter=1600 logmap=11 periodicity=10 colors=000FA2HA0LA0OA5S8CXAJaCQfEXkGcpIjuKqiJnYJkN\ JhKYLHk0Fd0DZ0BT09N08H0zh4zc8zECmCJcBOUAQK9QJAPKAK\ LBKMBKNCMOCSMKULRZKYaJeaIldHthKvmMurPxzRzzTzzXlz_`\ zdZqO_UNYTMWSLURKSQJQPJOOMZJWbFcfBci8mn4mu1zzCVXNb\ NYjDhlCbnBYoASq9Ns8Ht7CrAGpDKnFOmISkLWiN_gQcfSggcd\ hnaiyZhydgyjXqbMiWBaO0VH8TEFRCNQ9UO7`M4hL2oJ0vI0uJ\ 6uKFtLOtMWnbfhrqikojemjZkkTjlMhlGfm9dm3ch9YcESZKMV\ PGFcnJXnNRnRLnVFnZ9nY7cX5TW3JV18V00Y70`E1bK2TGHKDV\ BAhUsnNq`GoO9mA3l0LZ9bMLs9WtGRuMMuSHvYCvc7liMbo`Ut\ o_X4cR7gLAkFDoAGrMKuXNxhRzsUzzMzzEzz6zz0zz0cm1ar2`\ v3_z4WwCTtJQqRNnYKke4SV3PS2MP1KN4GV7Db8Ea8Ea9F`9F`\ AF_AG_BGZBGZ65h8Be9GbAL_BQYCWVD`SEePFjNPeLY`KgWJpS\ IeYEWbALg6Bl3FkAJjGNiMRhSVgYZfcbeifeo`hpWjqRlrLosG\ qtBsu8cf5OT29F3MI4ZK4kMDkRLkVUkZakbjkfrkjricrgXreQ\ rdKrbDr`6r_0jS4cL8XECQ7GJ0KNBGQMCUW9Xf5_p2XmCVjLSg\ UQdbObkTfiXihalgeofFZ6GR4 } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=real(p5)-2, bb=imag(p5)+0.00000000000000000001, 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(-aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 03-08-08 (Isle of View [6])
by Jim Muth 03 Aug '08

03 Aug '08

FOTD -- August 03, 2008 (Rating 6) Fractal visionaries and enthusiasts: What does one do on a lazy Saturday? Why search for fractals of course. Today's fractal required very little searching, but the day was so lazy that the FOTD was once again late. The image is a distortion of a Julia image closely related to yesterday's. It was distorted by double-rotating the slice 0.00015 of one degree from the Julia direction. A tiny rotation makes a huge difference this close to the Julia orientation. To see the pure Julia version change both the p1 and p2 parameters to 90,90. The undistorted version is an improvement, but I kind of enjoy imperfection in fractals. I named the image "Isle of View". For some reason it reminds me of a kiss. To see the connection between an island and a kiss, walk up to an attractive young lady and whisper this name to her. But be prepared to explain your remark or run like a deer if her husband overhears. I rated the image at a 6, which is a little above average, though far from outstanding. The calculation time of 1-1/2 minutes can be avoided by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and downloading the finished picture from there. Saturday began with a crackling thunder-storm here at Fractal Central, but by noon the sky cleared, leading to a pleasant afternoon with a temperature of 81F 27C. However at 5pm the serenity was spoiled by a surprise heavy shower that fell in full sunlight. After that the day ended spectacularly, with a double rainbow and clouds that had to be seen to be believed. The fractal cats observed the goings on with disinterest. In my department nothing much happened. The next FOTD will be posted in about 12 hours. Until then, take care, and search, search, search. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Isle_of_View { ; time=0:01:32.22-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot center-mag=0.00592736/\ 0/3.122/1/-90/0 params=-89.99985/90/89.99985/90/\ -17.45247/0/0/0/5/9 float=y maxiter=1800 inside=fmod proximity=0.0175 symmetry=none periodicity=10 colors=000ovmovpowrowtqnwkfqeZk_RfUJ`OBVJ4QD3H839O\ 6Vb9pW7lQ6hK4dE3`81X20T57R8EPBLNESLHZJKeHUlFcrDmuR\ zxdzzqzwfPtWPqMJmWDieJfbPd`VaY`_WfXTkVRjRTjOVhMPgK\ JfJDeH7dG1cH3bH4bI6aI7`J9`JAePLjUWn_esdpwizvewvauu\ YsuVqtRntNlsJjsGhtFhuEhuDhvChvBhwAhwAhsEgpHglKgiNg\ fQgbWaZ`XWfSSkNPpIQqLQrNQsPQsRRrXRqaRpgRolRnrRmwZs\ WblXffYj_ZmUZgWWaXTXYQR_NL`KGaI6hG8fLAePCdTDbXFa`H\ `dI_hK_GNWCPS8RP5RK4RF3IPI9YX1fk7ZmDRnJKpPCqU5rK8`\ AAJ1C1DQIPbY`omdlchiUlfKpcAta0rcHqdYpenofiofdnf_nf\ WmgRmgMlgHlgDlhKlhRliYlidlijjXehK`jPJlT1qTFqTKuRHw\ P4uK7lN9aWCUeSMlhEpzIqzMrmQsYShdTYjUNqVCw_Avd8ui7t\ n5ss3rx2qKvISnH_gHg`GoUGwNGtKQqHZnEglCp3jP8gUDdYIa\ bMZfRWkWTo_QsaKdcEQd9BW8`N8yQ9wS9vUAuWAsYBr_BqaBpc\ ElfGihJejLbiIYiFTiCPhAKh7Gh4Bh27g96gF6gL6fR6fX6BNm\ EPjHQgJRdMSaOT_UPcZMgdIkiFonCrpCprCnsCluCjwChxCfnF\ ieHkXJmNMpEOr5Qtotfouiouk } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=real(p5)-2, bb=imag(p5)+0.00000000000000000001, 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(-aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 02-08-08 (The Mystic Star [?])
by Jim Muth 02 Aug '08

02 Aug '08

FOTD -- August 02, 2008 (Rating ?) Fractal visionaries and enthusiasts: NEW FORMULA ALERT! Discard the formula that came with yesterday's FOTD, and substitute today's formula. Yesterday's formula has a small error, which I found soon after posting the FOTD. While working with yesterday's formula, I noticed that I was constantly getting two extra lobes on the elements. This is because I had forgotten to subtract 2 from the number entered as real(p5). This oversight explains why the elements in yester- day's image had 7 lobes instead of 5. But today's formula, which I am pretty sure is the final version, sets everything right. As an example, the value of real(p5) in today's formula is 5, and the image is filled with five-sided elements, indicating that all is once again well in fractal land. Today's image is a Julia set of a small valley at the outer edge of the third bud out the negative X-axis of its parent fractal, which resembles a moth-eaten Mandelbrot set. I did not rate it because I'm still not familiar with the potential of this latest formula. I named the image "The Mystic Star". Fractals are at least as mysterious as anything traditional mystics have been telling us. I wonder what a tiny rotation away from the Julia orientation would do to today's image. Perhaps we'll find out in tomorrow's FOTD. The calculation time of 1-1/2 minutes may make the trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> un-necessary. But the trip is lots of fun, so if running para- meter files is not your glass of orange juice, don't hesitate to dash out to the web site, where the finished image is posted for instant viewing pleasure. We certainly did not deserve the perfect weather that prevailed here at Fractal Central on Friday. After all, it's supposed to be midsummer, when we go around wiping away the perspiration or hiding within our air-cooled cocoons. Today's blue skies, puffy cumulus clouds, low humidity, and temperature of 86F 30C were unexpected but fully welcomed by human and cats alike. With not much work to do, this human worked on a fractal formula, while the fractal cats worked on trying to get an extra treat. The next FOTD will appear in 24 hours. Until then, take care, and if the mysteries of mysticism are not mysterious enough, look to modern science for some real mysteries. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Mystic_Star { ; time=0:01:28.15-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot passes=1 center-mag=0/0/3.963356/1/-90/0 params=90/90/90/90\ /-5.4262/0/0/0/5/4 float=y maxiter=1600 inside=0 logmap=11 symmetry=none periodicity=10 colors=000UGXUIXUKXUMXUOWUQWUSWUUWUWVUYVU`VUbVUdUU\ fUUhUUjUUlTUnTUpTUrTVxRUtTUqVUmXUjZUf`UcbU`dSaeRbe\ PceOdeMdeLeeJfeIgeHgeFhfEifCjfBkf9kf8lf6mf5nf4nf6k\ d8icAgbBe`Db_F`ZGZXHXWJUVKSTLQSMOROMPPJOQHNRFLTDKV\ AJW8HY6GZ4FZ2E_5G_8I_AKaDLbGNdIPeLRfOShQUiTWkWYmYZ\ m``ncbsdenecjebfeabe`Zf_VfZQfXMfWIgVEgUAgT4eQ6gS8h\ UAjWBkXDmZFn`GpaIqcKseLtfNvhPwjQxkRvjSuiSthTsgTrfU\ qeUpdVodVmcWlbWkaXj`Yi_YhZZgYZfY_dX_cW`bV`aUa`Ta_S\ bZRbYRYrjakfeeciZ_mTXqMTuGQxANdRVeTWfUWfVWgWWgXWhY\ Wh_Wi`WiaWjbXkcXkdXlfXlgXmhXmiXnjXzxhnkXc_MTOBxuOv\ tNusMsrMrrLpqLopKmpKloJjnJrnIzmHzlHzkGzkGzjFziFziE\ zhEzgDmiCcgDUfETeFSdzoczQaHP`IO_JNZKMYLLXLKVMJUNIT\ OHSPGRQFPQEORDNSCMTBLUCJTBKUBLVBMWAMXANXAOYAPZ9P_9\ Q`9R`9Sa8Sb8Tc8Uc8Vd7Ve7Wf7Xg7Yg6Yh6Zi6_j6_jB`hGaf\ LbeQccVdaZd`V`bRYdOUfKRgHNiDKk77tAHlCQeEZZJdnGgST`\ OdUKoNGpNHRorSelTWgUMbUDY } frm:DivideJulibrot {; draws slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=real(p5)-2, bb=imag(p5)+0.00000000000000000001, 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(-aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 01-08-08 (New Boy on the Block [?])
by Jim Muth 31 Jul '08

31 Jul '08

FOTD -- August 01, 2008 (Rating ?) Fractal visionaries and enthusiasts: NEW FORMULA ALERT! Today's FOTD uses a new formula, which I wrote today. The formula combines the DivideBrot routine with the Julibrot routine to draw different slices of the curious DivideBrot Mandeloids. The new formula is number 6 of the SliceJulibrot series. I wrote the formula to make it easier to work with both the Julia and Mandelbrot aspects. I have not yet investigated the odd slices, though they probably hold some interesting scenes. Today's image has no parent fractal. It is the parent fractal. The image is a Julia set of what remains of the Seahorse Valley of the ruined large minibrot on the main stem of the correspond- ing Mandelbrot set. To see the ruined minibrot in the Mandel- brot aspect, simply change both the p1 and p2 parameters from 90,90 to 0,0. At first glance, the image appears to have X-axis symmetry, but a closer examination will reveal that it has no symmetry at all. The imag(p3) parameter is extremely critical, with the slightest change totally altering the image. I have not yet tried different values of the remaining parameters, but I see much potential for excitement. The formula combines Z^2 and Z^5. From the way the image is filled with 7-sided elements however, one would never guess it. The calculation time of a very brief 25 seconds will cause no one any pain. Since I have no idea of the potential of the new formula, I could give today's image no rating. The name "New Boy on the Block" refers not only to the new formula, but also to the new tomcat that lurked around FC for acouple minutes this afternoon. The most convenient way to see the image is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> but before you will be able to work with the image, you will need the new formula entered into one of your Fractint formula files. Thursday proved to be a thoroughly delightful day here at Fractal Central, with blue skies, puffy cumulus clouds, lower humidity, and a temperature of 86F 30C. The fractal cats enjoyed the conditions, but became alarmed when they spotted an unwelcome beat-up tomcat prowling in the yard next door. Just as Nicholas reached full bristle however, the intruder moved on, returning peace to the cat community. My day was about average. The next FOTD will be posted in 24 hours, plus or minus a few. Until then, take care, and fractals are not only good for the soul, they might be what the soul is made of. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= New_Boy_on_Block { ; time=0:00:25.12-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot6 center-mag=0.0187793/\ 4.44089e-016/0.9861933 params=90/90/90/90/-14.1496\ 5667/0.0052/0/0/5/8 float=y maxiter=1200 inside=255 logmap=3 symmetry=none periodicity=10 colors=000_MjeSekXajZcj_eiagibiicjfagd_ebYc`WaZU_X\ TYVRWTPTRNRPLPNKNKILIGJ133GEHECECACA9A878656434212\ gi7_a5TU4MN3EF2771UGzSFwREtPDqOCnMCkLBhKAeI9bH9_F8\ XE7UC6RB6OA5L84I73FQnlUhmXbn`XocRogLpjFqmAqlErkIrk\ LsjPsjStiWthZuhbugevgivflwepwesxdwxdzxbvtarq`nnZjk\ YfhXceYdgZdh_dj_dk`dmadnbdpbdqcdsddtqdvhbwbbzc`zb_\ tbZsaYs`Wr_Vq_TpZSoYRoXPnXOmWMlVLkVKkXNiZPg_ReaTcb\ VadX_eZZgaXicVjeTlgRmiPokNpmMmlLjlKglJdlJalIZkHWkG\ TkGQkFNkEKkEX0AV4CT7DRAEPDFNGGLKIJNJIQKGTLEWMC_OAb\ P8eQ6hR5kSInUUqVesWfoUflSfiQfeOfbMg_KgWIgTGgQEgNCd\ MHaMLZLPWLTTKXQK`OKdCAKTuUOkP5_j7Vi8QhALgBGgEJeGLd\ INcKPbMR`OT_RVZTXYVZWX`VZbU`dTbaRdZQfXOhUNjRLkPKp`\ JtkIrjKpiLniNlhOjgQigRgfTefUceWadX`dZZc_XbaVbbTadS\ aed_ZpYSnXQmWOlVMlTMlSMlRMlQMlPMlOMlNMlMMlLMlKMlJM\ lIMlHMlGMlFMkHOjJQjLRiMTiOUhQWhRXgTZfV`fXaeYce_dda\ fdbgaYiZTkWPmTKoQFqNBsUHn } frm:SliceJulibrot6 {; draws slices of DivideBrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=real(p5), bb=imag(p5)+0.00000000000000000001, 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)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(-aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 31-07-08 (Chaplet of Fractals [6.5])
by Jim Muth 30 Jul '08

30 Jul '08

FOTD -- July 31, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Yes, I know I said there would be no FOTD for July 31, but the repair work at Old Fractal Central went astonishingly fast this morning, and by 11am I was on my way back to New Fractal Cen- tral. The only downer was Thomas, the one remaining old fractal cat. My sister said he has been very depressed since his brother Tippy passed on to cat heaven about 5 months ago. I tried to cheer him, and he did raise his head and murmur a few small purrs when he saw me, but then he rolled over, curled up and returned to sleep, where he likely is still with Tippy. Today's image shows an order-7 minibrot lurking in an almost- Mandelbrot set. The scene is located on the northwest shoreline of the bud immediately west of the large period-2? bud of its parent fractal. I never realized these higher-order minibrots could be so interesting. I rated the image, perhaps a bit liberally, at a 6.5. I named it "Chaplet of Fractals" when I noticed the ring of blossom-like elements surrounding the central minibrot, each blossom with a still smaller minibrot at its center. The calculation time of 2-4/5 minutes is worth the wait. And equally worthwhile is a trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the finished product there. Hot muggy conditions prevailed Wednesday morning at Old Fractal Central, while the conditions at New Fractal Central in the aft- ernoon were noticeably better. The temperature ranged from 95F 35C at O.F.C. to 88F 31C at N.F.C. The fractal cats greeted me reservedly when I arrived back at New Fractal Central unexpected- ly early, with enough time remaining in the day to crank out an unexpected FOTD. The next FOTD will be posted in 24 hours. Until then, take much care, and search for good fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= ChapletOf_Fractals { ; time=0:02:49.91-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 center-mag=-27.07629943909\ 749/+0.8305626339739348/7.520937e+011/1/-75/0 params=7/20 float=y maxiter=8500 inside=0 logmap=346 periodicity=10 mathtolerance=0.5/1 colors=000RBZSBZTCZUDZVDZWEZXC_YEZZFZ_GZ`HZaJYbKYc\ LYdMYeNXfPXgQXhRXiSWjUWkVWlWWkXWkYWk_Xk`XjaXjbXjdY\ jeYifYigYihYijYhk_hlahmckoeiqghrigskfsmermdrmbrmar\ m`qm_qmZpmWrmXpmYomZnm_mm_lm`kmaimbimbhmchmdgmegmf\ fmfekgeihdgideiccjbakb_laYmaWm`Un`So_QpZOzZMzVMzdM\ z`NzTJzXNs`QsdTsgWskZsoazrdtoetlftjfzgguegubhv_hvY\ ivViwTjwQjwNkxLkxIlxGlvImuKmtMmsNnrPnqRnpTooUonWom\ Ypl_pk`pjboicnhemgflggkfijejidkhcmgcnfboeaqd`rcerg\ `scWs_RsXMtTHtQCtM7tJ6rI6pHzzzzzz6jF5hF5gE5eDzsD5a\ C4_C4YB4WAhimcTz4R83P83N73L73J63I52G52E42C32A32822\ 723943A63B83CA4DB4ED4FF4GH5HI5IK5JM5KO5LP6MR6NT6OV\ 6PX7QY7R_7Sa7Tc8Ud8Ve8Wf8Xg0_h8YiFYjM_kTal_cmfenmg\ oyipvkqtmrrospqtnsuluvjwwhxxiyyjzzjzzkzzlzzlzzmzzn\ zznzzozzozzpzzqzzqzzrzzszzszztzzuzzuzzvzzyzzwzzvzz\ uzzszzrzzszzrzzqzzpzzozznzzmzzqzzmzzjzzgzzdzzazzZz\ zWzzSzzPzzozzozzozzozzozz } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 30-07-08 (Seven Squared [5])
by Jim Muth 29 Jul '08

29 Jul '08

FOTD -- July 30, 2008 (Rating 5) Fractal visionaries and enthusiasts: Due to a lack of time, today's discussion will be short. But many words are not necessary, since today's image speaks for itself. Today's image is a scene in East Valley of an almost-Mandelbrot set. The minibrot at the center is clearly of order-7, while the surrounding pattern holds quadratic features. All in all it makes an interesting, though not exceptional picture. I named the image "Seven Squared" because it contains elements of both Z^7 and Z^2 Mandeloids. I rated it at an average 5 because I can find nothing out of the ordinary in it that could make it worth more. The calculation time of 2-1/3 minutes is fast enough to make calculation, if not exactly a pleasure, then not too long an effort. And the finished image is available as always on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Another typical midsummer day passed uneventfully here at Fractal Central on Tuesday. The temperature of 86F 30C and hot sun was perfect for any outdoor activity. It was perfect even for indoor activity, as the fractal cats were unusually active most all day, thundering back and forth up and down the hallway, ducking in and out from behind the books on the shelves, chasing each other around for the fun of it. My day was rather busy, both with work and with preparations for the trip back to Old Fractal Central on Wednesday. Because of that trip, there will be no FOTD for July 31, but if all goes well, (as I hope will be the case), the FOTD for August 1 will appear on schedule in 2 days. Until then, take care, and you may already be a fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seven_Squared { ; time=0:02:22.53-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 passes=1 center-mag=+5.278336322581068/-0.0532935461935686/\ 1.004852e+009/1/-52.5/0 params=7/20 float=y maxiter=1800 inside=0 logmap=186 periodicity=10 colors=000XeTagSfjQlmPqmOvnWpo`knefljakoXitShyRirR\ jkRkdRlYRmRRnKRoDRo7WmE_kLdjShhYlfdqekucru`vq_pnXj\ hWbcUWYSNTPEPLDLJDIHDEFDADD7CDIZ8Tu3SoCRjKRdSQ__PU\ gPPoUMrZJucGxgDzdIvbNs`SpYXmWajUegen7giFieNjaVlYbn\ UjoQqY_XHiCGjFGkHFlKFlMZDVdG_iJcnMgsOk`TWJYG1b0A`4\ JZ7SXA`VEiTHrRKzPNwQPuQRsRTpRUnSWlSYjSZ8UvOSgcRTrQ\ FiLC`GASB7J65A23tmlrjdqhXoePncIhgGckFoFhjQff`dakbY\ u``kXbaTeTPgJLj9Hl0EoAKqJPsSUva_xjdzsiprdfr_YrVjWN\ w9FmDIcGKUJNLMPKSTKXWKb_KgbKmfKriN`J2xj5mi7chAUgCK\ gGIdJGbNE_QDYUBVX9T_8R`9Ua9Xa9ZbAacAdcAf`BeZCeXCeV\ DeTDeQEeOEeMFeKFeIGeGGeIIaJJZLKVMLSOMOPNLROHSPEPRD\ MUBJX9GZ8IY9JYAKYBMYCNXDOXEQXFRXGSWHUYIV_JWaKXcKWe\ NBgL1iICkKNmMYoOhqQgsVgu_fwdfxieynezr_zfUzWPzPzzJz\ zCzz6zz0zz3zz5zz7zzAzzCzzEzzGzzSzzczzfzzizzIzzKzzM\ zzO`zQfzSlzUhzYdz``zcYzfUziQzlNzoPz`QzMRz8nzMozPpz\ RkzSgzTbzUZzUUzVQzWMzWSzU } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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Fractal cats and weather
by Jim Muth 29 Jul '08

29 Jul '08

Fractal fans: I kind of miss reporting the local weather as well as writing about the antics of the fractal cats. After all, cats are fractal by nature. Their latest excitement came around 4am Saturday morning when two roaming tomcats got into a noisy fight in the back yard. The fractal duo dashed to the window and kept watch, protecting Fractal Central until we humans were up for the day. So I'll resume the brief weather and cat reports in the FOTD for July 29. But I will not post the FOTD to the philofractal list unless I have some genuine philosophy to go along with it. Jim Muth

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FOTD 29-07-08 (Frankenberries [7])
by Jim Muth 28 Jul '08

28 Jul '08

FOTD -- July 29, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today we return to the DivideBrot5 formula to check a fractal that is quadratic on the surface, but of order-7 in its depths. This oversized fractal at first appears to be a Mandelbrot set blown up like a balloon, but it is totally different once one wanders beneath its deceiving surface. At first the quadratic minibrots appear merely distorted, as though they were not critical, but they soon evolve into perfect order-7 minibrots, with far more interesting detail surrounding them than could ever be found in the simple Z^7+C Mandeloid. Today's surprisingly rich minibrot is located near a minor bud on the northwest shore line of the main bay of the parent near- Mandelbrot set. I especially enjoy the awkward way the 7 arms radiating from the minibrot merge into the quadratic pattern a little farther out. An outzoom will reveal more detail of this merge area. I named the image "Frankenberries". I think I did it because the wine-colored basins remind me of the color of rasperry ice-cream, which strangely enough I have a sudden urge for. The rating of a 7 is about FOTD average. The calculation time of 2-1/3 minutes can be eliminated by surfing to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoying the already-completed GIF image there. The weather report, back by popular demand, for Monday at Fractal Central in central Pennsylvania is one of typical midsummer conditions -- partly cloudy skies, a temperature of 86F 30C and contented fractal cats. The cats are contented because the wandering tomcats that had a noisy catfight in the yard a few nights ago have apparently moved on to other territory. My Monday was just a little busier than average. Tuesday will probably be the same. Early Wednesday the 30th I must take a 140-mile-each-way trip back to Old Fractal Central to arrange to have some repair work done on the old place, but I'll be back to New Fractal Central by Wednesday evening. As a result, there will most likely be no FOTD for July 31. The next FOTD, the one for July 30, will be posted in 24 hours or less. Until then, take care, and maybe what really is, really isn't. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Frankenberries { ; time=0:02:20.40-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 center-mag=-9.17759645799/\ +7.267304008055/2860593/1/7.5/0 params=7/16 float=y maxiter=13000 inside=0 logmap=118 periodicity=10 colors=000UI0VJ0WK0XL0YM0ZN0_O0`P1aQ1bR1cS1dT2eU2f\ V2gW2iY3jZ3l`3na3oc4qd4sf4wi3tg4re5oc5mb6j`6hZ7eY7\ cW8aU9ZT9XRAUPASOBPMBNKCGHALJCQLDVMF_OGdQIgTHiRJjQ\ KkPMlONmNPoLQpKSqJTrIVx5ZsHWoTTkdQieRhfRgfRegRdhRc\ hSbiS`jS_jSZkSYlTWlTVmTUnTUqRTnTSkVRhXQeYPb_O_aNXb\ MUdLRfNGfKPgIYgGfhFmjEnhEofEodEpbEp`EqZEqXErVEsTEs\ REtPEtNEuLEuJEvH4y9EvFNsLWpRdmWUmvTmtTisSerSapRYoR\ UnQPlQLkPHjPDhO9gO5fK7gH9hDBiACiMA`X8Si2Ig7KeBLdFM\ bJOaNP_RQZVSXZTWbUUfWTjXRnYQrZToYVmXYjW_hVbfUdcTga\ SiZRlXQnVPqSOsQNtPNuONrMMoKLlILiHKgFJdDJaCIZAIX8HU\ 7GR5GO3FN1EN2FO2GP2HQ3HR3IS3JT4JU4KV4LW4MX5MY5NZ5O\ _6O`6Pa6Qb6Rc7Rd7Se7Tf8Tg8Uh8Vi9Wj8Vk8Vl8Vm8Vn8Vo8\ Vp8Vq7Vr7Vs7Vt7Uu7Uv7Uw7Ux6Uy6Uz6Uz6Uz6Uz6Uz6Uz9Vz\ BWzCXzDYzEZzF_zG`zHazIbzJczKdzLezMfzNgzOhzPgzQfzRe\ zSezTdzUczVbzWbzXazY`zZ_z__z`ZzaYzbXzcXzdpzepzfpzg\ qzhqziqzjqzkYzlXzmXznWzoW } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 28-07-08 (Pyramidal Ribbons [7])
by Jim Muth 27 Jul '08

27 Jul '08

FOTD -- July 28, 2008 (Rating 7) Fractal visionaries and enthusiasts: Before giving up on the almost-linear Mandeloids, I ran the Z^(1.009)+C Mandeloid through the Fractint evolver feature and found a fractal with enough variety to actually be interesting. The real(p2) parameter reveals that I let the program find the parameters. I would never enter such a value on my own. This parent fractal is shaped like most Mandeloids in this range -- somewhat like a roughly parabolic, stone-age arrowhead. It has a bit of chaos on its southeastern shoreline. Today's scene is located in this chaos. I surprised even myself when I found today's image, which resembles festive colored ribbons twisting around the apex of a dark brooding, sickly green pyramid. I thought of the name "Pyramidal Ribbons" almost at once. The magenta-ish background pattern is truly fractal, with the herringbone pattern continuing unchanged at ever smaller scales, apparently without limit. Whether the image truly deserves its rating of 7 is up to the individual viewer to decide. In my opinion, the image is well worth the rating. The calculation time of just over 4 minutes could be a bit faster, but it is not beyond the range of reason. Another reasonable way to see the image is to surf over to the FOTD web page at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the image already calculated and posted there. The next FOTD will appear in 24 hours. At this time I have no plans as to the theme, so check in then for a possible surprise. Until that glorious moment, take care, and keep your fractals simple. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Pyramidal_Ribbons { ; time=0:04:04.65-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident float=y center-mag=-6.9182776751/-18.4032734921/11051.95/\ 1/-33/0 params=1.009/0/922.5954466383862/3500 maxiter=2500 inside=0 logmap=410 periodicity=10 colors=000KJAKJAKJAKJAKJAKJAO9AQ8CS8EV7FX6E_5Da4Cb\ 29c4Cd5Fe7Hf8Kg9MgBPhCRiDUjFXkGZkIalJcmKfnMhoNkoOm\ nNlmNllNlkMljMliMkhLkgLkfLkeLkdKjcKjbKjaJj`Jj_JiZI\ iYIiXIiYGhXIiXJjXLkXMlXNlXPmXQnXSoXTpXUpXWqXXrXZsX\ _tXYxX`tXbpXnmXfiXhf`qbXmZXoWctSXsPcuLhvHswIkvIptI\ msJcqJoqJVoJUmKkmKTjKTiKghLSfLSdLbdMRbMQ`MX`MPYNPX\ NWXNOUNOUSWUONQOOSSUSMNPOMUTUUSJVUJXXHYYG__EaaDccC\ deBfg9hi8jk7jm7lq6mo6mm6mk6mi6mg6mf6md6mb6m`6nZ6oX\ 6pW6qU6rS6sQ6tO6uN6vL6wJ6wH6wF6wD6wC6wA6z86z66z46z\ 37z67z88zA8zCBzQ9zP4zQ7zPAziCziEyiGxjHwzJuzLszNqzP\ ozRmzTmzUmzWmzYmz_mzamzcmzemzemzfmzglzgkzhizigziez\ jczjazkZzlUzlSzmQzmPznPzoOzoOzpNzlNzlMzmMzmLznKzoK\ zoJzpJzmIzmIzmHzmHzmGzmGzmHzmHztIzsIzrJzqJzoKznKzm\ KzlLzkLzjMzhMzgNzfNzeOzdOzcOzjazrczqczpczocznczmcz\ lczkczjcziczhczgczfczeczdczcczbczacz`cz_czZczYczQc\ zQczPczPczOczOczNczNczMcz } 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 24-07-08 (Ratcheting Onward [6])
by Jim Muth 27 Jul '08

27 Jul '08

FOTD -- July 24, 2008 (Rating 6) Fractal visionaries and enthusiasts: I have made a decision to stay more on topic. Starting today I will no longer post a copy of the FOTD to the philofractal list. Except for the FOTD, the philofractal list has been dead for years. The topic of the Fractint list is fractals, not my ideas about God, science, or the paranormal. There are quite a few forums where these things are eagerly and properly discussed. And I'm not too sure of the importance of the daily weather report from central Pennsylvania, which can always be found on the internet. If the goofy fractal cats do anything exceptionally goofy, I'll tell about it however. (Yes, FL did have something to do with my decision to stick more to the topic.) Today's image shows some of the unexpected stuff that goes on in the fractals created by the formula Z^(1.075)+C. The most surprising thing about these almost-linear fractals is that they actually contain fiercely detailed Minibrots, which can be easily found with my 'secret' method of finding minibrots. One of these unlikely minibrots lies at the center of today's image, at the very limit of resolution. I have not gone deep enough to make the minibrot visible in today's image because at that depth, the surrounding pattern breaks down into near total chaos. At the modest magnitude of today's image, the pattern is far more interesting, rather resembling a ratchet wheel surrounded by a lacy network of lightning. I named the image "Ratcheting Onward" because of the ratchet pattern. This heavily fractured, circular effect is typical of the minibrots in fractals of such a low order. The rating of a 6 is what I think the image deserves. The calculation time of 1-2/3 minutes is a real bargain. An equal bargain may be found at the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished GIF image is posted. Until next time, take care, and keep a stiff upper fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Ratcheting_Onward { ; time=0:01:41.60-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-14.94607802098338/-2.324758141946301/\ 8252035/1/-162.5/0 params=1.075/0/18/1500 float=y maxiter=1800 inside=0 logmap=131 periodicity=10 colors=0009G06H0AI6DJFHDKKKZOPdRVmUfuZitzksonrwnqz\ uphVsZ9uX8pV7lU7hS6dR6`P5XU5Tc6Nm6Zr6Zz6Zz6ZIlq3Wp\ BafIguPmuWruVzuUzuTluShuRhuQfuPduOcuPiuQnuRsuOmuMg\ uKUuLUuMUuNUuPUuQUuRUuSUuTUuVUuWUuXUuYUu_Uu`UuaUub\ ZucZueYufXugWuhVuiUukTulcUmcVncVpcWqcXrcXscYtcYvcZ\ wc_xc_yc`zc`ycaycaycbycbyccxccxccxcdxcdxcewcewcfwc\ fwcfwcgwcgvchvchvchvcivciucjucjuckuckuckucltIltImt\ ImtIntInsInsIosIosIpsIptHqsIpsIpsIprIprIprIorIoqJo\ qJoqJoqJopJnpJnpJnpKnoKnoKnoKmoKmnKmnKmnLmmLlmLlmL\ lmLllLllLllMklMkkMkkMkkMkkMkjMjjNjjNjjNjiNjiNiiNih\ NihOihOihOigOhgOhgOhgOhfPhfPhfPgfPgePgePgePgfIkePg\ eVcda_dgWcnSctOczKbZ8a60b70c80d91dA3eB5fB7fC9gDBhE\ DhFFiFHjGJjHLkINlJPlKRmKTnLVnMXoNZpO`pOamPbjQbhRbe\ SccSc`TcYUdWVdTWdRWeOXeMYeJZfG_fE_fB`g9ag6bg1bf3bg\ 4bg6bg7bg8bgAbgBbgCbgEbgFbgHbgIbgJbhLbhMbhNbhPbhQb\ hRbhTbhUbhWbhXbhYbh_bh`bi } 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 27-07-08 (The Limbo Factor [6])
by Jim Muth 26 Jul '08

26 Jul '08

FOTD -- July 27, 2008 (Rating 6) Fractal visionaries and enthusiasts: In today's image I tried to go down to an exponential level only half as far from unity as yesterday's exponent of 1.0125. But I could find nothing of interest in the fractals with an exponent of 1.00625, so I tried an exponent of 1.009375, which is 3/4 as far from unity as yesterday's 'forest floor' image. The searching down there was difficult, minibrots were nowhere to be found, but I finally found an interesting patch of chaos in the Z^(1.009375)+C Mandeloid fractal right at ground level of the complex hyper-ladder. Today's image shows a small sample of that interesting chaos. To me, the most amazing thing with the image is that the graph of its generating expression is virtually a straight line. But even such a tiny departure from straightness can do unexpectedly intricate things when iterated a sufficient number of times. In today's image we have areas of near total chaos, areas that are totally featureless, as well as areas of fractal patterns that repeat at ever smaller scales. There are also several dis- tinct fractal themes in the image. Despite the ridiculous expo- nent, today's fractal image is as fractal as any fractal could be. I named today's image "The Limbo Factor". After all, the point of the Limbo is to go as low as possible. Then I rated it at a 6. My inability to find a minibrot in the parent fractal cost the image at least one whole rating point. The calculation time of under 4 minutes on a computer running at 2000mhz is reasonably brief. And the trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the finished image there can be equally brief, if not briefer. The next FOTD will be posted in 24 hours. Until then, take care, and view the world through fractal-colored glasses. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Limbo_Factor { ; time=0:04:54.34-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-10.29306825/+0.0410706/163.76/1/142.5/0 params=1.009375/0/0/3500 float=y maxiter=16000 inside=0 logmap=456 periodicity=10 colors=000KBULBUM9UN9UO8UP8UQ8TR6SS6TT4RU4RU4RU2PU\ 2NU1NU1MU1MU0KU0IU0IU0HU0FU0FU0DU0BU0DU0DU0FU1FU4F\ U6HU9HUBIVDIVHIXIKXMKXNMYRMYSMYUN_XN_YP_aPabPafRbg\ RbiSblSdmSdpUdrUfuVfvVbvSdxUfxVgxXgyXiyYjy_jy_lzam\ zbozdozdpzfrzgrzgpslojomarmSulIxj8zg0zi0zj0zj2zl4z\ l8ymBxoFvoHupKspNrrRpsSosVmuYluajvbixfgxifyldymbzp\ azs_zvYzxXzzVzzUzzSzzRzzPzzNzzMzzKzzMzzNzzPzzRzzSz\ zUyzVxzXvzYuz_sz_rzapyboxdmvflugjsiirjgplfomdmmblo\ ajp_irYgsXfuVdvUbxSayR_zKVzNXzPYzS_zVYzU_zS_zRazPa\ zNazMbzKbzIbzHdzFdzDdzBfz9fx8fv6gs4gp2ip1ip0ip0jp0\ jp0jp0lp0lp0lp0mp0mp0mp0lr0lr0jr0js0is0is1gs4gu6fu\ 8fuBdvDdvFbvHbvKaxMaxN_xR_ySYyUYyVXyYXz_VzaVzdUzbV\ zbVzbVxbVubVrbVpbVmaXjaXgaXdaXbaX_aXXaXU_YR_YP_YM_\ YI_YF_YBgV1bX6_Y9XYDU_HR_KNaNKaRHbUDbX9d_6db2ff0gg\ 0fi0fi0fi1fj1fj1dj1dj2dl2dl0Kl0Km0Mo0Km0Kl0Il0Ij0I\ i0Hi1Hg1Ff2Ff2Fd4Dd4Db6Ba } 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 26-07-08 (The Forest Floor [8])
by Jim Muth 25 Jul '08

25 Jul '08

FOTD -- July 26, 2008 (Rating 8) Fractal visionaries and enthusiasts: Our asymptotic approach to unity continues today as we investi- gate the fractal that results when the formula Z^(1.025)+C is calculated 43 levels up the complex logarithmic hyperspiral with no function applied. Actually, I am not certain which, if any, function is the 'correct' one to use with the MandelbrotBC3 formula, or even if there actually is a correct way to deal with the infinity of 'correct' solutions to the multi-valued complex- logarithm. Today's parent fractal is an oversized parabolic-shaped thing with the focus of the parabola on the east-southeast side. This parent requires a bailout radius of 3600 to give it room to spread to its full extent. An area of chaos appears at its northwest extremity, with today's scene located in this chaos. There is a minibrot at the center of the image, but don't waste time trying to reach it. It lies far beyond the limit of resolu- tion. At the magnitude of the actual image, the picture reminds me of a scene in a forest, looking upward from the forest floor toward a mighty fir tree. I named the image "The Forest Floor". If I had more time, I might have made the fir tree likeness more convincing. As it is, even with its flaws, the image rates an 8, which is pretty good as fractals go. The calculation time of just under 6 minutes can be eliminated by viewing the already-calculated image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tomorrow's FOTD will be posted in 24 hours. Just for the fun of it, I'll reduce the exponent to 1.00625 to see if I can find anything. But with an expression whose graph is virtually a straight line, I can guarantee no success. Regardless, until then, take care, and stay on the straight and narrow fractal path. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Forest_Floor { ; time=0:05:55.52-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident float=y center-mag=-26.71933195088172/+9.587738968748848/\ 2.907681e+010/1.0234/-22.5/0 params=1.025/0/43/3500 maxiter=2800 inside=255 logmap=455 periodicity=10 colors=000KbzKczKdzKezKfzKgzKhzKizKjzKkzKlzKmzKnzK\ ozKpzKqzKrzKszKszKrzKqzKpzKozKnzKmzKlzKkzKjzKizKhz\ KgzKkzKizKgzKezKczKazKazKYzHgzCUz2_z8QzEOzKOzPRpPQ\ nOPzNUzMOzLWzKNzJMzILzHLzGKzFVzEJzDIzCHzCCzFHzHMzK\ MzMRzOWzR`zTez_jzgozntzwyzzxzzwzzxzzyzvzzrzzmzzhzz\ czzZzzUzzPzzJzzHzzGzzEzzCzzBzz9zz8zzAvzBrzCmzDhzEc\ zDZzCUzRUTRUTRUSQUSQUSQURQURPURPUQPUQPUQOUPOUPOUPN\ UONUONUOzcOzcNzcNzcNzcMzcMzzMzzLzzLzzLzzKKKKJKKJKK\ JKJJKJIKJIKIIKIHKIHKHHKHHKHGKGGKGGKGFKFGKGGKGGKGHK\ HHKHHKHIKIIKIIKIJKJJKJJKJKKKKKKKKKLKLLXLLYLMYMMZMM\ _MNaNM`MM`MM_MM_MLZLLZLLYLLYLLYLKXKKXKKWKKWKJVKJVJ\ JVJJUJJUJITJITIISIISIHRIHRIHRHHQHHQHGPHGPHGOGGOGGO\ GFNGFNFFMFFMFELFELFEKEEKEEKEDJEDJEDIDDIDCHDCHDCHDC\ GCCGCBFCBFCBECBEBADBADBADBACBACA9BA9BA9AA9A99A9899\ 89988988877877876876876765765764764753653653652652\ 6415415405405405516516527 } 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 25-07-08 (Into the Depths [7.5])
by Jim Muth 24 Jul '08

24 Jul '08

FOTD -- July 25, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: With today's image we continue the explorations of minibrots in the Mandeloids of very low order, going down from yesterday's 1.075 to 1.05. The parent fractal is a grossly oversized thing, shaped rather like a comet, with debris fields on both sides of its squared-off outer extremity. It was produced by calculating the formula Z^(1.05)+C at a level 13 turns up the logarithmic hyperspiral. Today's image is located at the edge of the southern debris field at the outer extremity of the parent. The exact spot is impossible to recognize on the surface, and I needed to use my not-so-secret method of identifying minibrots to ferret out the elusive little midget. In fact, I never did reach the minibrot itself. The resolution breaks down well before the minibrot becomes visible. But the pattern around it is quite interesting -- perhaps the best de- fined pattern I have yet found around a minibrot in a fractal of such a low order. Or maybe it's just that I put a bit of effort into the coloring. I named the image "Into the Depths", which is a fair description of the impression I get while studying it. I rated it at a 7.5, mostly because it is surprisingly rich for a scene in a fractal of such a low order, but also to give myself a pat on the back for the coloring. The calculation time of just under 2-1/2 minutes on a fireball 2000mhz machine should bring tears to no one's eyes. But compu- ters are notoriously prone to stubbornness, so to guarantee dry eyes, I recommend visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. The next FOTD will appear in 24 hours, most likely continuing the same theme with an exponent even closer to unity. Until then, take care, and take no fractal for granted. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Into_the_Depths { ; time=0:02:24.45-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-14.84534363332544/-23.4626947348403/\ 4.554307e+010/1/-21.75/0 params=1.05/0/13/1500 float=y maxiter=1500 inside=0 logmap=228 periodicity=10 mathtolerance=0.05/1 colors=0000FTWQh00fKDZWLa00ZGIZOHYWFSE4JUCZRAbW9JT\ QJUFdzuJwcLUL`UJeQUQRNSUGjT9dT3WU9bVFqzLnzMoVMoVNz\ zTzUOZUOzTPrT0qTQsSQzSGtSRtRSuRSzRTvRTvPUwNUwLVwJV\ wHWwFWwDXxBXx9Yx7Yx5Zx4Zx5`t5ap5cm5di5fe6gb6cZ6jV6\ lS6mO6nLDsFJc9NcGRyMVcSYyYacceziizolzuhxtdvt`ttXrs\ TpsPnsLlrHjrEirvN0qR7mVDiYJeaP`eVXh`TlfPplLsrCfS4U\ 18XAC_JGaRKd_OfgQccRa`S_XUYUVWQWUNXSKVXIT`HReFPiEN\ nCLrBMrDNrEOrGPrHQrIRrKSrLTrNUrOUrPUnMUjKUgzUczU`z\ UXzUUzUQzUNzROzOPzLPzIQzFQzCRzARzEUzHWzKZON`UQc`Te\ fWhlZjralxXgwTbwPYvLTvHOvDJu9Eu5AuCEzJIzKHzLGzMFzN\ EzOFzOGzPHzPIzQJzQKzRLzRLzRMzSNzSOzTPzTQzURzUSzUSz\ TRzSRzRRzRRzQQzPQzPQzOQzNPzNPzMPzLPXLPZKN`JLaJJbII\ cHGdHEeGCfGBgDAjA9m78pCDqHIrMMsRRtWVu`_vecw_YtVSqQ\ NnbrA`q9Zp9Yo9Wo9Vn9Tm8Sl8Ql8Pk8Nj8Mj8QkDUlHXmM`nQ\ cnUbmXblZbkaajcajeaihahj`gl`fo`fq_es_dv_cx_czX`wVZ\ tTXqRVnOTkMRhuAPXXrWVoWTm } 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 23-07-08 (Theological Puzzle [5])
by Jim Muth 22 Jul '08

22 Jul '08

FOTD -- July 23, 2008 (Rating 6) Fractal visionaries and enthusiasts: For today's image we return to the formula that has supplied more FOTD fractals than any other -- the MandAutoCritInZ formula. We check the fractal that results when 1.5 negative parts of Z^(-5.5) are combined with 1.3 negative parts of Z^(-1.3) and (1/C) is added. The parent fractal reminds me of a large ant complete with head, thorax and abdomen, crawling southward across the screen. Today's image is located in the east branch of the valley where the thorax meets the abdomen. When I named the image, I was pondering one of the unanswerable theological questions that I once pestered my religion teachers with -- why does an all-good, all-knowing and all-powerful god permit bad things to happen to good people. This explains the name I gave the image --"Theological Puzzle". I really should curb my theological pondering. It constantly gets me into trouble. God, whatever truth lies behind that idea, must lack at least one, and possibly all of these attri- butes. Perhaps God is not all-good. After all, goodness is a human concept, and why should God's idea of ultimate good be the same as ours? Or perhaps God is not all-knowing. Could even a god know absolutely everything, which by definition must include what every sub-atomic particle in the universe has ever done, is now doing, and ever will do -- things that by their nature are unknowable? Or perhaps God is not all-powerful. Could even an all-powerful god do something that is impossible, such as making 2 plus 2 equal 7? Of course, theology is not the only discipline with unanswerable questions. Check one of the popularized science books about cos- mology or quantum theory, or grab one of those currently trendy books about new-age mysticism. As I often say, 'we don't know what we don't know'. And to make matters worse, I don't even have the option of avoid- ing the theological question by trying to convince myself that God does not exist and then claiming to be an Atheist. Now that I have indulged myself in this theological diversion, it's time to get back to the fractal business at hand. I rated today's image at a 6, which is all I think it is worth. The cal- culation time of under 3 minutes will not be much of a problem. The finished image is also posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A light midday shower did not spoil the otherwise near-perfect midsummer weather on Tuesday here at Fractal Central. The high temperature of 86F 30C and lower humidity were great for everything but snowmen. The fractal cats imagined themselves tigers as they watched a chipmunk in the back yard grass. My day was average, which means nothing happened. The next FOTD will be posted in 24 hours. Until then, take care, and ponder the hard questions. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Theological_Puzzle { ; time=0:02:53.84-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+0.934500853218/+1.854567358803/14309/\ 1/-120/0 params=-1.5/-5.5/-5/-1.3/0/0/0/0 float=y maxiter=1800 inside=0 logmap=120 periodicity=10 colors=000lcmkamj_miYmfWmcUm`SnYOoVKpRGpOCqL7vL8qL\ 8mL8hL9dL9_R1bL9WGGPBNJGQKLTKQVLuYLZ`MzbMheNzgNud2\ vcBwbKwaTx`ax_jwKow4tu9utDurHuqLvoPvnTvr_svhpoinhk\ lanjVphLvkOrfRnaTjXWfSZbN`ZIcVDhS4eR8bRB`RFYRIVRLT\ RPQRSEXWORVXMUmHTwEWzB_m8bi5egFVfOLeXAde0ad8ZdGWcN\ TcVLVkQca_hdVkTQnImq7KmAIiDGeGEbIKWPPPWa5nUJaMWPFh\ DGeCHbCI_CJYCKVBLSBMPBMNBzzAFv9mrFQoLVlR_iWeezjbzo\ _ztXzoJzk6ziFzhOzgRzgTzfVzfXzj_zfZzcYz`XzYXzUWzRVz\ OUzHRzLUzOWzRZzU`zXcY_eTbgPXdORbNUa5M`M5j`FfbPcdZ_\ fiVigXgeYfcZda_c_`aYa`Xb_YaYYaWZ`UZ_S__Q_ZO`YM`YKa\ XIaXHjFubNsVUrOapGho9on7Rh52bBA`HIZNPXTXWZdUdkUjsZ\ pzclwhitmfrrcov`lzYjzVgzSdzPbzM_zJ_yGawDcuAesDgq7i\ o8km8mk8oi8qg8se9uc9wg9xl9yq9zuKzuUzuaztczudzuezvf\ zvgzvhzwjzwkzxlzxmzxnzyozypzypzupzqpznpzjpzgpzcvz`\ rzYozVkzThzQdzNazL`zO`zR_zU_zX`za_z_ZzZZzYYzXXzVXz\ UWzTezEWzSMzdDzqMzmVzjtzh } 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 22-07-08 (Non-Mass Confusion [5])
by Jim Muth 21 Jul '08

21 Jul '08

FOTD -- July 22, 2008 (Rating 5) Fractal visionaries and enthusiasts: Today's image is found in the Z^(1.875)+C Mandeloid as it appears when calculated 25.5 levels up the log ladder with no function applied. This parent fractal reminds me of nothing more than a Mandelbrot set with a hernia, rotated 180 degrees. The exact scene is located in a small valley on the southeast edge of the parent's main bay. I named the image "Non-Mass Confusion" for some reason that I have now forgotten. I rated it at a 5 because I consider it worth little if anything more. The minibrot at the center is nearly an exact replica of its parent fractal. Considering the appearance of the parent, this is nothing to brag about. The image takes a little under 5 minutes to calculate on the fireball 2000mhz computer. This is the very first time this particular scene has ever been viewed by human eyes, so the calculation time is well within reason. But to assure that unreason has no opportunity at all to raise its ugly head, the finished GIF image is available for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A fairly pleasant midsummer day at Fractal Central went un- noticed by the fractal cats, who were more interested in watching the local pigeons. My day was fairly average also. The next fairly average FOTD fractal will be posted in 24 hours. Until then, take care, and ask every question. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Non-Mass_Confusion { ; time=0:04:59.04-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.852267427778726/-0.442482399993808/\ 2523215/1/-172.5/0 params=1.875/0/25.5/0 float=y maxiter=5200 inside=0 logmap=333 periodicity=10 colors=000A0KE0MH0OM0QR0SU0V_0Yb0_g0fj0jo0lt0mx0oz\ 0qz0sz0tz0tzHozojzzeyz_szSlzNezHYz4_zC_zK_yR`u_`tg\ `smboubmzYhzblzeozjqzmtzqxzuyzyzxzzuzztzzqzzozzmzz\ lzzhzzestbzhhzlcjm_gj`ehbcgcbce`bgY`hWYjUWjSUlRRmN\ PoMNqKKsIItHHtb_WzR2uo7cz1ez5gzAgzEhzIjzNjzRlzWmy`\ ozlmzgmxcmo`mhYmbUmURmNNmHKjFNhEPeERcCS`AW_AYW9_U9\ `S7cP5eN5gK4hI2lF2mE1oH0zE0uC1qAAl9Kg7U`5cW4mR2uM2\ lW2bc2Ul2Yo2`q2bs2et2gu2jx0xz0qz2ly7gxAbxFWuIRtNMs\ RHsWAqz5zt1zt0zo0xg0mY0eP0YF0Q40450970E92IA4NC7SEA\ YFEbFFeHIjIMoKPtMRyNUzPYzR`zS`zjuzqszZtz_ozPcxNcsN\ cmNehMecMe_9PFFMNMeW0ocxzeSxb0yR0qW0h_4`bASeFKhAEc\ FChKClPCqUCtYCxbCzgCzlCzqCzx7ztCzsHzqMzoRzmWzl`uje\ shjmgohetecy`bzY`zSbz0`z4_zP0zzCzzIPxHRzHRzHSzHUzI\ MzHUzF`zEgzCmzAtx5yzAztFzmKzgzz`zzUzzNzzHzzAzz4zz0\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzz1zz1zz1zz1zz0zz1zz5zz\ 9zzEzzAzzEzzHzzKzzNzzRzzU } 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 21-07-08 (Six Discontinuities [4])
by Jim Muth 20 Jul '08

20 Jul '08

FOTD -- July 21, 2008 (Rating 4) Fractal visionaries and enthusiasts: In today's image we return once again to the Z^(1.875)+C Mandeloid as it appears 26 levels up the complex-log hyperspiral with the 'floor' function applied. This Mandeloid closely resembles the Mandelbrot set. The main differences are the lack of a main spike and the 180-degree rotation. Today's scene is located on the west side of the south branch of Seahorse Valley of the parent, which becomes the north branch when the fractal is rotated 180 degrees to the 'normal' position. I named the image "Six Discontinuities" after the six almost- invisible discontinuities that interrupt the perfection of the spiral seahorse tails leading to the central minibrot. Unfortu- nately, these breaks are an inescapable part of all fractals created with fractional powers of Z. They must always spoil the sought-after fractal perfection. I rated the image at a humble 4, which can be considered no better than barely adequate. Let's face it, the image is basically nothing more than another scene in Seahorse Valley, the first place every tyro fractalist checks. Actually, this parent Mandeloid is basically a 'ground level' one, and can be created far more simply with any formula that can calculate (-Z)^(1.875)+C, which is another reason I was so stingy with the rating. The calculation time of 7 minutes on a P4-2000mhz unit just makes things worse. But with today's super-machines that move at the speed of a tachyon, that time may be cut significantly. The unlucky few with machines that have a panic attack when they see a DOS program can find the finished image posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Very summer-like weather prevailed here at Fractal Central on Sunday. The morning and first half of the afternoon were sunny, hazy, hot and humid, with a temperature of 93F 34C. But a thunder-shower moved in during the late afternoon with a wind squall and heavy rain that knocked the temperature down to 73F 23C, bringing welcome comfort to both cats and humans. The next FOTD will appear in 24 hours, so be right here when that paradisiacal moment arrives. Until then, take care, and fractals are never so good that they can't get better. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= SixDiscontinuities { ; time=0:07:16.33-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=mandelbrotbc3 function=floor passes=1 center-mag=+0.7461139806164767/-0.0627672807415249\ 6/5.887638e+007/1/-10/0 params=1.875/0/26/0 float=y maxiter=5000 inside=0 logmap=652 periodicity=10 colors=000PFqOEpNDoMCnLBlKAkJ9jI8iH7hG6gG6fLCcQHaV\ N_ZSXcYVhbTlgRcdQVaPM_OQ`MTaKXbJ_cHbdGfbKjaOn_SrZW\ uYZrX_oX_mX`jW`gWaeWabWb_VbYVcVVcSUdQUdNUeLUeNVfOW\ fPXfQXfRYgSXgTWgUVgUUhUThTShSRhRShQRjOQkMPkINmFJoB\ GpEJoGMnIPmKSlMUlOXkQ_jSbiUdiNgjGjk9ml2pmAidIcXQXO\ YRGdL8ePCeSFeVIeYLe`OecRfgVfjYfm`fpcfsffvifylZxmSw\ nLvoEup7upBsnErlIqjLphOofSndVmbYl`akZdjXgiWheXhbXh\ _XhWYhTYhQYhMZhJZhGZhC_h9_h6_kCbmIepOhrUku_nweqyjs\ ultrmtonulouhpveqvbrw_twXuxTvxQwyNxyKyzHzzKywMytPx\ qRxnUxkWwhZwe`wccv`evYhuVjuSmuPotMrrJtpHslIrgIqcIp\ `JoZJnXJmVKlSKkPKiQLmOLlMLiILaMc_QdYUdWYeUZeSVfQUf\ PUgSTgVThXTm_jra`zcRqfDmh8cj9UmABoB6qB2jA3f93b83_7\ 3Z63Z53Y53X66W79V7CU8FR9IO9LLANIBQGFTFJWGNZHRaKVcN\ ZeQbgTfiWjkZkmakodjpgjpjipjipiiphhohhoggogiogmofro\ fwoexneyndznczncznbznbznazmzzmzzmzzmzzmzzmzzlzzlzz\ lzzlzzlzzlzzkzzkzzkzzkzzk } END PARAMETER FILE=========================================

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FOTD 20-07-08 (What's It All About [5.5])
by Jim Muth 20 Jul '08

20 Jul '08

FOTD -- July 20, 2008 (Rating 5.5) Fractal visionaries and enthusiasts: Today's image is not so bad for such a hurried one. But due to being out in the Poconos having fun all day Saturday, I have little time for the fractal discussion. Surprisingly, at level 26 of the hyperladder, and with the function set to 'floor', the fractal created by the formula Z^(1.875)+C closely resembles a Mandelbrot set with X-axis symmetry that has been rotated 180 degrees. The scene of today's action is located in a minor valley on the eastern shore line of the large southern bud. (If the parent fractal is rotated 180 degrees to the 'normal' position, this is the western shore line of the northern bud.) I was a bit generous when I rated the image at a 5.5. It really has little going for it other than coordinated confusion. When I named it "What's it all About", I was thinking of the 'real' 'objective' world, which we all assume to be really 'out there'. The older I get, the more I doubt that the world is actually 'out there' rather than 'in here', or more likely a combination of both. The calculation time of 7-1/2 minutes is more than the image is worth. I strongly recommend visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and saving the effort of running the parameter file. If, due to the unusual hour of this posting, the image is not yet posted, check back in a few hours or bite the fractal bullet and run the parameter file at once. Typical midsummer weather prevailed at Fractal Central on Saturday, and it is prevailing again today. The fractal cats are ignoring it. The next FOTD will be posted in about 8 hours. Until that brief time passes, take care and search for the elusive truth. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Whats_It_All_About { ; time=0:7:30.00-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=floor passes=1 center-mag=+0.09083559731196626/-0.751949802458988\ 10/3.635092e+009/1/-165/0 params=1.875/0/26/0 float=y maxiter=7500 inside=253 logmap=420 periodicity=10 colors=000SDfUEgWFhYGi`HjcIkfJliKmlLnoMor0pu4qzBhz\ HZzFYzEWzEWzCVzCUzBUzBSz9Rz9Rz8QfrBfqBhq9ho9io8in8\ jn7jn7iq8hs9fv9eyBdzCbzCazEazErPzmVziawdhs`mnWsiRz\ eNz`JzWfIzdQzaYsZenWmhUuaRzWWvaaqfekjjhoobusYyySzz\ PzzMzyLswJmuIfsH`rFSqEMnCFmB8k91j80iC0iF0iJ0iM0iQ0\ iS0iW0iZ0ia0ie0ih1ik1in1ir3iu3iw3eu5as7Yr8Vo9RnBNm\ CLjEHiFChH9eI5dJ1bL0aM0jP1sR3zSHyZSvddsi3zd8zeEzeJ\ zePzfUwfYvfbshhqhmnhrkiwiizhizikzjmzknzmqzzzwwztsz\ qoznlzkjzhhxeeubbq__kXXdUUaRR`OP_LO_ILZFITCCOZFQ`E\ PbCNv9Lo8JzPIz5HzVFvBJvRNiPQhVUh`Yhf`fmdzzhmyjYnmQ\ dnIUq9Jr18u00v4SmEudRqbdmaziaqaMqV5jY7e`7Zb7Ud8Nf8\ Ii8Bj95m90o90q90oE0oI1nM4nQ7mU9mYCkaFkdIkhLjkNjoNi\ sSiwVhzYhzZhzbkzenzhqzksznvzqzyuzwwzvzzuzzszzkvzeq\ zYjzRhzJazCVzLPzSIzZJzfQznVzuazzfzzdzzazwZzrWzmUzh\ RzbPzYMzRJzMHzHEzBBz58z05z07z08z08z19z3Bz5Bz7Cz8Ez\ BEzCFzFHzHHzIIzHJIFLzFMzE } 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 19-07-08 (Green Dumplings [6?])
by Jim Muth 18 Jul '08

18 Jul '08

FOTD -- July 19, 2008 (Rating 6?) Fractal visionaries and enthusiasts: Today's fractal image reminds me of green dumplings. I can't help it. That's what I see, so that's what I named it. I could not decide on a rating, so I let the image go with a rating of a questionable 6. The parent fractal was created when I calculated the formula Z^(1.875)+C just 3/4 of one level up the logarithmic ladder with no function applied. This fractal resembles nothing that one is likely to see in what is commonly known as the real world. In fact, it consists of several separate Mandeloids, with today's scene located in the East Valley area of a small Mandeloid lying to the west of the main Mandeloid. The image is one of the most jagged I have yet found. It almost looks a bit sinister. A good part of it consists of inside stuff colored a deep blue. A better coloring might have been possible if I had put a bit more effort into it. The calculation time of the included parameter file is 3-1/2 minutes, but the wait to see the image can be reduced substantially by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. The 91F 33C heat and high humidity here at Fractal Central on Friday was not broken by a shower in the evening, as it was on Thursday, thereby making the fractal cats irate. And irate fractal cats are certainly no fun. Except for the irate cats, my day was pleasant enough, and with a similar day expected tomorrow, FL and I might plan a little outdoor enjoyment. If so, the FOTD for July 20, might be 15 hours or so late. Until next time, whenever that is, take care, and search for reality in the least likely place -- your mind. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Green_Dumplings { ; time=0:03:31.98-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-1.820586956762904/+0.1116182311689719/\ 7.098603e+007/1/92.5/0 params=1.875/0/0.75/0 float=y maxiter=3600 inside=255 periodicity=10 colors=000Q7KL5JG3HB1F60EA3OE6XI9eMBnYHgiN`uTVnVVg\ WV`XVUYVNZVG_VSYWbWXmUXlS_jRaiPcgOeKMe2LeaJeZIfYGa\ YFZXD`XCaWAbW9cU8aT7`S7`R6`V6aZ5bY5bX4cW4cR7cM9UHC\ PCEK7HA2J06L39N6CP8FQBJSEMUGPWJSXMWZOZ`RabUdcWeaSf\ _PfYLgXIgVEhTBhS8ro6ujBweGyaLxbMxcNxcOxdOwePweQwfR\ wfRvgSvhTvhUviUujVujWukXukXvd_wZbwSexMhxFky9ny3pBA\ iGAjKAkOAkTAlXAl`AmeAniAnmAorAovApzApyLnxVlwejvoiY\ IiWMfUPdSSbQV`OYZM`XLcVJfTHiRFlPDoNBrL9uJ8xHHvOQtU\ Zr`gpfpnmylsymtyntyotyotyptyqtyrtyrtystzzzwzzzztxr\ qxoowllwijvfhvceu`cuZatWZtTXsQUsNSrKQrHNqELqCJqFMq\ IOqLQqNSqQUqTWqVYqY_q`bqbdqefqhhqjjqmlqpnqrpppnonm\ nmlnkkmjjlhikfgkefjceibdh`ch_b_aZSbVJcRBdOEeRHfTJg\ WMhYPi_RjbUkdWlgZmiankconfpphqrkokmmdokYqiRsgKfQYh\ OajMdlKgnIkpGnrErtCuvBxvDuvErvGovHlvJivKgvMdvNavPZ\ vQWvRUiUNXXHK_A8b4Da5I`6N`6S_7XZ8`Z8eY9jXAoXAtWBxW\ BwZAv`Avc9ue9ug8tj8tl700P } 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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Re: [Fractint] FOTD->AOTD
by JackOfTradeZ＠comcast.net 18 Jul '08

18 Jul '08

. Animation of FOTD 7/9/08 (fractal black hole) is posted: http://www.fractal-animation.net/vid/blackhole.zip 12 Meg download. Noone commented on the last few - does that mean they suck? Hope you like this one. .

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FOTD 18-07-08 (Too Much Too Early [5.5])
by Jim Muth 17 Jul '08

17 Jul '08

FOTD -- July 18, 2008 (Rating 5.5) Fractal visionaries and enthusiasts: Today's image takes us back to the Z^(1.875)+C Mandeloid. This time we examine the version that appears 1 level down the complex logarithmic ladder when the 'floor' function is applied. At this basement level, the formula produces a fractal shaped like a puffed-up kidney bean with a large bud hanging from its bottom. Today's image is located in a curiously striated area on the western shore of this bud. When I delved into this area, I did not find the infinitely divided striations I expected. I found an area exceedingly rich in random detail but with no unifying theme, leading me to the name "Too Much Too Early". The rating of 5.5 indicates my dis- satisfaction with the plethora of detail, while including a half- point bonus for my modest coloring effort. The calculation time of 7-3/4 minutes is somewhat slow, so why not speed up things by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished GIF image there. An uncomfortably muggy day here at Fractal Central on Thursday was mitigated by a brief but heavy thunder-shower in the late afternoon. The rain dropped the temperature from 90F 32C to 73F 23C, and made the fractal cats happy in the process. My day was once again on the busy side, but better things could happen tomorrow, when the next FOTD fractal appears. Until then, take care, and now, even some physicists are saying that the universe, as well as empty space itself, might be a great fractal. Maybe the skeptics and Atheists are wrong when they claim it's all a meaningless accident; maybe the believers are wrong when they claim that a supernatural God did it. Or, maybe I'm wrong when I think the answer lies far beyond the ability of the human intellect to comprehend. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Too_Much_Too_Early { ; time=0:07:48.57-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=floor passes=1 center-mag=-0.331401349423654/-0.801267905838342/\ 2.180413e+007/1/-10/0 params=1.875/0/-1/0 float=y maxiter=7200 inside=0 logmap=725 periodicity=10 colors=000NASOASPASQASRASSASTASUASVASWASXASYASZBS_\ CS`DSaCSbBSbASc9Rd9Qd9Pe9Oe8Nf8Mg8Lg8Kh7Jh7Ii7Hi7H\ WQBNRMCQVFRWIRWLRWOSWRSWUSWXSWZTWaTWdTWgTWjUWmUWpU\ WrUWhWW_XWQZWH_WN0RT7NZ8JaBFl88jGBiNDhVFgaIfiKepMd\ wOetPerPeoPemPejPehPeePecPdcQeaPe_OeYNeWMfULfSKfQK\ fOJgMIgKHgIGgGFgEFhGJhINiKRiMViOZjQbjSfjUjkWnkYrjY\ ykZvk_sk`qkanlbklcildfledmfamgZmgXmhUniRnjPnkMnlKo\ mHonEooCop9op7loAjnDhmGelIckLajOZiQXhTVgWSfYQe`Odc\ LceJbhHakE`mC_pAZs7Zy8Yu9XrAWnBVkCUgCQZDUdEYiEanFe\ sFhxGcuH_rIWpJSmIPnJOkKOiKOfLOdLObLO_NOYNOWNOTOORO\ OPRRRUTSXVT_XUbZVdXXgcYjeZmg_pi`tt`rvaqkapwankbmkb\ ljbkjbischjcgjcfjcdidvndbid`ie_ieZheYseWhfVhfUZfQf\ hThfVieXjdZkc`mbbnado`fp_hrZjsYltXuuanvWgwQ`xKUyEO\ z9QzBVzDZzFczHhzJmzKrzMvzOzzQzzSzzUzzVzzRzzOzzLzzI\ zzFzzCzz2zz9zzFzzLzzRzzXzz`zzbzzdzzfzzhzzizzkzzmzz\ ozzpzzLzzMzzNzzOzzPzzQzzR } 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 17-07-08 (Eastern Lights [7])
by Jim Muth 16 Jul '08

16 Jul '08

FOTD -- July 17, 2008 (Rating 7) Fractal visionaries and enthusiasts: Due to an excess amount of real work, the fun work of fractals was cut short on Wednesday. But I did find time to delve into the parent fractal that results when the formula Z^(1.875)+C is calculated 36 levels up the logarithmic ladder with the 'floor' function in effect. This parent fractal resembles a Mandelbrot set that has been put through a wringer. Its most interesting feature is a much smaller distorted Mandelbrot set just to the east of the main set. Today's image is located in the East Valley area of this mini-M-set, which curiously lies on the mini's west side. There is not much more to be said about the image, though there is much to be seen when viewing it. I named the image "Eastern Lights" because it's on the eastern side of its parent, and rated it at a 7 because that's what I think it's worth. The calculation time of a nominal 2-1/2 minutes may be avoided by viewing the finished fractal on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With added haze, higher humidity and a temperature of 88F 31C, Wednesday was a comedown from the previous day here at Fractal Central. The fractal-cat duo showed their displeasure by camping most of the day under the cool-air vent. My day was busier than I would have preferred. With any luck at all however, tomorrow, when the next FOTD will ne posted, will be an improvement. Until then, take care, and speak softly with nature. I hear that, at its smallest scale, it may well be a fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Eastern_Lights { ; time=0:02:27.61-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=floor passes=1 center-mag=+0.786337062833908/+0.5106500816556531/\ 70165.7/1/40/0 params=1.875/0/36/0 float=y maxiter=2400 inside=0 logmap=175 periodicity=10 colors=000AAwAAtAApAAlAAhAAdAA`AAX8AU7AQ57M43N55L6\ 7M78Q8AP8BR9DTAEUBGVCHWCJYDK_EIbFNbGPcGJgHLcIMbJKa\ JI`KG_LEZMCYMAXKCVJETIGRHHPGJOELMDMKCOIBQGARFCTHDV\ JEXKFZMG_NHaPIcQJeSKgULhVMjXNlYOn_Po`WdVaUQhJKn9Fl\ BIjCLhDOfERdFTbHW`IZZJaXKdVLfTNiROlPPoNQrMRtKPrJOq\ INpGLoFKnEJmDIlGMkJPjMSiPVhUZgZafcdehgdmjcrnbvqazt\ `zw_zz_zwYztXzqWvnVrkTmhShfRccQ``PYYNWVMUSLSPKQNJO\ QKMTLKVMIYNG_OEbPDdQCgRCiSClTCnUBjYBg`BddBagHeZNiR\ SlJTkIUjIUjIViIWiIWhIXhIYgIYfIZfI_eI_eI`dI`dIgZRnT\ _tNhpPelRciT`eUZbWXZYUWZSS`PPbNLcLIeIEgGBhEDeHFbJG\ `LIYNJVQLTSMQUONWQLYRI`TFbUDdWAfX8hZAi`CibEjcGjeIj\ gKkhMkjOllQlmSloUmqWmrYmp_jo`gnbdmcakeZjfWihThiRfj\ OelLdmIcoFapC`r9_s6Zt4asAcsFfrKhrPjrUmqZoscquhtwmv\ xrxzwrzvmzvgzubzuXzuzztzztzztzzlzzezzYzzRzzJzzCzz4\ zz1zz2zz6zzAzzFzzJzzNzzKzzH_zEWzBSz9QzBPzCNzEMzFKz\ HJzIHzKGzLEzMDzOBzPAzR8zS } 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 16-07-08 (Naturally Fractal [7])
by Jim Muth 15 Jul '08

15 Jul '08

FOTD -- July 16, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's image returns us to the complex logarithmic hyperspiral, which we have not visited in about a month. The parent fractal was created by the formula Z^(1.875)+C as it appears 33 levels up this abstract spiral when the 'floor' function is used. This parent resembles a ragged, somewhat squashed Mandelbrot set rotated so that its main spike points northeast. I chose the exponent 1.875 because it is 7/8 of the way from 1 to 2, which is close enough to 2 to create minibrots resembling recognizable quadratic ones, yet far enough from 2 to create fractals of infinite variety. Today's scene is located in a filament extending from the period-5 bud on the southwest shore line of the large minibrot on the main spike of the parent fractal, very near the point where the hairline filament emerges from the chaos. I named the image "Naturally Fractal" in recognition of the fact that nature is filled with and possibly made of fractals. I rated it at a 7 because it not only leads to pondering, it also is attractive in its own way. And no one will complain about the calculation time of a mere 30 seconds. For added convenience, the finished image is posted for fast if not instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Another perfect midsummer day went unrecognized by the fractal cats of Fractal Central on Tuesday. The temperature of 86F 30C was made quite bearable by the low humidity. My day was a bit too busy for total enjoyment, but I still managed a half-hour under the mulberry tree, pondering the mysteries of the outer world and man's pathetic efforts to comprehend it. The next FOTD, which BTW is still a mystery, will be posted in 24 hours. Until then, take care, and fractals can cause deep thinking. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Naturally_Fractal { ; time=0:00:29.98-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=floor center-mag=+1.298046570238266/+1.385392696646682/\ 1.09e+007/1/65/0 params=1.875/0/33/0 float=y maxiter=1200 inside=0 logmap=70 periodicity=10 colors=000OKOOKNOKNOKLOKKOKKOKKOKKOKKNKJMKILKEKKAJ\ J9II8HH7GG7FF6EA5B54814K46P77V99bCAgJCiHDzfCoJEzzD\ f3Fh0JimNj2Qk2Ul2Xm2`p1_n2cm2fl2ij3mi3ph3sg3va8uXc\ tSGsMLrHcrCTv1mz7mvCXrHWmMWhRWRWVL`VEdY3eV8fSCfPHg\ MLgJPiKRkKSmKUoKVzXNpKWb6og8dlAVqCKvEAzF0qO3iW5ad8\ UlAMdMEYYIZVMZTP_RT_PX_N_`Lc`Jf`HlRQrHYqMXpQXoUWnZ\ WmbVlfVqhPljVhl_cnd_oiVqnRssNtxHskBs_5rO0rC2cQ4Qc0\ Aw5CpAEjFGcE6XKHYPRYU`YswSZjY5eiEYbMQXUIQ`CGaAKa8N\ b6Rb5Uc3Yc1`c0cbDgaPk`ao_ms_ywfyjmyYtyLzy82i7czQ`r\ RZjSXbTVVUTOUTOUTOUTNTTNTTNTTNTTMTTMTTMTTMTTLTTLTT\ LTzLTzKTzKTzKTzKTzWkzTfzQazNXzgfzfeueetddscdrccqbc\ zabz`bz`az_azZazY`zX`zX_zW_zVZzUZzUYzzYzzXzRXzzXzQ\ WzzWzzVzzVzzUzMUVzTzzTzz2zz3Cz3Cz4zz4zz5zS5zz5zR6z\ z6Ez7Fz7Fz8zz8zz8zQ9Gz9zzAHzAHzBzzBzQBzPCzzCzPDJzD\ zPEJzEzPEzOFKzFKzGLzGLzHLzHLzHzzIMzIzzJzzJzzKNzKzz\ KzzLzzLOzMzzMPzNPzNPzNQzO } 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 15-07-08 (Hyper Ultra Hyper [6])
by Jim Muth 14 Jul '08

14 Jul '08

FOTD -- July 15, 2008 (Rating 6) Fractal visionaries and enthusiasts: I spent most of the time on today's philosophy, which appears below, so I have little time for the fractal discussion. Today's image is from the same parent fractal as yesterday's image. This parent was created by combining 0.4 part of (1/Z) with Z^100 and adding C. Whereas yesterday's image is located on the west side of the open area of its parent, today's is found in a vestigial East Valley on the East side. I named the image "Hyper Ultra Hyper", which means nothing. I rated it at a 6, which is a half step down from yesterday's image. The calculation time of one minute will bring only happiness. And that happiness may be assured by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished GIF image there. Out of the blue Monday afternoon, FL made one of her comments that are intended to be innocent, but really get me pondering. She commented that she thinks I might be losing faith in science. How insightful a statement! Science is supposed to work in exactly the opposite way from faith. The claims of science must be objectively provable and falsifiable, while faith is based on unverifiable and unfalsifiable doctrines stated by priests, plus lots of hope, and yes, a bit of wishful thinking. When one loses faith, it means that the person can no longer believe a particular religious doctrine. A person may lose faith in the existence of a supernatural creator God because so much of the universe has been shown to have a perfectly natural explanation. They may lose faith in the existence of an immor- tal soul because the conscious mind is known to be intimately connected with a healthy functioning brain. Or the person may simply be unable to believe in things he cannot observe. But at the same time, science also requires us to have faith in things that we cannot observe. No one has ever directly seen an atom or any of the sub-atomic particles. We see only the written scriptures of physicists serving as high priests, who claim to have observed some high-energy phenomena that only they can interpret for us. We have the words of the religious priests written in the holy scriptures of religion; we have the words of the physicist priests written in the holy scriptures of published scientific papers. We have apologists for religion; we have apologists for science. The religious faithful are quick to defend their religious beliefs; the scientific faithful are just as quick to defend their scientific beliefs. I see little difference. In my case, my greatest doubt is that it is possible for a theory of everything to even exist, much less be worked out mathematically. Not the least problem is that the concept of 'everything' is an unrealizable ideal, not an objective reality. Finding a theory of everything is as likely as finding every possible fractal. Physicists have been chasing a chimera for over a century. But the chase is fun, and the chasers get their books published, and their shows fill the television channels, so the futile chase will likely continue well into the 22nd Century. But even then, the number of calculated fractals will have yet to scratch the surface of the total number of fractals that potentially exist. Monday opened with clouds here at Fractal Central, but by late morning the clouds had cleared away, leading to one of the most delightful afternoons of the summer. The fractal cats were too busy watching a tailless cat hanging around the area to bother with the 84F 29C weather. In my department, the real work was finished early, leaving ample time for today's image, which, despite sufficient time, still fell short. The next FOTD image will be posted in 24 hours. Until then, take care, and keep the faith. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Hyper_Ultra_Hyper { ; time=0:01:02.84-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=+0.5274268482159935/-0.0000290600313758\ 7/6.88186e+009/1/-166/0 params=1/100/0.4/-1/0/0/0/0 maxiter=1500 inside=0 logmap=116 periodicity=10 colors=000`UK_UKZUKYUKXUKWUKVUKUUKTUKRUKPUKNUKLUKJ\ ULHVMFXKDZIBaF9cD7eB6g99jCBlEDnGGpJIrLKtNNvQPxSRzU\ Pz_OziOzsMzzKzzKzzauzqeUzP0z90z20zU0sc0wm0zm0zm0zK\ 2zR9zYGzeMzkPoIMO0Kc0Oq0Rz0Wz0Yz0Uw0Rm0Oc0MU0IK5G9\ 9DRGYiKqzOz00z00z9DzOWz_mzz09z0Gz5KzBPzGUzMYzRczYg\ zakz_gzYczW_zUWzRRzRPo55e000c00Y00RG0MU0Ie0Bs05z00\ z0Bz0Mm0WY0eI0o00y00m07cGIRUPIg_5ug0zq0uy0gz0Uz0Gz\ 00z00z02z5IzGWzPiz_wwizqszkzzayzRwzIuu7qi0oW0mI0k5\ 0oD0sK0wR0zY0zc5zk9zqDzw9zm5sc0gU0WK0M9G50_00q00i0\ 0a00U02M0D052MG9cOGwWKzcPzkUzcYzYasPceKgUDiOOyDyz9\ zcOz0Iz0Bz5Oz9IzDBzI7zKmzDzz7zzPzzezzuzzmYzg2za0zW\ Gz0Oz0WzGczUkzeKz0Rz9YzOczaizmuz_zzMzz7zz0QKPXPKbT\ GiYCoazuezeRzQDzPPzP`zPlzTVzXDzTGzPIzMKzINzEPzBRz8\ Yz5dz2kz4hz5ez6cz7`z8Yz9WzATzBRzTYzidzzjzthzogzifz\ ddzZczUbzTdzRfzQhzPjzNlzMnzKpzJrzIszOszTszYszbszhs\ zmszrszwsztmzrhzpcznZzlTz } 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 14-07-08 (Hidden Jewels [6.5])
by Jim Muth 13 Jul '08

13 Jul '08

FOTD -- July 14, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image lies in the curious fractal that results when 0.4 part of (1/Z) is combined with Z^100 and straight C is added. This parent fractal appears as a circle with an open bay filling the right quarter of its interior. Today's scene is located on the X-axis in the rich detail at the left edge of this bay. I named the image "Hidden Jewels" for no good reason, and rated it at a 6.5, allowing myself a half point bonus for the extra coloring effort. The calculation time of a minute will seem more like 10 seconds once the scene starts to appear on the screen. For added convenience, the finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A hot muggy morning with ample sunshine led to clouds and rain showers in the afternoon on Sunday here at Fractal Central. The dynamic cats slept through most of the non-excitement. The next FOTD will be posted in 24 hours. Until then, take care, and for insomnia, read "Finnegan's Wake". Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Hidden_Jewels { ; time=0:01:08.12-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.03805276306469168/0/198852 params=1/100/0.4/-1/0/0/0/0 float=y maxiter=1500 inside=0 logmap=32 symmetry=xaxis periodicity=10 colors=0000iM0eO0cO0_P0WR0RU0PU2OcMMmaKkmIcsGczGcz\ Pcy_viizUszDzz0zz0zz7zzUzzozzzzzzy0Dm09c05R00I0050\ 0000000009O7UzGRzUPz_OziOzsMzzKzzKzzauuqeUzP0z90z2\ 0zU0sc0wm0zm0zm0zK2zR9zYGzeMzkPoIMO0Kc0Oq0Rz0Wz0Yz\ 0Uw0Rm0Oc0MU0IK5G99DRGYiKqzOz00z00z9DzOWz_mzz09z0G\ z5KzBPzGUzMYzRczYgzakz_gzYczW_zUWzRRzRPo55e000c00Y\ 00RG0MU0Ie0Bs05z00z0Bz0Mm0WY0eI0o00y00m07cGIRUPIg_\ 5ug0zq0uy0gz0Uz0Gz00z00z02z5IzGWzPiz_wwizqszkzzayz\ RwzIuu7qi0oW0mI0k50oD0sK0wR0zY0zc5zk9zqDzw9zm5sc0g\ U0WK0M9G50_00q00i00a00U02M0D052MG9cOGwWKzcPzkUzcYz\ YasPceKgUDiOOyDyz9zcOz0Iz0Bz5Oz9IzDBzI7zKmzDzz7zzP\ zzezzuzzmYzg2za0zWGz0Oz0WzGczUkzeKz0Rz9YzOczaizmuz\ _zzMzz7zz0zz0zz0zz00z07zUKzzUzz_zmezRkz5wzDzzKzzP0\ z70zM7zYIziRzuizazzIzz0zz2zz7zz9zzYzzszzzzzzazzWzz\ RzzOzzKzz7zz0zgIzoczwyzzzzzozzOzz0zz0zi0zBRzWszozz\ zyzsMzPgzePzRKz07zz0zI0zK } 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 13-07-08 (Back to Basics [6])
by Jim Muth 13 Jul '08

13 Jul '08

FOTD -- July 13, 2008 (Rating 6) Fractal visionaries and enthusiasts: Today's modest effort takes us back to the warhorse formula, the MandAutoCritInZ. I was away from this formula for so long that I almost forgot how it works. After a few minutes trial and error however, my memory was refreshed, and I found today's image in the fractal that results when various negative portions of Z^(-1.6) and Z^(-6) are combined and (1/C) is added. The parent fractal is a string of four large north-south oriented bays, with today's image located just inland from the western shoreline of the southernmost bay -- the bay with the shoreline that most closely resembles the shoreline of the M-set. The scene lies in a field of scattered and disconnected debris. The character of this debris is reflected in the patterns of today's image. I named the image "Back to Basics" because it is a return to the basic workhorse formula. I rated it at a 6 because I think it's worth no more. The calculation time of 20 seconds is blessedly brief, as is the trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the pre-calculated image there. But due to the unusual hour of this posting, give Paul a chance to get the image up. Saturday here at Fractal Central was on the hot side, but the temperature of 91F 33C was made bearable by a moderate breeze and humidity that was not too high. The fractal cats spent much of the afternoon playing with a few japanese beetles that some- how got inside. After clearing the beetles from FL's roses and giving the plants a good spraying, I had an acceptable day. The next FOTD, good or bad, will be posted in 24 hours. Until then, take care, and if the world is not really out there, then where is it? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Back_to_Basics { ; time=0:00:20.36-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip inside=0 center-mag=+0.3555098124098118/-1.390142792952676/\ 5.287551e+009/1/83.5/0 params=-6/-1.6/-1.6/-6/0/0/\ 0/0 float=y maxiter=500 logmap=46 periodicity=10 colors=00000000000000200600820C60EE0CL0AH08P06N24J\ 62RA0eC0zKCzcNzkZzvimobXbVERN0EGz2AzPHziNzzm0zczz`\ 0zz0xb0od0gdu`0oe6kiHgoVdseZxsVzzRzzNzzRzzVszZizb`\ qeRggH`eH`eJ`eJZeJZeJZeJZdJXdJXdJXdLVdLVdLVbLVbLTb\ LTbLTbNRbNRCz4Rz0ez0ux0zu0zs0zqPzqvzzTmz0szEvzRzzd\ zzqzvzzszmsqNsR0s04o0Cm0Jk0Ri0Ze0ed0mb0s`0X0iV0gT0\ eT6dRHbPT`Pb`NeeNiiLkoLosLsvJuzJxzJzzdsqvk`zeJ0Cz0\ kg0zL0xv0dz0JzGXzbizxvzimgVdRGXAVi8iu6xz4zz2zz0zzJ\ vzbgzuTzzVzzVzzVzuVxoXugXqbXmXXkRZdV`XZbRbdVXeZRg`\ LidHkgCmi6om0qo0xg0zb4zX8ddzZizVmzPqzLuzHzzCzz8zz4\ zzEvzLizVXzbHzk4zs0zg0kZ0TN0AE00G00G00G02G06H4AHAC\ HGGHLHRRJZVJeZLodLvgNzkNzoNzmNzmNzmNzkNzkNzkNzkNzi\ NziNziNzgNzgNzgNzgNzeNzeNzePxdPxdPvdPvdPvbPubPubPs\ `Ps`Ps`Pq`PqZPqZPoZPoXPmXPmXPmXPkVPkVPiVPiTPiTPgTP\ gTPeRPeRPeRPdPPdPPbPPbPPbNP`NP`NP2zz4xz6vz6uz8uzAs\ zAqzzz4quEb`LNGT0RE0HA0A4 } 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 12-07-08 (The Higher Glory [8])
by JimMuth＠aol.com 11 Jul '08

11 Jul '08

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FOTD 11-07-08 (Sand Castles [7])
by Jim Muth 10 Jul '08

10 Jul '08

FOTD -- July 11, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's image reverts back to version 4 of the DivideBrot series of formulas (formulae for the well-educated). I needed to go back to version-4 because it allows control over the bailout radius. Today's image uses a negative exponent of Z, and nega- tive powers of Z create fractals that tend to evaporate at very large bailout radii, such as the one-million of the version 5 formula. The parent fractal is a variation of the Z^(-3)+C Mandeloid, with a Mandelbrot set lying in the sandy fractal stuff at its center. Today's scene is located in an elephant-trunk spiral in the East Valley of this Mandelbrot set. The sandy stuff filling this area of the parent has infested the entire image, rendering the typical East Valley pattern almost invisible. Only the broad but careful coloring makes the spiral pattern visible. I named the image "Sand Castles" after the overall sandy effect. I rated it at a 7 because . . . well, I think it's worth it. The calculation time of 2-2/3 minutes makes the job of running the included parameter file, if not a gale, at least a breeze. And I'm not blowing hot air when I say that the finished image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Absolutely perfect weather conditions prevailed here at Fractal Central all day Thursday. The deep blue sky and total sun were made even more enjoyable by a temperature of 79F 26C and the low humidity. The fractal cats must have agreed, for they got into a minor squabble over who would sleep in the spot of sunlight on the living room floor. My day was satisfactory. Tomorrow should be the same. The next FOTD will appear in 24 hours. Until then, take care, and the world is what you make of it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Sand_Castles { ; time=0:02:41.15-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot4 passes=1 center-mag=+0.04014873876952896/-0.000578747776991\ 23/1.679661e+008/1/177.5/0 params=-3/0.15/-90/0 float=y maxiter=5000 inside=0 logmap=172 periodicity=10 mathtolerance=0.05/1 colors=020IQzIQzISzIUzIUzIWzIZyIZyI_yIavIdvIdtIftI\ htIhrIirnktwkzwnzmpzIpzIrzItzItzIwzIyzIyzIzzIzzMzz\ KzzIzzIzzGzzGzzEyzEyzCwzCtzAtzczzczz7wz7nz5kz5kz3i\ z3hw1hs1fq0do0dn0am0_l0_k0Zi0Wg0We0Uc0Sa0S_0QY0OW0\ OU0MU0KU0KU0IU0GU0GU0Ez0Cz0Cz0Bz09z0Bz09z09z09z09v\ 07r07m07h07c05Z05U05R05O03M03K13I33G52C72A827A25C2\ 3E25E25E25G25G27G27G27I27I27I28I28K28K28K2AK2AM2AM\ 2AM2AO2CO2CO2CO2CQ2EQ2EQ2EQ2ES2ES2GS2GS2GU2GU2IU2I\ X2IX2IX2IX2KY2KY2KY2KY2M_2M_2M_2MX2UY2QY2O_2M_2Kb2\ Ib2Gb2Ed3Cd5Ae98eB7gC5gE3gG1jI0jK0lM0lO0nS0nU0nW0p\ Z0p_0ra0rd0tf0th0nr0pn0rk0ti0vh0yf0zd0zf0zh0zi0zk0\ zn0zp0zr0zt0zw0zy0zz0zw0zr0zn0zi0zf0zf0zf0zf0zf0zf\ 0zf0zf0zf0zf0zf1zf1zf3zf5zf7zf7zf8zfAzfCzfGzfEzfCz\ fCzfAzfAzf8zf8zf7zf7zf5zf5zf3zf3zf1zf1zf0zf0zf0zf0\ zf1zf1zf1zf3zf3zf3zf5zf5zf5zf7zf7zf7zf8zf8zf8zfAzf\ AzfAzfCzfCzfCzfEzfEzfEzfG } frm:DivideBrot4 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1), d=real(p2)+100: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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FOTD 10-07-08 (Floating Fractal [7])
by Jim Muth 09 Jul '08

09 Jul '08

FOTD -- July 10, 2008 (Rating 7) Fractal visionaries and enthusiasts: I named today's image "Floating Fractal" because it lies floating amid much other debris in the interior of the western part of the main bay of the parent fractal, which seems unable to decide whether it is a Mandelbrot set or a quintic Mandeloid. The rating of a 7 seems about right for the undecided fractal. The five large amberish elements surround a skeletal quintic minibrot, which the inside=fmod option makes very obvious, and perhaps even too obvious. Actually the scene is filled with ghostly skeletal minibrots, all of which are made obvious by the 'fmod' option. The calculation time of 25 seconds, even with passes=1, is certainly right. With passes=g the calculation time is an astonishing 11 seconds, but at the cost of some missed detail. The passes=t option calculates the image in 17 seconds, but still misses a bit of detail. A satisfactory compromise is to surf out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and see the finished image posted there. Heavy clouds and heavy rain in the midday hours gave way to hot sun and high humidity later in the afternoon here at Fractal Central. The fractal cats kept cool in the temperature of 84F 29C under the cool air vent. I kept cool by taking it easy. The next FOTD fractal will be posted in 24 hours. Until then, take care, and be of sound constitution but don't disturb the peace. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Floating_Fractal { ; time=0:00:25.30-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 center-mag=-1.63458176/\ +0.13479938/588.4 params=5/3 passes=1 maxiter=1500 inside=fmod float=y proximity=0.04 periodicity=10 colors=000JmfKmfPJSXR_dYfg_cja`mbYodVrfSugPziMzjJx\ fIucIs`IoYHkVHfTHbSHUXJNcLGjM9qO2xP5jL8XH7_I7aJ6dJ\ 6fK5iL5kLKhPZeSlbVfgT`kRVoPPsNJwLSkR``XiPbrEgjIfbM\ eVQdNUcFYbKVWPSPUPJZMCcK6_P6WU6SZ6TX5UV4UT3VR2VP1W\ N0WM0UNDTOPRPaQQmPQyRMtSJpTFkVCgW8bX5ZW4_V4`U4`T4a\ S3bR3bQ3cQ3cXEcbOciYcogcuqctmasi`re_qaZpZYo_an`dma\ glbjkcmjdpiesZbgO_WDYKNaVWeddinby1ht3mo4rk5im9anCU\ pGMqJErMEsvMllUebaZTiSJqLAmN9jP8gR7dS7gV4fS9eQEeOJ\ dMOdKTcHXcFabDfbBka9pa7tZBoXFkVJgTNbRRZPUVMYQKaMIe\ IGiDEm9Cp5Eo8FoAGoCHoEIoGJoIKoK0KT3NU5QU8TVAWVDYWF\ `WIcXKfXNhYPkYSnZUqZWsZUo_Sk_Qg`Oc`M_`KWaJSaHObFKb\ DGbBCc98c85cC6bF6bI6bM7bP7bS7bW8bZ8aa8ae9ah9ak9aoA\ arAauAanE_hIYaMWWQUPUSJYQCaO6eN7gR7iV7jY8la8ne8oh9\ ql9sp9ts6xt6ws6vs6vs6us6ts6tr6sr6rr6rr6qr6qr6qr6qr\ 7pq7pq8pp8pp9po9poApnAonBonBomComColDolDokEokEnkFn\ jFnjGniGniHnhHnhIngImgJmg } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 09-07-08 (Fractal Black Hole [8])
by Jim Muth 08 Jul '08

08 Jul '08

FOTD -- July 09, 2008 (Rating 8) Fractal visionaries and enthusiasts: Today's fractal mixes features of the Z^512+C Mandeloid with features of East Valley of the Mandelbrot set. The order-512 minibrot fills the frame like a black hole gobbling up its surroundings. In fact, it reminds me so much of a black hole that I named the image "Fractal Black Hole". I rated the image at an 8. The smooth blending of the outer Mandelbrot set features with the perfect order-512 minibrot in the center is unusual enough to earn such a high rating. The calculation time of 5 minutes is slightly slow, but nothing that a modern S.O.T.A. fireball machine cannot handle. And to be doubly sure that all is under control, the image has been posted already calculated to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Lots of heat and humidity made it feel like real midsummer here at Fractal Central on Tuesday. When the temperature reached 90F 32C the fractal cats retired to the coolest spot they could find. When the work was finished for the day, I retired to the kitchen for the coolest drink I could find. The next FOTD, hopefully a cool one, will be posted in 24 hours. Until then, take care, and if not even light can escape from a black hole, how can the gravity get out unless it moves faster than light? (which I hear is impossible) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fractal_Black_Hole { ; time=0:05:02.09-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 center-mag=+63.11313720331\ 825/-0.04854690917159258/1.455609e+011/1/70/0 params=512/250 float=y maxiter=7500 inside=0 periodicity=10 mathtolerance=0.05/1 colors=000ukAtmAroApqAnsAltAjuAhv4jwAkvFluKntPosUp\ rUoqUopUlqUjqUgqVerWbrY`rZYs_WsaTsbRtdOteMtfOqkPnp\ QkuRhzSexSbwS`uTYtTVrTTqSUoRUnQUmPVlOVkNViMWhLWgKW\ fJXeIXcHXbGYaFY`EY_F_YG`XHaVHbUIcSJdRKePKfOLgMMhLM\ iKHhTDh`9hhBeiDbjF_kHYkJVlLSmNPnPNnRKoTHpVFpTHqRJq\ PLqNNqLQpKTpIVpHYpF`pEboCeoBho9jo8mo6pn5rn3un2vn1u\ l2sj2qf3nc3k_4hW4dT5_P5VM6QI6ME7IB7E77A4BB8ECBICEL\ DIPDLSEOWFSZFVbGYeGaiHdlIgpIksJnvJqqHnlGkhFicEfZDc\ VCaQBZLAWH9UC8R77O36M6AP9DSCHVFKYIO`KRcNUfQYiT`lWd\ oZgr`juXirUhoQglNfjJegGddDcbCa_C_YCYVCWTBUQBSOBQLB\ OJBMGAKEAIBAG9AE6AD4EH6HK7KO9ORARUCUYDY`F`dGcfIfgJ\ eeOdaTcYXbTaaPf`Lj_GoZCtZ8x`9tbAqdAmfBjhCgjCclD`nD\ YoL`pTcp_eqchqgj`fWKTINPEPRBRTJTVRVXZXZfYbmZ`nZ_oZ\ ZpZXqZWrZVsZUsTTqNToHSmAToBSmCSkGQgKOcOM_SKWUISVGO\ VEKWDGWDCXC9YC9YCAZCAZCAYEDYFGYGJYHMYIOYJRYKUYLXYM\ _aNaeTUkYNnbFsgAvlAvlAvlA } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 07-07-08 (Elephant Ring [8])
by Jim Muth 07 Jul '08

07 Jul '08

At 07:39 PM 7/6/08 -0500, Jonathan Osuch wrote: >I could hard code your DivideBrot5 formula and add arbitrary precision >support. The problem with arbitrary precision and most formulae is the >use of the function variables. We currently don't have all the >functions coded in arbitrary precision. > >Jonathan Hard coding the DivideBrot5 formula so that arbitrary precision math could be used would be appreciated. Since the formula uses no functions, the lack would be no problem. Jim M.

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FOTD 08-07-08 (Everyday Scenery [7])
by Jim Muth 07 Jul '08

07 Jul '08

FOTD -- July 08, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's obviously hexic (Is that the right word for equations of the sixth order?) scene lies in a bit of almost invisible detail in the interior of the main bud of its parent fractal, which on the surface resembles a Mandelbrot set. It is very rare to see such a perfectly proportioned minibrot of order 6. But the DivideBrot5 formula seems to be ideal for doing this kind of stuff with higher-order midgets. I have not yet done much exploration in the very high range around order-500 or so, but I'll get to it in a few days. I am hoping that, when I do, I will find something more than a lacy spiderweb network with little else of interest. I named today's image "Everyday Scenery" and rated it at a 7. The calculation time of a superluminal 50 seconds will cause no irritation. The finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Haze, heat and humidity prevailed all day Monday here at Fractal Central. The humidity made the temperature of 86F 30C feel more like 100F 38C. The evening lightning along the southern horizon made it look more like Independence Day. The fractal cats ignored the mugginess and spent most of the day resting. My day was moderately busy. Tomorrow is due to be the same. The next FOTD will appear in 24 hours. Until then, take care, and stand tall with your fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Everyday_Scenery { ; time=0:00:50.34-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 center-mag=-7.430006747510\ 589/+0.3879413753396198/2.657317e+012/1/-4.2/0 params=6/7 float=y maxiter=750 inside=0 logmap=49 periodicity=10 mathtolerance=0.05/1 colors=000KPEKNDKLBKJAKH9KF7KD6KC5OGWRJaUMfXPj`Slc\ VmfYpiZrhYqhXnhVkgThgQegObfM_fKXfIUeGReEOeCLeAJfGK\ fLKgQLgVLg_LhdMhiMinNisNixNlwGivJgvMeuPcuRatU_tXYs\ ZWsaTsdRrfPriNqlLqnJpqHptFpvGqsGqpGrnGrkGrhGsfGscG\ s`GtZGtWGtTGuRGuOGuMAlI5dE0XB7ZDE_FKaGRbIYcKceLjfN\ qfLpgOogRngUmgXmh_lhbkhejhhnfgjhjgjlcln`npXprVryUq\ tUppUolTnhTmdTl`SkWSjSSiORhKRgGTeARgCPhENiGzkHzlJz\ mLzoNzpOzqQzsSztUzuVzwXzxZzy`zzazyYzxUzxRzwNzxJzyG\ zzCzz8zz9zzAzzAzzBzzBzzCzzCzzDzzEzzEzzFzzFzzGzz9zz\ DzzGzzJzzMzzPzzSzzNzzVzzbzznzzizzezzrzzazzIzzKzzLz\ zMzzNzzOzzPzzQzzRzzUzzWzzZzz`zzczzevzhvzjuzmuzouzr\ uztozmizgdz`ZzVTzOOzIIzBAz0Dz5Gz9IzDLzHOzLQzPTzTWz\ XYz``zdczhezlhzphzyizvjztkzrkzplzmmzknzinzgbzfYzbT\ zZPzWKzSFzPAzL6zI7zK8zM8zO9zQAzSAzUBzWCzYCz_DzaEzc\ EzeKz`PzWVzR_zMdzHjzCoz7tz3rz6pz8nzAmzCkzFizHgzJfz\ LmzGJzOKzMKzLKzJKzIKzHKzF } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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REAL fractals in plastic
by Tony Hanmer 07 Jul '08

07 Jul '08

http://www.evilmadscientist.com/article.php/fimofractals Marvellously named site gets down to the nitty-gritty of making a fractal by hand, from mouldable plastic which hardens nicely in the home oven. So simple I'm jealous. Tony Hanmer www.geosynchronicity.blogspot.com

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FOTD 07-07-08 (Elephant Ring [8])
by Jim Muth 06 Jul '08

06 Jul '08

FOTD -- July 07, 2008 (Rating 8) Fractal visionaries and enthusiasts: Today's image shows a scene obviously lying in East Valley of its parent Mandelbrot set. The elephants with their spiralling trunks are there as expected, and the minibrots are found as expected where the trunk-spirals come together symmetrically. But what has happened to those minibrots? The minibrots are not the quadratic ones that would be expected, they are order-32 ones that would never be expected. This is because I have contaminated the parent Mandelbrot set with some Z^32 stuff, which becomes prominent only at a considerable depth. This mixture has the top halves of four proto-elephants arranged in a ring around the circular minibrot at the center, with various bits and pieces of other elephants scattered randomly through the rest of the scene. Once again I have gone to a very large magnitude to find the image, which is why the mathtolerance entry is included in the parameter file. These high-order minibrots grow more interest- ing the deeper they lie. It's too bad that arbitrary precision does not work with type=formula. It's probably due to the DOS memory limit. (When, if ever, we have a S.O.T.A. Windows ver- sion of Fractint, I assume this will be changed.) The ring of elephants inspired the name "Elephant Ring". I rated the image at an 8 because I like rings of elephants. The calculation time of 2 minutes will bring peace and contentment to all fractal visionaries. Fractal enthusiasts can find peace on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the already-rendered GIF image is or soon will be posted for instant viewing. A muggy high temperature of 86F 30C made Sunday feel more like a July day here at Fractal Central in central Pennsylvania. The local fractal cats kept the holiday spirit alive as they dashed up and down the long hallway and attacked their catnip rats. My day was slow enough to keep the philosophical pot aboil. The next in the apparently endless string of FOTD's will be due in 24 hours. Until then, take care, and when you make colorful philosophy, be sure that your conclusion is not colored by wishful thinking. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Elephant_Ring { ; time=0:02:03.47-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 passes=1 center-mag=+14.46\ 740554090629/-0.678528302118716/1.90372e+012/1/-40\ 0 params=32/50 float=y maxiter=1800 inside=0 logmap=218 periodicity=10 mathtolerance=0.05/1 colors=000nv_ovcqvfsviuvmwvpxvsvspqqmlnigkfahcYf`S\ eYPdYRdYSeYUfYVgYWiZYjZZkZ_lZamZbo_cp_eq_fr_gs_iq`\ jpakoblmcmlcnkdoiephfqgfregsdhtciubirZgpWfnTelPcjM\ bhJafG`dCZb9Y`6XZ3WUDZQM`LVbHcdDlf_`TvQGwPDxPByO8z\ O6zO4tP5oP5jP5eP5`P5WP5RP5MP5HP5FOCDNICMPALV8Ka7Jg\ 5In3Ht2Gz4Jx5Lw6Ov7Qt8Ss9VrAXpB_oCanDcmC`jBZgAXdAV\ a9TZ8RW7PT7NR6LO5JL4HI4FF3DC2B92973E84J85O86T87X88\ a89f8Ak8Bo8ApAAqB9rC9sD9tF8uG8uH7vI7wK7xL6yM6zN6zO\ pesrdmschuccvbZxaUyaPrYQkURdQSYMTRIUKEVDAW66X03Y75\ XD7WJ9VPBUVDT`FSfHRlIRiHSgHTdGUbGV_FVYFWWEXTEYRDZO\ DZMC_JC`HBaFBaED`EE_EFZEHYEIXEJWEKVEMUENTEOSEPRIWN\ NcI9U89`79g59n49u38nI7hW6bi6XwBam`t4GfdLjWQoMVtDvF\ HnVCfi8w_bohRgpm3qmAsmHtmzvmzwmztmzumzvmzvmzw5zw5z\ x4zo3zZ0zb1ze1zh2zk2zo3zr3zu4zMyzbfzf_zjUzmNzqHzuA\ zPa9XVzcOzjHzqAzrhztYzuOzwEzIHzXCzj8zXRzbMzhHzmDzs\ 8zdizgczjYzmSzpMzsGzvAz6K } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 06-07-08 (It's Stuporfractal [7])
by Jim Muth 06 Jul '08

06 Jul '08

FOTD -- July 06, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's FOTD takes us to an overblown Mandelbrot set contamina- ted with remnant Z^49+C debris. The scene is located on the west-northwest shore of the main bud of the M-set, rather deep in Scepter Valley. The more I use the DivideBrot5 formula, which is an unusually simple one, the more I find in it. As today's image shows, it can change those normally hopeless high-order minibrots into 'brots with recognizable quadratic and other types of patterns around them. Today's minibrot consists of 48 lobes, but don't try to see them. The image is at the absolute limit of definition, and any further enlargement will cause a breakdown that might serve as a new style of art, but is most unattractive when seen in a fractal. When I named the image "It's Stuporfractal", I was thinking of an old Daffy Duck cartoon, where Daffy, as Stuporduck, tries to save the world from the forces of evil. The rating of a 7 means the image could have been better but also could have been worse. The calculation time of under 3-1/2 minutes means relief for the time challenged. The finished image will also be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> as soon as Paul can run the parameter file and post it. The weather turned unexpectedly pleasant here at Fractal central on Saturday, so FL and I decided to take another day off. The fractal cats gave no complaints as we filled their dishes and headed for the outdoors. The only thing to suffer was the FOTD for July 6, which is now almost one day late. The next FOTD will be posted nearly on time in about 10 hours, so keep close watch on your e-mailbox until then. Until next time, take care, and when you philosophize about the meaning of existence, be sure to come to a conclusion you can live with. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= It's_Stuporfractal { ; time=0:03:26.96-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 center-mag=-125.0134222714\ 524/+0.9222603476751394/2.565149e+010/1.0451/40/-2 params=49/100 float=y maxiter=32767 inside=0 periodicity=10 mathtolerance=0.05/1 colors=000NIqPHpRHnTGmUFkWEiYEh_DfaCecBcf9bdBbbCb`\ EbZFbXHbVIbTJbVLdXMfZOg`PibRjdSlfUmhVojXplYrn_sp`u\ q`uqavlbuhbtcbs_crVcqRcpMdoIdnDdm9dlCbiF`fHZdKXaNW\ ZPUXSSUVQRXPPXPOXPOYPOYPNYPNYPNZPMZPMZPMD2BJ8EOEHU\ KKhsWfoUekTdgSccRLUQLWPLZNLaMLcKLfJLiHLkGLnELpD1Td\ 5WZ9ZUDaPHcKLfFPiATk5Vi4Xh4Zg4_f4ae4cd4dc3fb3ha3i`\ 3k_3mZ3nY2pX2rW2sV2uU2wT2xS2tT3pT4mT5iU6eU7bU8ZU8V\ V9SVAOVBKWCHWDDWEAWE9YF9_F9`G9bG9dH9eH8gI8hI8jJ8lJ\ 8mK8oK8pK9oJAoJBoJCoJDoIEoIFoIFoIGoHHoHIoHJoHKoGLo\ GMoGMoGNoFOoFPoFQoFRoESoEToEToESYbR`fPbiOemNgpQfnS\ emUdlWdkZcj`bibbhdagg`fi`ek_dmZcoZbjW_eUY`SWWQUSOR\ NMPIKNDIL9GJDKLHNNLRPPUQSYSW`U_dVchXflZjo_nsarvcux\ dpt`knYfhVabSYWOTQLOKIJDFF8CNHEVQFbZGjgHqoIy1mrsGp\ oKnlOmiSkfWib_h_cfXgeUkaYlZalWelTilQmlNqlMvjKtlIrn\ GqpForDntBlvAkxCevD`tEWsFRqHMoIHnJClK7jIDRL2iL4kL6\ lL8mLAnLCoLEpLGqLIrJKuLJs } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 05-07-08 (Pancake With Syrup [6])
by Jim Muth 04 Jul '08

04 Jul '08

FOTD -- July 05, 2008 (Rating 6) Fractal visionaries and enthusiasts: With today's image I introduce the ultimate, final, absolutely last version of the DivideBrot series of formulas -- version number 5. It draws the same images as version 4, but with two minor changes. I have added a value of 0.00000000000000000001, or 10^-20, to the imag(p1) parameter. This insignificant addition avoids a blank screen when the parameter is set to zero, and has no effect on the calculation time or image. I have also elimina- ted the real(p2) parameter and inserted a hard-coded bailout radius of 1,000,000, which eliminates the need to raise the bailout as the imag(p1) parameter is increased. The result is a simpler formula with less chances for mistakes. I named today's image "Pancake With Syrup". (The syrup is blueberry flavored.) I rated it at a 6, which indicates that I do not consider it anything out of the ordinary. The magnitude of the image is large enough to make the math- tolerance entry necessary. This assures that the parameter file calculates at the correct magnitude. The parent fractal is another almost-Mandelbrot set, with today's image located on a spike on the northeast shoreline of the main bay of the large midget on the negative spike of the parent M-set. As is true of many almost M-sets, the main bay as well as the buds are filled with tiny bits of debris, which prove to be entire universes when enlarged. The calculation time of only 42 seconds exceeds the speed of light, showing that the theory of relativity is flawed. The completed GIF image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> While we were relaxing in our lawn chairs this afternoon, FL casually asked me whether I believed in science or religion. Not being in the mood for philosophical rambling, I replied that I believe in both of them, since both science and religion are real. This reply saved a lot of words, but I'm not sure what I would have said if she had worded the question differently and asked me whether I consider faith or reason to be the the better path to ultimate truth. The question brought my philosophical muse to life however, so expect some enlightening or not so enlightening words about faith and reason before long. Heavy clouds and threatening rain made Friday less than ideal at Fractal Central. And the temperature of 73F 23C hardly felt like Independence Day, which is usually as hot as a firecracker. But it stayed dry, the neighborhood cookouts were a success, and the fractal cats made the most of the marginal conditions. The next FOTD will be posted in 24 hours. Until then, take care, and watch for runaway fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Pancake_With_Syrup { ; time=0:00:42.81-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 center-mag=-10.45034361189\ 851/+0.00241713891946783/2.225036e+012/1.001 params=6/6 float=y maxiter=1500 inside=0 logmap=105 periodicity=10 mathtolerance=0.05/1 colors=0009MUDMUHMULMUPMUTLUWLUYLV_LWaLYcK_eL`bQa`\ VaZZbXcbUhcSlcQqdOudPtfPtgPtiPtjPtlPtmUsjYshasffsc\ jsans_rnYpjUofQm`MiWIgSEgPAfM6eJ3b00A`zDYqGVhIZjLc\ lOgnRlpTprZeedVTjKGpA3qC5qD7rF9rGBsIDsJFsKGlMbfOyb\ Io_DeW8WT3NS5KR7IQ9GPBEODCNFANG8IEFDDL8CR4BXDJUMQR\ O_IQi9Sr1LpVEowGrlHuaIwSMvUPuVStWVsYYrZ`q_cp`9VhWW\ `qXUoZXm`Zka`icbgddagfWigQliLnjFql9sm4unHneUhYfbQr\ XIiXL`XNSXQJXSBXUEVWGTYIR_KPaMNcOLeQJgSHiPQaMZVKgO\ HpHFyAIiIKUQMEYPKVRPSTUPWZMYcJ_hH_YC_N8_D4VrF_ubcw\ ycCffIhhOikTkmZlocmsSQvG2vJ8vLEvNKvPPvRVvT`vUfvYko\ amiencioYmpSqqMurGxsAztFzqJznNzkRzhVzzZzzbzzazz`zz\ _zzZzzYzzzzzzzizzizzizzizzXzzazzetzfozgkzggzhbzhZz\ i`ze_zf_zfZzfZzg8z0Dz7IzDNzKSzQXzXazbezhXzdPz`GzX8\ zUCzTGzSJzRNzRRzQUzPYzO`zOezQizRmzSbzWTz_Jzc9zfNz6\ TzIYzUUzPRzKOzGLzBIz6Fz2JzBNzKRzTVzaZzjMzjOzhQzeSz\ bUz_WzYazUgzR8zb4zd0ze5zb } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 04-07-08 (Perfectly Cubic [8])
by Jim Muth 03 Jul '08

03 Jul '08

FOTD -- July 04, 2008 (Rating 8) Fractal visionaries and enthusiasts: In a recent letter to the Fractint list, JoTz noticed that the parent fractal of the "Order Septemdecem" FOTD image, which resembles a Mandelbrot set and was posted on June 27, has a bit of unexpected detail in its interior. I have known about this extra stuff since I started working on the DivideBrot formulas. The extra detail in the parent of the septemdecem fractal is actually the fragmentary remains of a Z^17+C Mandeloid, which appears when the imag(p1) parameter is set very close to but not exactly at zero. (I usually use the number 0.0000000001 instead of zero. In this case, the exponential form [1e-010] inserted in the formula does not work. This will be corrected in version number 5.) When imag(p1) is set to virtually zero, the resulting fractal is the normal Z^17+C Mandeloid. But as imag(p1) is increased, this Mandeloid gradually grows in size and morphs into the tradition- al Mandelbrot set, leaving order-17 debris to dissolve in the interior of the forming M-set. Some of the intermediate steps are quite interesting, but due to the size change, an animation with consistently sized elements would be difficult. The basic rule is: the smaller the value of imag(p1) the smaller the size of the resulting fractal and the more prominent the higher order shape, while at the same time, the greater the value of imag(p1) the larger the size of the resulting fractal and the more prominent the classic Mandelbrot-set shape. Today's scene takes advantage of the dissolving high-order debris in the center of the main bay of the parent 'almost-a- Mandelbrot set'. The scene is located in what first appears as a tiny dot, but when blown up reveals itself as an entire fractal universe. Due to the unusually large magnitude of the image, an outzoom to the parent fractal is quite a trip, but very interesting. But be sure to turn off the logmap feature before taking the backwards trip. BTW, the DivideBrot4 formula will soon be superseded by the DivideBrot5 formula, which will be used for all future fractals of today's type. I rated today's image, which shows an unusually well-defined cubic minibrot, at an 8. It's worth it. I named it "Perfectly Cubic" for the same reason. The calculation time of 47 seconds will cause no pain to those with computers that are not over-qualified. Those with machines that can surf the web in a flash but cannot run Fractint may still see the image by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoying there the image that Paul calculated. Lots of clouds, only a little sunshine, high humidity, a tempera- ture of 84F 29C, and a threat of rain followed by actual rain, made Thursday less than ideal here at Fractal Central. Not concerned with weather, the fractal cats spent a good part of the day trying to catch a fly. When one of them eventually caught it, the exhausted duo settled down to sleep. My day was busy, mostly because tomorrow is a holiday. The FOTD does not take time off for holidays however, and will be posted on schedule in 24 hours. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Perfectly_Cubic { ; time=0:00:47.85-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot4 passes=1 center-mag=-0.606\ 3981173832952/+0.006169462807566/5.040456e+012/1/\ -83.80/0 params=3/3/3/0 maxiter=1000 logmap=58 float=y inside=0 periodicity=9 mathtolerance=0.05/1 colors=00097UAAWBDYCG_DJaEMcFPeGSgHViIZkKbmMfoOkqQ\ rsroumpsllqkhnjfliejgcheaec`caZa_Y_XWXUUVRSTOQROO_\ JMXUKVdKSoUQzcOymQxmRwmTvmUumVuzXtzYsmZrc`qUaqWcpY\ do_znazmczmdzq_ztVzwQzzLzzIzzFzzDzzAzz7bz5azHazTaz\ dazleztizzlzlbzZTzLJzlEzpGztIzxKzzMzvOzqPzlQzfRzaS\ zXTzRUzMVzHWzGRzGMzFHzFCzE7zE2zSGzdUzqfztPzw8zqGzk\ OzeWz_bzUjzOrzIyzHtzHozGjzGezF`zFXzESzENzDIzDDzD9z\ EFzELzERzEXzEazLZzRWzXUzbRzhOwnMumOsmPqmQolRmlSklT\ ikUgkWekXcjYajZ_j_Yi`WiaUibVf`Y`_`WZcSYfOXhPWiPWkP\ WlPWmPWoPWpPWrPWsPWtPWvPWwPWxPWuSVsUUqXUoZTm`SkcSi\ eRggRkhQnhPqhOtiNwiMziMtjPokRikUdlW_mZUm`PncKoeEoh\ 9pj4pl6qk8rkAsjBtjDujFviHwiIxiKyhMzhOzgPzgRzgzzfzz\ fzzfzzhzzjzzkzzmzzozzpzzrzzszzdJzQIz4Cz36z21z2Lz3d\ z4zz5zz6zz7zz7zz8zz8zz9zz9zzAVzASzBPzBMzCJzCGzBDzA\ BzA8z96z93z81z87zEDzJJzOPzTVzY`zbfzglzlqzqrzsszttz\ vuzwvzywzzrztnzniziezcQzk } frm:DivideBrot4 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1), d=real(p2)+100: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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FOTD 02-07-08 (Creepy Crawlies [No Rating])
by Jim Muth 01 Jul '08

01 Jul '08

FOTD -- July 02, 2008 (Not Rated) Fractal visionaries and enthusiasts: Because of a big rush that we expect in, I will post no FOTD for July 3. The FOTD for July 4 will return on or near schedule. Today's image lies in the fractal that results when the formula Z^sqrt(2)+C is iterated 5 levels up the logarithmic spiral when the function 'one' is applied. Actually, I'm not convinced that this is a function at all, but it makes some rather interesting fractals, so we'll let it go. This parent fractal resembles nothing as much as a duck with a turned-up bill. Today's scene is located far out on a filament extending eastward from the duck's breast. I named the image "Creepy Crawlies" because of the cloud of hairy filaments surrounding the sorry excuse of a minibrot at the center. But try as I might, I could not decide on a rating. The calculation time of 1-1/2 minutes if fast enough to keep everyone happy. Happiness may also be found on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the completed image is posted. The Tuesday weather was totally perfect here at Fractal Central. The fractal cats enjoyed the near perfection to the utmost. My day was busier than usual due to squeezing three days' work into one day. Since there will be no FOTD for July 3, the next FOTD will appear in 48 hours. Until 2 days have passed, take care, and be eager to discover the next fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Creepy_Crawlies { ; time=0:01:34.27-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=one passes=1 center-mag=+1.126434310277434/-0.0602249097173638/\ 1.282804e+008/1/-35/0 params=1.4142/0/5/0 float=y maxiter=2500 inside=0 periodicity=10 colors=000bXYbXZbX_bY`bYabYbbYcbYccYbcYacYacY`dY_d\ Y_dYZdYZdYYeYXeYXeYWeYWfYVfYUfYUfYTfYTgYSgYRgYRgYQ\ hYPhYPhYOhYOhYNiYMiYMiYLiYLjYKjYJjYJjYIjYIkYHkYGkY\ GkYFkYFjXGiXHiXHhXIhXIgXJgXJfXKeXKeXLdXLdWMcWMcWNb\ WNaWOaWO`WP`WP_WQ_WQZWRZWRXUTWSVVRWUPYTO_SM`RLbQJd\ PIeOGgNFhMDjLClKAmJ9oI7qH6rG4tF3uG5vG7vG8vGAvGBvGD\ vGEvGGvGHvGJwGJwGIwGIwGHwGHwGIwGKwGLwHNxHQxHSxHVxH\ XxH_xHaxHdxHfxHiyHlyHmyHoyHpyHryHsyHuyHvyIwzIxzJyz\ JzzJxvKvsKsqLomLkiLgfMcbM__NXYNVWNTUORROPPPNNPLLPJ\ JQHHQFFQEDOFGNFKLGPKGUJHZHHcGHhFImDIr7LvCJzBJz9Kz8\ KzTcERaGQ`IP_KNZMMYOLWQJVSIUUHTVGSXERZDP`CObANd9Mf\ 8Lhsseqqfppfnofmnfkmfjlfhkfgjffigdhgcggafg`egZdgYc\ gWbgVagU_hSZhRYhPXhOWhMVhLUhJThISiHRiFQiEPiCOiBNi9\ Mi8LiWt2Vr4Uq5Tp6So8Sn9RmAQlCPkDPiEOhGNgHMfIMeKLdL\ KcMJbOJ`PI_QHZSGYTGXUFWWEVXDUYDS_CR`BQaAPcAOd9Ne8M\ g7Lhkssenq`jpWeoRanMXlHTk } 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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Re: [Fractint] FOTD 27-06-08 (Order Septemdecem)
by JackOfTradeZ＠comcast.net 30 Jun '08

30 Jun '08

. Zoom-in to FOTD 27-06-08 is posted. WMV, 640x480, 41 sec, 10 Meg. http://www.fractal-animation.net/vid/order_septemdecem.zip . Strange. If you zoom out to the parent fractal it looks pretty much like an ordinary mandelbrot. But you see a few lit pixels - single pixels - in the main black lake, especially the secondary bulb. I thought it was a monitor glitch or video artifact, but if you zoom in you see detail and structure. Whatsup with that? Stay amazed! JoTz .

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FOTD 01-07-08 (Feeling Testy [6])
by Jim Muth 30 Jun '08

30 Jun '08

FOTD -- July 01, 2008 (Rating 6) Fractal visionaries and enthusiasts: In today's FOTD we continue the investigation of higher order minibrots in apparent classic Mandelbrot sets. Today's order-7 minibrot was found in the star of a high-order bud rather deep in the East Valley of its parent. To add a bit of oomph to an otherwise routine image I rendered it with the outside set to 'tdis', which is really quite useful when no other coloring options seem to work. But even with the 'tdis' outside the image rates only a 6. This is not too bad, but I would like to have a rating a bit higher. I named the image "Feeling Testy", which has nothing to do with my mood. The words simply came to mind as I studied the scene. In comparison with yesterday's image, which calculates in 20 seconds, today's image takes almost 9 minutes to finish. To ease impatience, I recommend going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Monday turned out quite pleasant here at Fractal Central, with enough sun to keep everyone happy and a temperature of 82F 28C, which was made quite comfortable by the lower humidity. The fractal cats agreed. A moderate thunder-shower came up at 9pm to end the day with a bang. My day was very average. I only hope tomorrow can be the same. The next FOTD will appear in 24 hours. Until then, take care, and if you know it and know that you know it, then you know it is true. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Feeling_Testy { ; time=0:08:52.83-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot4 passes=1 center-mag=+1.791011102984003/-0.0049543843970271/\ 8.664403e+007/1/12.5/0 params=7/7/500/0 float=y maxiter=4500 inside=0 outside=tdis periodicity=10 colors=000`rHZrGZpGXpGXnDXnDVmDVmBUlBUl9Sj9SKwSHwQ\ HwQGwOGwODwODwMBwM9wK9wK7wH7wH4wH4wG2wG2wh0wh0wh0w\ h0wh00h00h00h00h00h00h00h00h00h00h00h00h00h00h00h0\ 02h02h02h02h00h00h00h00h00h00h00h00h00h00h00h00h00\ h00h00h00h00h00h20h20h20h20h20h20h40h40h40h40h404z\ 04z07z07z07z07z07z07z07z07O07Q07S07V07X07Z07`09a09\ c09e09f09h09j09l09n09p09r09s29u29v29w2By2Bz2Bz2Bz2\ Bz2Bz4Bz4Bz4Bz4Bz4Bz4Bz4Bz4Bz0Gz4BzD7zM4zU0z`0sf0m\ m0es0`r0Zr0Xp0Vp0Vn0Un0Sm0Sm0Ql0Ol0Mj0Mj0Kh0Hh0Hf0\ Gf0De0De0Bc09c07a07a04`02`02Z00Z00X00Z00Z00Z00`00`\ 00`00a00a02a02a02c04c04c04e04e07e07e07f07f09f09h09\ h0Bh0Bj0Bj0Bj0Dj0Dl0Dl0Dl0Gm0Gm0Gm0Hm0Hn0Hn0Hn0Kp0\ Kp0Kp0Mr0Mr0Mr0Mr0Os0Os0Os0Ou0Qu0Qu0Qu0Sv0Sv0Sv0Sw\ 0Uw0Uw0Uw0UzhzzevzcrzamzXmzZlzZlz`jz`jzahzahzcfzcf\ zeezeezecz`czZazVazS`zR`zR`zRZzbZzaXzfXzjVzmVzpUzr\ UzrSzsSzsQzuQzuOzvOzvMzwM } frm:DivideBrot4 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1), d=real(p2)+100: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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FOTD 30-06-08 (Haste Makes Waste [7])
by Jim Muth 30 Jun '08

30 Jun '08

FOTD -- June 30, 2008 (Rating 7) Fractal visionaries and enthusiasts: Due to too much time spent pondering irrelevant other-worldly things, I find myself running behind in the FOTD schedule. But I'll cut today's discussion short and get right to the point, hopefully quickly getting caught up once the point is made. After years of searching for something attractive in the higher order Mandeloids, I think I have finally found a way to create higher-order attractiveness. Today's image lies on the main spike of its parent pseudo-Mandel- brot set, in the remains of the Scepter Valley of the largest minibrot between the main minibrot on the spike and the body of the set itself. This minibrot is quite a sight, caught as it is in the act of changing from a quadratic minibrot to a minibrot of order-7. Actually the image is quite attractive. The order-7 minibrot at the center sparkles with gold trim, and the smaller surrounding minibrots are of all shapes and sizes, making each of them inter- esting in a different way. I named the image "Haste Makes Waste" when trying to find an excuse for my recent tardiness. I rated it at a 7, which might be a bit of an exaggeration. One thing not exaggerated however is the lightning speed of the included parameter file, which with a running time of an incred- ible 19-3/4 seconds, is one of the fastest ever. But we must never forget the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted, making the task of running a parameter file totally unnecessary. Sunday turned out unusually muggy here at Fractal Central, though with a temperature of 84F 29C, not unusually warm. The mugginess led to a series of torrential showers in the afternoon and evening, which squashed any thoughts of outside activity. The fractal cats disliked all the water on the other side of their window, but soon went back to sleep. My day was quite relaxing for a change. Tomorrow, when the next FOTD is due, will probably be busier. Until then, take care, and don't think about reality too much. You might find that it's not there. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Haste_Makes_Waste { ; time=0:00:19.44-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot4 center-mag=-24.47168928461\ /0/157925.5 params=7/15/1500/0 float=y maxiter=1500 inside=0 logmap=44 symmetry=xaxis periodicity=10 colors=0000AQ0AS0AU0AW0AY0A_0Ac0Ag0Fk0Ko0Ps0Uw0Zq0\ cm5hi6ed7b`7`X8YS9VOASKBPFCMBCI7LM8TU8a`8im8rr8zz8\ soAzcBzUDoKEfCFZEGRGHNJIJLIGNJCQK8SL5UL4PM4LM4HN4C\ N48O44O40OBBRIMTPWVWfXbpZYeVTVSPLPUMNYNMbNLfOKkPJo\ PImTHkWHiZHhaGfdGdhGbkGanF_qFYtFXwF_sJbpMelQgiTjeX\ mb_o_blZajZ`hY`fY_dXZaXZ_WYYWXWVXUVWRUVPUVNTULTTJT\ TKVQLXOMZLM`JNbGOdEOeCywS40c65_8AW9FSBKPDPLEUHGZDH\ cAGSSGGi8khElbJmXOmRTnLYoFbo9XmASkBNiCHgCzhDzmEzrE\ zvKzZPzXUzVZzTczRhzQmzTkzWjzZiz`kzamzcnzdpzeqz`izW\ azzVzzNzzGzzMzzdzzwzzpzzjzzdzzZzzTzzUzzVzzWzzXzzYz\ zYzzUzzZzzczzhzzmzzrzzvzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzpzMgzHYzCPz7MzKJz\ XTzNazDjz3az5Tz6Kz7Cz8BzEBzJBzPBzUAzZAzdAziAznlzJl\ zLlzNlzOlzQlzRezQ_zPUzP8zy7zt7zo6zk6zf6za5zY5zT5zP\ 9zICzCFz6JzJNzWRzhszBjzSbzgdzafzWhzRjzLlzFnzAPzV0z\ o4zq7zsAztEzvHzwKzyNzzQzt } frm:DivideBrot4 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1), d=real(p2)+100: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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FOTD 29-06-08 (Five Strikes and You're Out [6])
by Jim Muth 29 Jun '08

29 Jun '08

FOTD -- June 29, 2008 (Rating 6) Fractal visionaries and enthusiasts: I'm not sure whether this borderline stuff is exactly on topic, but fractals certainly hold higher-dimensions, so why not our so-called 'real' world. I recently claimed to have experienced precognitive dreams. But this does not mean that I believe it is possible for Madam Zucchini, who runs a fortune-telling shop down on the corner, to know the future. If it were possible to do so, she would not need to run such a questionable business. She would merely need to buy a lottery ticket. She would know the winning number by using her occult powers. What such fortune-tellers do is known as cold reading, where they fish information from their patrons by clever questioning. It's a technique known to every aspiring magician, which in- volves nothing more than a bit of everyday psychology and a bit of good old common-sense. Spiritualist mediums run their busi- nesses pretty much the same way. But at the same time, I do not claim that it is impossible for information about the future to get into the past. In the case of my precognitive dreams I did not at any time *know* the future. After the attack happened, I realized that information from the future had somehow gone back into the past and in some manner had affected my dreams. But this in itself is incredible. It is even more paranormal than so-called communication with spirits of the dead, where all that would be needed would be for spirits of the dead to actually exist and to be able to communicate with the living, two perfectly intuitive, if not apparent, things. By contrast, there appears to be no possible way for information to now exist about an event that does not yet exist. In fact, if such backwards causality were ever shown to be true, we would need to adjust the entire philosophical foundation of science. The only way out of the situation that I am aware of is to claim that such intense precognitive dreams such as mine are one of those extremely unlikely coincidences, which against all odds, sometimes happen -- perhaps a one-in-a-googol chance. In comparison with precognition, I am firmly convinced that there are no space aliens visiting earth in their UFO space ships. The distances involved are far too vast and worm holes are unlikely in the extreme. Also, no clear pictures of UFO's have ever been obtained even with the ever-increasing number of video cameras and cell-phone cameras, which now are almost everywhere. In my opinion, aliens in UFO's are an example of suggestibility combined with wishful thinking. Yet despite this disbelief of most 'borderline' things, I must still face the fact that information somehow now exists about events that do not yet exist, and this pre-information actually can affect peoples' minds. If I do not accept an impossibly unlikely coincidence, I must accept that the outer world has hidden dimensions, (which physicists also claim), or the human mind has hidden dimensions, (which occultists claim), or perhaps both. One thing for certain however, which can be demonstrated at will, is that fractals have hidden dimensions. In fact, this might be why I enjoy them so. Today's image is a perfect example of a hidden dimension. Inside the parent fractal, which appears as a Mandelbrot set, lies a whole hidden quintic world. The image shows one of the quintic minibrots in the parent's depths. It is located in the East Valley of the largest mini- brot on the filament complex extending from the large period-3 north bud of its parent Mandelbrot set. I rated the image at a 6. It's a little too mundane to be worth more. I named it "Five Strikes and You're Out" when I recalled what the Ednor Gardens Eagles used to yell at the umpire when we thought he was too generous with the opposing batters. The calculation time of 2-1/4 minutes is well within reason even if getting information from the future is not. And as always, the finished image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A muggy day here at Fractal Central on Saturday, with a tempera- ture of 88F 31C, was climaxed by an exciting thunder-storm at 10pm, which dropped to temperature to 72F 22, making the fractal cats as well as the local humans very comfortable for the night. I totally avoided work during the day, which made both myself and FL very happy. The next FOTD fractal will be posted in 24 hours. Until then, take care, and truth is elusive. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= FiveStrikesAndOut { ; time=0:02:15.93-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot4 passes=1 center-mag=-1.544312331880741/+10.29436557667572/\ 1.202258e+012/1/-97.5/0 params=5/10/525/0 float=y maxiter=5000 inside=0 logmap=244 periodicity=10 mathtolerance=0.05/1 colors=000KCQKDSKGUKIWKKYKM_KOaKQcKSfKUhKWjKYlK_mJ\ anIatI`zIbzKbzMazOczQezSgzTizUkzXiz_kzamzdozfqzWtz\ MwzCze1z54zG7zR9z`CzkEyuLuoSqiZmcejY`bWXWUSOSOHQJ9\ OF2NSEScPXo_auZ_zYYvV_rT`nRajPbfNcbLdZJeWHfZIaaJXd\ KTgKOmLKmMFmMBmLFmKJmJNhJRfIVdHZbGbaGfYEaUDXQCSMAN\ I9IP8EZAChCBrNAvS9zU8wTFtRLmLRcMYUKUQKUMKUFKU9n921\ PzobvmYrlTnjOjiJfhEbf9Ze4Wd0c`KjYbhXcgWceVddUdbTda\ Se_ReZReXTgVUiTVkSWmWXnZXobYpeYpQRwMPXJN7FURB`jLB2\ ML9NUFNcLOlROuXUjf__odaihbcmcYqeSvfMzgGudJpaLkZOfW\ QaTTXRVSPXRRZRZ`UcbcldmtezzTzzGmd4wjKufNscQq`TpXVn\ UYlR`kObfLYaJTYHPTFKODFKBBF96B72IAAPDHVGPaJWgMcnPj\ tRqqWko_fmc`khWilQgpLcqN_rPWsRSsSztUzuWzvXzwczxj`y\ qgzxizZkz9nzGpzMrzTtzZvzdWzeXzgYziZzj_zl`znazobzqb\ zr_zkYzeWz_UzUSzOUzTWzYYza_zfazkczogzgjz`mzUpzMszF\ vz8yz1tz8pzFlzMhzTdzZczWczTczQczNczLczKbzJbzHbzGbz\ FazEazDazC`zA`z9mzLjzPfzT } frm:DivideBrot4 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1), d=real(p2)+100: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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FOTD 28-06-08 (No Fault Lines [7])
by Jim Muth 27 Jun '08

27 Jun '08

FOTD -- June 28, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's formula, DivideBrot4, is another new one -- the final version of the DivideBrot series. The only change from DivideBrot3 of the series is in the real(p1) parameter, where the number 2 is subtracted from the entered value before iteration begins. This change permits the order of the minibrots to be directly defined by the value entered as real(p1). The real(p2) parameter defines the escape radius. The imag(p2) parameter is not used. The imag(p1) parameter controls the prominence of the higher-order elements in the resulting fractal. A smaller value of imag(p1) results in a greater prominence of the higher-order elements. A larger value gives more prominence to the underlying order-2 Mandelbrot set, while at the same time enlarging the size of the fractal, which makes the real(p2) parameter necessary to expand the bailout radius so that the entire fractal fits within it. Today's image is named "No Fault Lines". I gave it this name because the central minibrot is of the order 3.5 and such fractional-order minibrots are always surrounded by discontinui- ties, which spoil the surrounding patterns of the minibrots. Today's minibrot however is a horse of a different color. Its surrounding pattern consists of seven elements, and these elements are intact. Seven, of course, equals two times 3.5, the order of the minibrot. The name refers to the lack of discontinuities. The image is located on the west side of the northern branch of the Seahorse Valley of the oversized Mandelbrot set that is its parent fractal. The Seahorse Valley characteristics are very prominent throughout the image. The order-3.5 characteristics are obvious only in the shape of the minibrot. I rated the image at a 7. It consists of too much mathematics and not enough artistic value for a higher value. Rendering the scene with the outside set to 'tdis' helped a little, but not enough to grant the image a rating of 8. With its calculation time of 1-3/4 minutes, the job of running the included parameter file should offend no one. But in this modern day and age, some computers have forgotten the old ways and don't know what to do with DOS programs such as Fractint. Those with such new-fangled instruments may still see the image however by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing it there. Warm temperatures, high humidity and showers prevailed here at Fractal Central on Friday. The fractal cats dislike a tempera- ture of 86F 30C, so they were not too happy with the conditions. But cats are cats, and before long the feline duo had found a cooler place in which to sleep. My day was kept busy by a customer of the worst kind -- one who needs his job at once, but doesn't know what he wants, and as a result, keeps calling in changes. In the end, common sense won out. I refused to answer the phone after the fifth call. The last I heard, he was satisfied. The next FOTD fractal will be posted in 24 hours. Until then, take care, and look up. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= No_Fault_Lines { ; time=0:01:44.21-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot4 passes=1 center-mag=-7.662916327120194/+1.181354355289796/\ 3.256997e+007/1/-98.25/0 params=3.5/10/1000/0 float=y maxiter=5000 inside=0 outside=tdis logmap=110 periodicity=10 colors=000JP3UgDP0DK99FH65zX7mN9`DhsH_kDRcAIW6NwsH\ rbFjUDcLBWCW8Nor4ah3OZ331vtV3My`IlPE`EnHocJbULRKNF\ xjg`ZpUWcNUSGRFIeXEXIGwHKVhGTVDRH3Wj5U_7SP9QEToyOh\ jJaWEVHrStcRbPQLY91SD2MH2GL3lXV_ULNRCbluTrxOtXJu6J\ iGJYPJMYXHfiCov7wsAhpCVmFGkH2_aJPv_`dblNd2126THAsV\ BXcCAlT4LYWNbwPPfECR4rEPWKE47X6CP7GI9LAOQJHPBveti`\ fYXUMTG4iC6c97Z79U52LPKFtFKU`wQUnKNeEGX8SYENVBJT8E\ R58H99K7AN5AyTrUAfS8WR6LQ4ROvMPhIPVEPHnH3UL3GbhEYV\ CTHDf6BY4eWPYUJQSEIQ8DMICNEBOAAP6oa7aX5OT4QaEIV8JT\ `GRPDQEh3LXBFLI9MaJGVBBp4Ai3Ab3AW3S4p9TLASGARCAQ7t\ YLhVGXTCLR7NLxINdEOMWE6HsRFkLDcFBW9WHEOKAHN6SJVJMH\ XpTLbG7sCcfBWa9PY7HT5p5naCZOJJdbQPWEK6yHBjFGWCLHQM\ 4IO3H42FA3DF3BK3O3HJBCEI7Z4JMhz8csDYmCVfBRG6EX8KIt\ LDhI9PL6XCTPHKHLBBMvANhAOVAPHKeFBadAXSATFERCCQ7AI5\ Ac4Ac4Ac34cR6mJ8mBOmr4m36m3zz3zzuzzgzzUzzGzzRzzFzz\ jzzWzzHzzezzWzzMzzCzz2zz3 } frm:DivideBrot4 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1), d=real(p2)+100: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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FOTD 27-06-08 (Order Septemdecem [6])
by Jim Muth 26 Jun '08

26 Jun '08

FOTD -- June 27, 2008 (Rating 6) Fractal visionaries and enthusiasts: Today's image was created with the third version of the DivideBrot formula, which is notably faster and more intuitive than version 2, the version I have been using until now. I will probably make a few more changes before finalizing the formula as DivideBrot4. Today's image shows an order-17 minibrot lying on the negative spike of the parent Mandelbrot set, very near the escape radius. I know that it's impossible to have order-17 minibrots in a fractal that on the surface appears exactly like the classic Mandelbrot set, but I suppose something in the formula never got the message, for this is what we have in today's image. The image was spiced up a little by rendering it with the outside set to 'tdis'. Everything else comes from the numbers themselves. I could have used a little more time to work on the coloring, which explains the rating of only a 6. The name of the image "Order Septemdecem" is simply a fancy way of saying 'order-17'. The calculation time of today's image is an astoundingly brief 13 seconds. So why not take a moment to run the included parameter file. Those with machines that get a case of indigestion when faced with Fractint may go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and see the finished image in its full semi-glory there. Thursday began with heavy clouds and light rain here at Fractal Central. But the rain ended at 10am and the sun appeared around noon, leading to an afternoon that was hazy, warm and humid, with a temperature of 86F 30C. The fractal cats enjoyed the sun when it first appeared, but sought cooler spots when it got too warm. I spent my free time working on the new formula and responding to an e-mail on the Fractint list. I'll probably make a few more changes in the formula before I have a final version. The next FOTD will appear in 24 hours. Until then, take care, and seek the elusive fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Order_Septemdecem { ; time=0:00:13.42-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot3 center-mag=-23.99999459284184000/0/6.080533e+011/1 params=15/12/485/0 float=y maxiter=15000 inside=0 outside=tdis symmetry=xaxis periodicity=10 mathtolerance=0.05/1 colors=000kiMjkJegHacGY_FTWDPSCLOBGK9CG88D79IC_0mA\ SLAXQBaUBfZBjbEeZH`WKWSNRPQMLTHIVCFU8Fa9HiAJpBKlKO\ iTSfaWcj_dgVeeQfcLfaGg_BhY6hW1PWVZcVWKHYOJ_SLaWNb_\ PdcRfgThF0gM7gTDgZJgeP06_MRXjohineimchmahlZgkXtYJo\ bNkgRdgNehPfiRgjT51XA7WFDWKJWPPWUVVZ`VcfVyjgskbmkZ\ lqjjofinbhlZZkl4GmALjGQgMUdRZbXb_bgXr0Op6PoCQmIRlO\ SkUTi_UheVEZMMbPKbWJcZOfUSiPWlK`oFdrAhu6atDWsJQrPK\ qWEpa8pg7mh6ji6gj5dk5bk4_l3Xm3Un2Ro2Po3Wl3aj3gh5_c\ 7TZ9LUBEPC7K9JS6V_4ff5_b6U_7OX7IU8CR96O90LE5NJ9OOE\ PTIRYNSbRTgWVl_WqdXvhYlfScdMUbGL`AC_5AY78W96UA4SC2\ QE0OF4QI8RLBTNFUQIWTMXVPZYT__Wab_bebdgfejifljdjkbh\ kagl_emYdmXbnVaoT_oSZpQXpPWnRXlSXkTXiUXhVXfWYeXYcY\ YbZY`_Y_`YYZWXXUWVTVURUSQTQOSONRNLQLKPJIOHHNGFMEEL\ CCKBBX8Ch5Dt3Dq5E_0ml9EjBEgCEeEEbGE`IEYJEWLETNERPE\ PQEXSLcURkWYrYcnb`kgYglVdqS`vPYzN_wOatPbrQdoRfmSgj\ TihUkeVlcWn`XoZYnaVmdSlfP } frm:DivideBrot3 { ; Jim Muth z=0, c=pixel, a=real(p1), b=imag(p1), d=real(p2)+100: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 26-06-08 (A Higher Reality [8])
by Jim Muth 26 Jun '08

26 Jun '08

At 12:20 AM 6/26/08 -0400, Michael Traynor wrote: >And if only you'd posted about these before 9/11, you'd have >something, but you didn't and there's no way now to check the >extent to which your later knowledge coloured your memory of >the dreams. Consider how unreliable eyewitnesses are when it >comes to demonstrable events and how suggestible eyewitnesses >are and you might understand the skepticism and maybe even >apply some of it to your own recollections. Mike: You are right! If I had posted my dreams on the seven consecutive days, (Sep 4 to Sep 10), before Sep 11, I would have made a much stronger case for something like precognition. However I did not realize the significance of the dreams until after 9-11, when it was too late to post them beforehand. But the point of telling of the dreams now is not to supply proof that will convince skeptics. Probably nothing but personal experience could do that. The point is to tell that I am convinced that at least one of the so-called impossible things considered paranormal does in fact exist. And if precognition does exist, the iron wall of denial has been breached. How many more claims of the paranormal are also true? (BTW, when I say things like this, I feel almost like a traitor to the cause. The skeptics' fight against the flood of irrationality and superstition is difficult enough as it is, even without those like myself going over to the other side.) But I experienced what I experienced, and I know what I experienced because I described the dreams in my dream journal on the mornings after they happened. I know the power of suggestion and wishful thinking. I realize the existence of human credulity and gullibility. If, before I experienced my own dreams, someone else had told me of similar precognitive dreams, I would have said he was either lying or unconsciously adjusting the dream memories to fit the later events, and called it a harmless fantasy. But in my case, I wrote of dreams of crashing planes, horrendous explosions, fire, smoke, and falling buildings on seven cunsecutive days before the event. I have computer files dated before Sep 11 '01 to prove this to myself, but it is still possible to change the dates of computer files, so this is no scientific proof either. (After all, extraordinary claims require extraordinary proof.) The main point of all this is that after 9-11, I became very interested in occultism and the paranormal. I read every serious book I could find, and I am still doing so. I still consider most popular stuff like astrology and UFO aliens to be entertaining fantasies. But I found that there is a serious aspect to the paranormal, which I had previously been casting aside as foolish nonsense not worth wasting time on. I now wonder whether skeptics are doing us a service or a dis- service. Are they saving us from drowning in superstition or denying us a realization of greater realities beyond anyone's wildest fantasies. JIM (still skeptical of some things) M.

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FOTD 26-06-08 (A Higher Reality [8])
by Jim Muth 25 Jun '08

25 Jun '08

FOTD -- June 26, 2008 (Rating 8) Fractal visionaries and enthusiasts: My thoughts today are rambling, but here goes: Today's image introduces us to a higher fractal reality. Yes, I know that skeptics amd materialists grow uncomfortable when the subject turns to metaphysical philosophy, which they distrust. But I am fascinated by metaphysical things, particularly the things commonly known as paranormal, some of which I have discovered in recent years to be true. This interest in the paranormal goes back to the seven days immediately preceding 9-11-01, when I had seven consecutive precognitive dreams that changed me from a questioner to a believer, or more accurately, a knower.) The TV channels are filled with not-too-convincing shows about paranormal things such as Astrology, ghosts and fortune telling etc., but where are the shows about fractals -- things that do not exist in the normally accepted way, yet can still be object- ively pictured with the correct equipment? I can remember only one or two TV shows devoted entirely to fractals, and they were aired many years ago. Perhaps people are now more concerned with alien space ships and getting a message from the recently departed uncle George than with that dull mathematical stuff. Or maybe things are not so bad, and there actually are a few hard science channels that I have yet to hear of which actually program real rational science. Of course, if all the paranormal stuff is for real, which it very well might be, then it is the hard-core science channels that are behind the times when they try to explain everything in a common-sense rational way. Now back to the fractal at hand. I named today's image "A Higher Reality" in recognition of the higher realities that visionaries, including the fractal variety, sometimes experience, and also the fact that the minibrot in today's image is of an unusually high order. And yes, get those skeptical knees jerking in disbelief. By higher realities I do mean higher spiritual planes as depicted in occult lore. Today's image lies on the main spike of the parent fractal, which on the surface resembles a Mandelbrot set but deep inside has order-12 characteristics. It is located a short distance east of the large main-spike minibrot, which must be seen to be believed. With the DivideBrot2 formula, the order of the deep minibrots is the sum of the absolute values of the real and imaginary parts of the p1 parameter. I rated the image at an 8, since it's just about the best order-12 minibrot I have ever seen. The calculation time of 42 seconds is one of the briefest of all time. Of course, nothing could be briefer than the few seconds required to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the finished image there. Another near perfect day prevailed here at Fractal Central on Wednesday. I knew the day was near perfect when it earned the seal of approval of the fractal cats, who enjoy lots of sun and a temperature around 82F 28C. In my departmant the day was suitably busy. Tomorrow will not only likely be the same, but it will also bring another FOTD. Until then, take care, and I have found that it is indeed possible to enjoy rational science, which can demonstrate the truth of its statements, and at the same time know that some claims of the paranormal, which are scientifically impossible, are true nevertheless. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Higher_Reality { ; time=0:00:42.08-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot2 center-mag=-17.30747127039\ 474/0/9.789325e+011/1 params=2/-10/10/1500 float=y maxiter=5000 inside=0 logmap=139 symmetry=xaxis periodicity=10 mathtolerance=0.05/1 colors=0009FWAFYBGZCH_DI`EIbFJcGKdHLeILgJLiKLkKLmN\ KoQJpSIpVHqXGp_GpaLpdQqgVqi_sldsnitqnusszvxzxzzszz\ zzzzzzzzzbzzZzzVxzRszNszIszEszAsz6sz2sz9szGszNoPUn\ U`m_gldnkiujnhp`WvNIz7Jz9KyALvBMrCNoDOlFPhGQeHRbIS\ ZJTWLUTMVPNWMOWJPWJPXJQXJQXIRXIRYISYISYHSZHTZHTZHU\ ZGU_GU_GVaEY_GV`FW`FW`FW`FXaEXaEYaEYzzzzzzzzzzzzzz\ zzyzwtytrwqpuomsmkqlhojflicig`ffZcdX`cUZaTYZQYXNXX\ KXVIWVGUTESSDQQBOP8OQ6RTCTW9W_9YbE_cJfbIgbHlaGsB08\ C09D0AD0AE0BE0BF0CG0DG0DH0EH0EI0FJ0FJ0GK0HK0HL0IM0\ IM0JN0JN0KO0LP0LP0MQ0MQ0NR0OS0OS0PT0PTEQUGQVLRVQSW\ VXW_aXdfYikYnoZsszxWzzWzzXzzXzzYzzYzzszzszzszzszzs\ zzszzszzszzszzszzszzszzszzszzszzszzdzzdzzczzczzbzz\ bzzazzazz`zz`zz_zz_zzZzzZzzYzzYzzGzzGzzHzzHzzHzzIz\ zIzzJzzJzzJzzKzzKzzLzzLzzLzzMyzMxzNwzNvzNuzOszOqzP\ ozPmzPkzQizQgzRezRczRazS_zSYzTWzT`z7Yz9UzBRzDOzFLz\ HHzJEzLBzN8zP5zR6zT7zU8zV } frm:DivideBrot2 { ; Jim Muth z=0, c=pixel, aa=real(p1), bb=imag(p1), dd=real(p2), ff=imag(p2)+100: z=z^aa/(z^bb+dd)+c |z| < ff } END PARAMETER FILE=========================================

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