April 2004 - Fractint - mailman.xmission.com

More Mandelbrot sets????
by Raymond Filiatreault 07 May '04

07 May '04

I don't know if this is the proper forum to ask my questions. If not, may someone be kind enough to give me proper directions. Fractals have been one of my numerous hobbies for several years. Another one of my hobbies is programming. Lately, while programming another one of those zillion fractal generators (in assembly as a challenge and by curiosity), I accidently stumbled on two "fundamentally" different simple formulas which produced the exact same fractal!!! In addition, that fractal is a replica of the Mandlebrot set in approx. a quarter of its size and shifted approx. +2 on the X axis. The Julia sets are also replicas, similarly reduced in size and shifted. My questions are: 1) Have different formulas producing the same fractal been reported in the past? 2) Are there currently known formulas, other than the z^2+c, producing a replica of the Mandelbrot set? In other words, am I re-inventing the wheel? Raymond _________________________________________________________________ MSN Premium: Up to 11 personalized e-mail addresses and 2 months FREE* http://join.msn.com/?pgmarket=en-ca&page=byoa/prem&xAPID=1994&DI=1034&SU=ht…

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FOTD 29-04-04 (Beyond the Limit [5])
by Jim Muth 05 May '04

05 May '04

FOTD -- April 29, 2004 (Rating 5) Fractal visionaries and enthusiasts: Today's image has been named "Beyond the Limit". But don't succumb to skeptic's panic. We are not headed into the supernatural. Since fractals have no limit of their own, the limit mentioned in the name is the resolution limit of the math routine used by the program to generate the image. The diagonal smearing visible in the image is the first sign of resolution breakdown. I needed to include the mathtolerance entry in the parameter file to be sure that the image is drawn at the correct magnitude on all machines at all screen resolutions. When this is done, we find ourselves with a rather pleasant star-like image, which, if it were not afflicted with resolution breakdown, would rate a 7. As it is, I can rate the image no higher than a 5. The render time of 6 minutes makes the overall value an 82. Don't even think of checking the midget at the center of the image. Nothing but colored splotches are down there. The midget needs a few more magnitudes of resolution before it will reveal itself. The best way of viewing the image is to download it from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and then step back a bit from the screen to where the impending breakdown is not visible. A sunny but chilly day here at Fractal Central on Wednesday was marginally satisfactory for the cat duo, who would have preferred a temperature of 70F 21C rather than the 59F 15C that actually prevailed. Today is starting equally sunny and notably warmer. The two ex-tomcats should be happy. For me it's just another routine day of too much work and too little play. But the work *will* be finished, and 24 hours from now the next FOTD fractal *will* appear. Until then, take care, and we don't even know what we don't know. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Beyond_the_Limit { ; time=0:06:07.62--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+3.429528921055553/+0.2562473412832469/\ 1.909924e+012 params=1/-1.5/0.01/-150/0/0 float=y maxiter=1200 inside=0 logmap=135 periodicity=10 mathtolerance=/1 colors=000N5CN8IMANMCVLFYLHdKJiKM\ qJOvJQzDSw7UvFZkMc`ThQ_zFzq5ki4ob4tW3xP3sRAnTHiVNe\ XU`Z_W`fSal`g`XUYTGVQ3ST9YWFbZKgaQldVqedczmRfzEzlJ\ hbNiTRiJVgKReLOcMLaMH_NEYOBXO8YPBYQEZRHZRK_SN_TQ`T\ T`UW`VZaVaaWdbXgbXjcYmcZpcZsWaqPdoIgmBil6OC9QEBSGE\ TIGVKIXLLYNN_PQaRSbTUdUXfWZgYai_ckaelbdjecigbgiafk\ `en_cpZbrZatXZrVWqTTpRQnPNmNKlLHkJEiHBhF8gD5fLLiS`\ kRbiRdhRefQgeQhcQjbQkaqhcskZunUwqPytKzwFozKdzPVzUU\ zWUzXUzYUzZUz`UzaUzbUzcUzeUzfUzgUzhUzjUzkUzlUzm`zr\ fzwmzhtzUzzFwzJtzNqzRozVlzZizbfzfdzjaznZzrWzvUzyWz\ vXztZzr_zpazmbzkcziezgfzehzbiz`kzZlzXmzVYz`Ize2zj6\ zf9zcDz`GzYKzVNzSRzPUzLYzI`zFdzCgz9kz6nz3qz0sz9uzH\ vzPxzXyzdyzVyzLyzCuzBqzBmzAjzAfz9bz9Zz8Wz8Sz7Oz7Lz\ 7Oz9RzBUzDWzFZzHazJczL`zOZzQWzSUzURzWPzYMz`KzbHzdF\ zfCzhAzj8zlAzfBzaCzXEzSFzNGzIHzDSzMazUZzTWzSTzSPzW\ MzZJzaGzdDzgAzj7zm4zp7zk9zgszzhzeZzLPz1Oz7 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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POV-Ray Fractal Raytracing Contest
by Paul N. Lee 30 Apr '04

30 Apr '04

Greetings, The following is a very interesting posting taken from the Usenet Newsgroups, and is well worth a visit to the specified site: _______________________________________________________________________ The final results of the POVRay Fractal Raytracing Contest have been announced, point your browsers towards the final presentation page. http://astronomy.swin.edu.au/~pbourke/povray/povfrac/final/ _______________________________________________________________________ Sincerely, P.N.L. ------------------------------------------------- http://home.att.net/~Paul.N.Lee/PNL_Fractals.html http://www.Nahee.com/Fractals/

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FOTD 30-04-04 (Gossamer Glory [5])
by Jim Muth 30 Apr '04

30 Apr '04

FOTD -- April 30, 2004 (Rating 5) Fractal visionaries and enthusiasts: There are some days when I just can't think of anything signifi- cant to mention about the day's fractal. Today is one of those days. My mind is a total blank. Normally my mind is just plain blank, but today the blank is total. Even the e-mail informing me that I have won the New Zealand Lottery had no effect. In fact, it actually caused me a bit of concern, since I cannot find the winning ticket, and I have forgotten where I purchased it. Oh well, at least I'll still be able to afford fractals. They are free. Unable to find any really good or bad features in the image for today, I rated it at an average 5. I don't recall why I chose the name "Gossamer Glory". It has a rather pleasant sound to it, though the image is not really all that delicate appearing. The parent fractal was created by combining portions of Z^(-1.95) and Z^(-5.91), then adding (1/C). The resulting fractal is an oversized thing consisting of the typical indescribable main bay filled with debris, with a much smaller satellite Mandeloid lying very near the eastern edge. Today's scene is located on a filament in the area between the satellite Mandeloid and the main debris-filled bay. The image contrasts broad flat areas with areas of intricate fractal detail, all of which surround a typical central midget. The render time of the included parameter file is a speedy 2 minutes. This bargain price raises the overall value of the image to 241. The image may also be seen by downloading it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A very pleasant sunny day on Thursday, with a temperature of 77F 25C made the fractal cats very happy. They passed the after- noon under the holly trees, checking the little mounds that the cicadas are building up as they get ready to emerge. In the evening the duo came inside without urging and settled to sleep peacefully. I have about three hours work to finish before I return to fractal land to find the next FOTD, which will appear in 24 hours. Until then, take care, and see the light. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Gossamer_Glory { ; time=0:01:10.42--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+1.69671384233176200/+0.032306360356109\ 19/1040471/1/-82.5/-1.65398982704401121e-009 params=1/-1.95/0.33/-5.91/0/0/0/0 float=y maxiter=1000 inside=0 logmap=37 periodicity=10 colors=000000000000000000000000VszmmzaTtdTvhTxkTzc\ SkURYURK_UMaWOcZPe`RgcSieUjhVljXnmYpo_rr`ttbuvcrud\ otdmsdjsdgrdeqdbpe_peYoeVneSmeQmeSnfTnfUnfVofXofYo\ gZpg_pgapgbqgcqhdqhfrhgrhhrhirhftjcuk`vlYxmVynSzoU\ wnWtmXqlZnk_kjahibehdbhf_ggXfiUejRdlOcmLboIapFalRW\ haQdmKaxEbvGbuHcsJcrKdpMdoNemPelQfkSfiTghVgfWheYhc\ Zib`iaahb`gb`gc`fc`fd`ed`ee`de`df`cf`cg`bg`bh`ah`a\ h`_ccYcfXciVclTcoScrQcuPcwNcrLcnJcjHceGcaEcYCcUAcP\ 8cL7cH5cC3c81d40f01h42i83jC3kF4mJ5mN5mQ6mU7mY7m`8m\ d9mh9mkAmoBmsBmvRhXec8ccBPcLBcVHcONcITcBZc5XcFWcOV\ cXUcfTcoScxQcqOckMceLc_JcUHcOFcIEcCGdDHeEIfEJgFKhF\ LiGMjGOkHPlIQmIRnJSoJTpKUqKXrV_sebtpduzavy_wyYxyWy\ yTzxRzxPzxNzxKzwIzwGzwEzwCzwPzqazknzezz_szalzbezcZ\ zdSzeQzdOzcMzbLzbJzaHz`Gz`Ez_CzZBzZ9zY7zX6zX5zZ5z`\ 5zb4zc4ze4zg4zh6ze8zcAzaBz_DzYFzVHzTIzRKzPMzNNzLQz\ JhzWdzcbzX`zR_zLYzEWz8Vz2 } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Xfractint questions
by J Kotta 29 Apr '04

29 Apr '04

1. In the various file selection screens (e.g. loading par files), I can't get to other directories. There's no '..' like in DOS fractint, or any subdirectories. I could live with this except for... 2. How do you set default paths? I have a directory for pars, one for frms, etc. Xfractint seems to only look in the directory that I start it from. 3. This par was posted to the list about a month ago by SherLock Merfy; I finally tried to render it today. It starts out fine, but fractint eventually hangs and I have to kill it. Out_Of_Orbit {; Animation. Border tracing _treats_ periodicity, ; too. How would you check if the white line is dithered? ; Default map is too sticky in FRACTINT. reset=2003 type=mandel passes=b periodicity=-11 showorbit=yes center-mag=-0.765332/6.66134e-016/0.7772216/1.4732/90/3.88578058618804\ 789e-016 params=0/0 float=y maxiter=255 fillcolor=1 sound=beep colors=000<4>00000000zzz0000<4>000z000zzz0zzz00zzz0zyy00yyy0yxx00xxx0x\ ww00www0www00www0wvv00vvv0vuu00uuu0utt00ttt0tss00sss0sss00sss0srr00rrr\ 0rqq00qqq0qpp00ppp0poo00ooo0ooo00ooo0onn00nnn0nmm00mmm0mll00lll0lll00k\ kk0kkk00kkk0kjj00jjj0jii00iii0ihh00hhh0hhh00hhg0ggg00ggg0gff00fff0fee0\ 0eee0edd00ddd0ddd00ddc0ccc00ccc0cbb00bbb0baa00aaa0aaa00```0```00``_0__\ _00___0_ZZ00ZZZ0ZYY00YYY0YYY00XXX0XXX00XXX0XWW00WWW0WVV00VVV0VUU00UUU0\ UUU00TTT0TTT00TTT0TSS00SSS0SRR00RRR0RQQ00QQQ0QQQ00QQP0PPP00PPP0POO00OO\ O0ONN00NNN0NNN00MMM0MMM00MML0LLL00LLL0LKK00KKK0KJJ00JJJ0JJJ00III0III00\ IIH0HHH00HHH0HGG00GGG0GFF00FFF0FFF00EEE0EEE00EED0DDD00DDD0DCC00CCC0CCC\ 00BBB0BBB00BBA0AAA00AA909990099909880088808880077707770077606660066606\ 550055505440044404440033303330033202220022202110011101000 } Thanks, JK

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Time and again
by darryl＠itworks.com 28 Apr '04

28 Apr '04

Jim Muth wrote: "There is something strange about time." Truer words are rarely written. This has long been one of the little idiosyncrasies that I use to describe The Human Condition ... we can easily conceive eternity in one direction only: forward. The human mind can grasp the concept of a line with no end, whether that line is time, space, or whatever. A line with no beginning is a different kettle o' fish. It's my contention that we cannot grok the concept. Oh, we can describe it, and tell ourselves that it exists, but in our minds, when we try to "see" it, our brains won't let us. It always starts somewhere, even if the starting point is in motion. The most common thing people do is to say that they are the same; I look forward and there is no end, I look back and there is no end. In that case the starting point is the point of view of the observer. Try as we might, we must, as humans, always start somewhere. We just don't end anywhere :)

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FOTD 28-04-04 (Fractoid [6])
by Jim Muth 28 Apr '04

28 Apr '04

FOTD -- April 28, 2004 (Rating 6) Fractal visionaries and enthusiasts: I have before me the May '04 issue of 'Scientific American' magazine, which arrived in the mail yesterday. This magazine features articles of scientific interest that have been watered down and stripped of most mathematics so that they can be understood by the average educated person. The cover story is titled 'The Time Before Time', and proposes that time did not start with the so-called 'big bang', but might stretch backward forever into the past. If this is so, then time will never end. If an end to time were possible, it would already have happened, and we would not be here wondering about the start and end of time. There is something strange about time. In a way it is even more strange than space. To imagine a limit to time is as impossible as imagining it going on forever. I suspect that something is wrong with the questions we ask about time. Perhaps, instead of wondering whether time is limited or limitless, we should be wondering whether time is truly as objective as we assume. Our universe is four-dimensional. We know this. But why do we perceive one of the dimensions in such a different way? I have no answers, only ideas without proof, which some will agree with and others disagree with. But one thing certain is that the task of rendering of today's image has a very short extent in the space-time dimension -- 12-million miles to be almost exact. This distance seems long only because we compare it to our immediate surroundings. When compared to the size of our galaxy, 12-million miles is like an atom in a baseball. I could rate today's image no higher than a 6. It is more a demonstration of the outside=real option than a fractal discovery. The parent fractal is an indescribable thing created by combining Z^(-2) with Z^(-4) and adding (1/C). Today's image lies on a filament at the northwest edge of this parent. I named the image "Fractoid" a nonsense word that has a nice sound to it. perhaps the best feature of the image is its very short render time of one minute, which raises to overall value to a huge 566. This value will not be lost if the image is downloaded from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tuesday was fair enough here at Fractal Central. The cats did not notice the blue skies and puffy white clouds, though they did enjoy the sun and temperature of 66F 19C. A rain squall arose in the evening, but by then the duo was safely indoors. Today is starting sunny but chilly. For me the day is starting with work to be done. Only then can I tackle the world of fractals. Until next time, take care, and never forget that FOTD accuracy is not guaranteed. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractoid { ; time=0:01:04.10--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-2.10780498607015700/+0.387334621764656\ 80/3984544/1/-145/5.90356517361084743e-006 params=1/-2/0.5/-4/0/0 float=y maxiter=300 inside=0 outside=real periodicity=10 colors=000UM8zQ9zUAzYCzaDzeEwaHuYKrUMpRPmNRkJUiGWk\ KZlN`nQboUdqXgr_isckufmvipxmryptzsvvpusmupkumhujfu\ fcucau`ZuYWtVUtRRtOPtLMtIKtFHtCFtFIpILlKOiNQePTaSW\ ZUYVX`R_cOafKdhGfkDin9kp6gm9dkB`hDYfFVcHRaKOZMKXOH\ UQESSHRVJQXLPZNO`QNcSMeULgWLiXPfYSdZVb_Z`_aY`dWahU\ bkSbmQVmLNmGGmB8m61m1KmDbmPtm_om`kn`gp`cr`ZtaVvaRx\ aNwaKwSIwIGw8EwACwBBwC9wD7wE6wF7wG7wH8wH8wI9wI9wJ9\ wKAwKAwLBwLBwMBwMEwJHwGJwILwKNwMPwORwQTwRVuTWsVYqX\ _oZan_coaepcgreisgjthkrglqgmofnnfolepkeqidrhdsfcte\ cucbvbbw`ax_ayY`yX`rZck`edbhYdjRelSfjSfhTgfTgdUgbU\ h`VhZViXWhVWgTXfRXePXdO_cVbc`dcfbcd`cbZc`Xc_VcYTcW\ ScVQcTOcRMcQKcOIcMHcLLcKOcJRcIVcIYcH`cGccFgcFjcEmc\ DpcDgcHZcKRcNIcR9bU1eX3eW5eW7eV9eVBeVDeUFeUGeUFdRE\ dPDdNDdKCcIBcGAcDAcB9b98b67b47b28d49e5Af6Bg8Bh9CiA\ DjBEkDFlEFmFGnHHoIIpJIqKJhOK`SLaWMb_NccOcgQceRcdTc\ bUc`_cJXcHVcFScCQcANc8Lc6 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] Monitor display question
by PCMASPEC＠cs.com 28 Apr '04

28 Apr '04

Paul, Thanks for your suggestions. I'll see what I can do with them. When I did a search for "Fractint" in CompuServe, I got a home page for Fractint that told me to download 20.0 as the newest version. I was pretty skeptical because I've had 20.0 since it was new. I downloaded my first Fractint well over ten years ago, but I have used it very little in recent years. I've had my XP machine for almost a year and hadn't discovered the problem until today. I appreciate the help. Dick Teeter

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FOTD 27-04-04 (Iterative Hyperbolae [8])
by Jim Muth 27 Apr '04

27 Apr '04

FOTD -- April 27, 2004 (Rating 8) Fractal visionaries and enthusiasts: With today's image we return to the image quality that makes fractals worth the effort. The rating of an 8 is the highest in some time. Hopefully, this is a sign of things to come. To create the parent fractal, I mixed together Z^(-1.77) and Z^(-7.71), added (1/C) and let the mixture iterate for 1200 cycles. The resulting fractal is beyond description, an oversized thing consisting of numerous bays, valleys, long looping filaments, scattered bits and pieces, a curious almost- midget, as well as assorted other items of interest. The east side of the main bay is decorated with a prominent valley, which at first glance might be taken to be an East Valley. From the center of this valley extends a zig-zag filament strung with dewdrop-like nodes. Today's scene lies rather deep in one of these nodes. Surprisingly, the area has almost none of the typical 'East Valley' features. The standard equal-iteration-band rendering gives a good-enough image, but the evaporated version of the scene is better. It is this evaporated version that I used as today's FOTD. I made the totally-inside material visible by using the bof61 inside fill. Other fills might work equally well, but I have not yet tried any of them. When searching for a name, I noticed the hyperbolic elements and named the image "Iterative Hyperbolae". When figured into the 6-minute render time, the rating of an 8 gives an overall value of 135. What the overall value might be when the image is downloaded is up to the individual to decide. The download is available at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Rain fell all day here at Fractal Central on Monday, while the temperature reached only 59F 15C. The cats did not approve and showed their disapproval by flipping into their sulking modes. A treat of tuna in the evening helped a bit, but a dish of fish cannot make up for a missed afternoon in the yard. Today looks somewhat better, so we'll see how it goes. For me it's a day of work before fun. Until next FOTD fractal, take care, and be at ease. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ IterativeHyperbole { ; time=0:05:55.50--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+2.40024400180910400/-0.000531620471100\ 73/3.385291e+010/1/15/0.000876059279207246078 params=1/-1.77/0.23/-7.71/0/1e+100 float=y maxiter=1200 inside=bof61 periodicity=10 colors=0000V`0b_0jY0rW0mQ0iL7dGC_BIW5OS2qty`nfLjP`\ `YqTdzLmzGdzCYz7Pz3Hz0Az03zD2zY2yq2uiFq`QmTciLpfDz\ iKwkQqnYkqcfti`pfZmcYj`WgZVdWTbTS_QQYOP_WS`bTbiVcp\ WdwYfzZLg0Wj0dk0nn0xp0zq0zjTudutgwtixrkyrmzqnzqqzp\ rzptznpynmumjpmgkkdgkbbj_ZjYVzW`zVgrVnjVubVzWVzTSt\ QPfPMTMKGLH3GCIB7Z52n00zceC3OI0OF0OB0M80LD3LHADMGB\ QOAWV8_`5cg4ip3mw0rz0wz0zz0yu0ym0rf0uZ2rS2qK3mD3mC\ 7mBBnAFo8IpAMqFPsKTuPYwU`xZdycgzhkzmpzrtzrzzrzzrzz\ muzhrzcpzZmzUjzPgzKfyFcxH`xIZwLWuOTuPQtSOrTMrTItTF\ tTAtT5uT2uT0uP5qMDmKKiHSdD_`OYzPVzPTuPSpPQkPPfPO`P\ MYTOVWOSZPP`PMcPKtYbzdtzfpzgkzigzjdzk`zmYzmVgZ`PKg\ 75n00tSTjzzbzxWwqPrkKndDjZ7fT2gV0gW0iW0iY0jZ0jZ0k_\ 0k_0fT7bMDZGKTAQP3YL0cH0jO0dV0``2Yf4Tm8OtBKzFGzHCr\ Y7fk2Vz0Tt5SmFQfMP_WPVcMPVKLMIGDGC5F80PAD_BSjCftDu\ pFqmGmjHigHdcI``KYZLTWLQPOWKQ_DTd8Wi2Zn0`r0cwitCfq\ GdpKcnObmS80m50j35g0Dd0Lc } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 26-04-04 (Sir Fractal [7])
by Jim Muth 27 Apr '04

27 Apr '04

FOTD -- April 26, 2004 (Rating 7) Fractal visionaries and enthusiasts: Today's image lies in an immense parent fractal that is too large to display in its entirety, and in fact might be infinite in its large as well as its small aspect. This huge parent was created by combining Z^(-1.25) with 0.24 as much Z^(-5.21) and adding (1/C). The location of today's scene at -11519.6 on the X-axis and -6756.86 on the Y-axis shows that we have wandered far from the familiar home grounds around the origin of the parent, into the dark mysterious outer reaches of Fractal Land, beyond which lies the unknown. Even way out here, we find the same scattering of midget copies of the Mandelbrot set. Apparently, Fractal Land is like the Physical Universe -- the general laws are the same in all its parts, no matter how distant those parts might be. This does not mean that the laws of Fractal Land are the same as the laws of the universe. There is no cosmic speed limit that corre- sponds to the velocity of light -- at least none that I am aware of. But there does appear to be something similar to gravity, which appears when two midgets approach to within a certain distance, and can be visibly seen stretching toward each other. Fractal Land is eternal. It does not change with time unless we ourselves make a series of separate images and join them into a single animation. But even here, it is we who have created the illusion of motion by joining in our minds a series of separate images into a single moving object. The situation is similar with the physical universe. We are told that there exists in physical reality a shortest possible length of time known as the Planck time, which is 10^-43 of a second. If this is true, then all the motion we think we see around us is an illusion of our own creation. Nothing is moving, we are merely observing a sequential series of eternally frozen three-dimensional universes and merging them in our minds into a single dynamic three-dimensional universe that changes in a time that we ourselves are creating. Our intellect has reached a stage where we are beginning to recognize the illusory nature of what we have long taken as the one external reality. Objective and subjective are no longer absolute. It appears that once we develop the long-sought-for 'theory of everything', the question will then become 'what is having the illusion?' And I would not be at all surprised if we were to discover that the universe, and ourselves as well, are merely intricately detailed fractals. Well, I appear to have gotten distracted from the business at hand, which is the FOTD. I have named the image "Sir Fractal" because in my opinion it has a certain solidness about it -- a nobility that would be expected of knights. I rated the image at a 7. This is an improvement over the recent images, which have not been the greatest. Combined with the render time of 6-1/2 minutes, the overall value rates a 107. Those who lack the time to render the image from the included parameter file may download the completed image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunday remained cloudy and chilly here at Fractal Central, with a temperature that never rose above 64F 18C. Luckily the rain held off and the cats had a pleasant but slightly cool afternoon in the yard. But this morning is proving damp and foggy, with occasional light rain. It remains to be seen how the dynamic duo will react. What I'm going to do is the work that needs to be done. And when I finish, I'll take a trip to Fractal Land to worry about that great illusion. What I find there will appear as the next FOTD. So until tomorrow, take care, and see you soon. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Sir_Fractal { ; time=0:06:32.66--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-11519.6/-6756.86/0.02217445/1/-12.5/\ 4.329384e-013 params=1/-1.25/0.24/-5.21/0/0 float=y maxiter=1200 inside=0 logmap=106 periodicity=0 colors=000ZZF__G``HaaIbbJccLddMeeNffOggPhhQiiSjjTk\ kUllVmmWnnXooVppUqqSqrRqsPqsOqsMqsLqsJqsIqsHqrFqrE\ qrCqrBqp9qn8ql6rj5rh3rf2rd1sb2t`2uZ3wX3xU4yP4zK4wF\ 3t93qA3nA3kB2hC2fC2cD2`E2YE1VF1SG1QG1NH1KI0HI0EJ0B\ K09K0EP7JUEOYLTbSXfZShUOjPKlKGmGKfJN`MQVPTPSWJVZDY\ a7``6d_6gZ5jY5mX5qW4tV4wV4zT6xS7vQ8tP9rNAqMBoLCmJD\ kIEjGFhFGfEHdCIcBJa9K_8LY7MX9NWANVBNUCNTEOSFORGOQH\ OPHSNHVLHYJH`HHcFHfDHiBHl9Ho7Hr5Hu3Hx2Ju3Ks4Lp5Mn6\ Ok7Pi7Qf8Rd9TaAU_BVXBWVCYSDZQE_NF`LFbIGcGHdDIeBJf9\ Je9Jd9Jc9Jb9J`9J_9JZAIYAIXAIVAIUAITAISAIRAIOFGLJFI\ NEGSDDWCA_A8d95h82l70p68pEGpMOpUWpabpidmgekeficgga\ _h`Sh_LiZDiY6iXBeUFbSK_QOXNTULXQJaNHeKEjHCnEArB8tX\ 6uV9vTCwRFxPIyNKzLNzJQzHTzFWzDYzB`z9cz7fz5hzUnzUoz\ UozUqzUszUuzWwzUxzWyzYzz_zzazzczzczzczzczzczzczzcz\ zczzczzczzczzczzczzczzczzczzczzczzczzczzczzczzczzc\ zzczzczzczzczzczzczzczzcz } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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