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FOTD 26-09-02 (Eight or Sixteen [6])
by Jim Muth 26 Sep '02

26 Sep '02

FOTD -- September 26, 2002 (Rating 6) Fractal visionaries and enthusiasts: There must be a name for someone as obsessed with fractal midgets as I am, but if there is, I have yet to find it. Today's image features yet another midget. The little thing might be too small to be visible, but be assured, it is there at the center, waiting for revelation, though looking little better when seen in person than it does at this distance. The formula behind the image combines portions of Z^(-0.414213562373) and Z^(-2.414213562373). These two numbers are reciprocal to each other, and even more curious, the decimal parts of these numbers are equal to the decimal part of the square root of 2. This curious coincidence might have a deeper mathematical meaning, or it might not. In any case, the coincidence has little effect on the appearance of the fractal the numbers generate. The parent fractal resembles a first-quarter moon, (last-quarter in the southern hemisphere), with today's scene lying in some rather unique appearing material on the northern terminator of the moon. For unknown reasons I named the image "Eight-or-Sixteen". Because it is only a bit above average, I rated it a 6. Because the 7-minute render time is a bit slow, it might be more convenient to download the pre-rendered GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> and thereby save a few minutes. The fractal weather Wednesday featured increasingly thick clouds as the moisture from a tropical storm drifted this way. But the temperature was a comfortable 75F 24C, and all else was under control, giving the fractal cats a pleasant day, actually romp- ing in the yard. When their fun was done, the dynamic duo had an enjoyable treat of tuna. All-in-all they had one of their all-time best days. I hope their mood is just as congenial this week-end when I try to take up-to-date photographs of them for the soon-to-appear FOTD CD. As for me, my day will be the best only when I get the work done. And if I hope to do that, I've got to get started. So until next FOTD, which will appear on schedule on Saturday the 28th, take care, and solve the mysteries. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Eight_or_Sixteen { ; time=0:07:13.37--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.73830742505459010/+4.543148571881168\ 00/7.456448e+008/1/-60/-8.19321895876440331e-005 params=1/-0.414213562373/3/-2.414213562373/0/525 float=y maxiter=1000 inside=0 logmap=134 colors=0000QS0Qh1Qx3Qm1QzLQzLQzLQzFUzLQzPUzLQzVUzV\ QzbRzaFzeBzfFzfBza8z`3xY0sZ0nL0nY0aD1fD6QDBLDFF3J9\ 0M30N33P3BQ3RS3VS3ZU3aW3iY3l_3sa3xa3ve3ze3zf3zh8zj\ BzjFzlJznNxnPuoSsqWoq_nscjufhuhesccqYaoSYoNWnHUlBQ\ l6Pj0Nh0Lh0Pe0Sc0Wa0__0cW0fU0jS0nQ0qN0uL0xJ1zH6zF9\ zDDzDFzDHzBJz9Lz8Nx6Pw3Qw8QwBQwFPwJPxNPxQNxSNxWNx_\ LzcLzfLzjJznJzqJzsJxzLczYHzjDzHBz06z01z00z00z10z60\ z90sD0lF0fJ0_L0UP0NQ0HU09W03_00a00c00h90nN6sY9wjFz\ uJzzPzzSzzNzzHzzDwz8qz1jz0ez0Yz0Sz0Wu0_n1af6e_9fSF\ jLJnDNo6Qs0Uu80Q90S90UB0UB0WB0WD0YD0YF0_F0_F0aH0aH\ 0cH0cW9ahQ_wfYzwWzzUzzSzzQzzPzzNzzLzzJzzHzzFxzDwzB\ sz9qz8oz6lz3jz1hz0ez0az0_z0Wz0Uz0Qz0Nz0Lz0Hz0Fz0Bz\ 08z06z01z00z03z06z19z3Bz6Fz8Hz9JzBNzFPzHSzJUzLYzN_\ zPazQ_zSYzUWzWUzYSz_QzaPzcNzeLzfJzhHzjFzlDznPzaSzQ\ WzWWzWak8ak9clDcmFelJejLfgPfeQfcSjrjliznez7mShnnRh\ _coL_f6Yh0We0Jl06g00p00hg } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 24-09-02 (The Emerald City [7])
by Jim Muth 24 Sep '02

24 Sep '02

FOTD -- September 24, 2002 (Rating 7) Fractal visionaries and enthusiasts: Today's image is named "The Emerald City". The name has nothing to do with the name of the city in the land of Oz, where the wizard dwells. The image contains nothing even vaguely resembling buildings. The name simply reflects a feeling that the image produced while I was studying it, searching for a name. At first glance, the image appears to have been rendered with some exotic coloring algorithm, but it was actually rendered with the default equal-iteration-bands method. As in nearly all my FOTD fractals, the fancy coloring is created by the nature of the iterated formula, which in today's case adds portions of Z^(-1.1) and Z^(1.1) to (1/C). The resulting parent fractal does not quite fit onto the default screen, but an outzoom reveals a fractal rocket flying east. Today's image lies in the chaos at the north edge of the rocket's fins, in an area that is highly sensitive to changes in the bailout radius, which is determined by adding 100 to the imag(p3) parameter. I have rated the image at a 7. I can do this honestly, since the overall effect is above the average. The render time of 7 minutes can be bypassed by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The Monday weather here at Fractal Central took on a more autumnal mood, with partly cloudy skies, brisk northerly breezes, and a temperature of 75F 24C. The fractal duo, Thomas and Tippy, must have agreed, for they passed the entire afternoon exploring the yard, every inch of which has been explored many times before. The only problem arose when Thomas came hopping to the door with a thorn in his right forefoot. A single pull of the tweezers removed the thorn and relieved his not-very-serious distress. My distress will be relieved when the day's work is finished and my desk is clear. That moment however is several hours away, and some intense effort will be required to achieve the goal. Until next time, which will arrive on Thursday the 26th, take care, and is it rational to believe in extra-sensory fractals? Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ The_Emerald_City { ; time=0:00:00.00--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.813599976005038/+1.08444716716314/16\ 37126/1/-97.5/-2.42503677833072473e-008 params=0.7\ /-1.1/0.77/1.1/0/40 float=y maxiter=750 inside=0 logmap=63 symmetry=none periodicity=10 colors=000YNCzPAzP8zTAzVCvXCsZEo`GkbGedHbeJZgJVkLR\ mNNoNHqPEsRAuR6vT2xV0zV0vZ0sb0od2mg2ii2em2dq4`s4Xv\ 4Vx4Rz6Nz6Lz6Hz6Ez8Cz88z84z82z20z00z00z00z00z00z66\ zGGsRPi`Z`igRsqHooGmmGikGgiGegEbgE`eEZdEVbET`CRZCN\ ZCLXCJVAGTAERACPA8PA6N84L80J80H80H80N60T40Z20`00b0\ 0d00e04g0Ai0Gk0Lk0Tm0Zo0dq0is0ou0uv0zx0zx0zz0xz0uz\ 0qz0mz0iz0ez0bz0Zz4Vz6Rz8NzCJzEGzHCzJ8zN4zP0zT0zV0\ zZ0z`0zb0zi0qo0bv0Nz08z00z20z44x6Aq8GiALbCRVEXLGbE\ Hg6Jm0Ls0Nx0Nz0Gz08zA0zR0ze0zd0zd0zd0vd2ud2sd4ob6m\ b6kb8ibAebAdbCb`EZ`EX`GV`HT`HP`JNZLLZLHZNGZPEZPCZR\ HVTLRVPNVTJXXGZ`CZd8`g4bk2do0ds0ev0gz0gz0iz0kz0kz0\ oz0qz0uz0vz0xz6zzCzzHzzPzzVzz`zzezzdzzdzzdzzbzzbzz\ bzz`zz`zz`zzZzzZzzZzzXzzXzzXzzVzzVzzVzzTzzTzzTzzRz\ zRzzRzzNzzLzzJzzHzzGzzEvzCszAoz8kz6gz4dz0`z0Xz0Tz0\ Pz0Lz0Hz0Ez0Az06z02z06z08z0Cz0Ez0Hz0Jz0Nz0Pz0Tz0Vz\ 0Zz0`z0Pz0zzNzzLzzJzzGzzE } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 22-09-02 (Autumnal Equinox [6])
by Jim Muth 22 Sep '02

22 Sep '02

FOTD -- September 22, 2002 (Rating 6) Fractal visionaries and enthusiasts: The autumnal equinox is almost here, heralding the season of blue skies, colorful falling leaves, and acorns. The mystery is why the leaves, which are so enjoyable while they are on the trees, become so unenjoyable once they fall to the ground and have to be raked up and disposed of. The answer to that mystery may never be known, but the fact that eight colorful oak leaves appear in today's FOTD image cannot be denied. The formula that produced the leaves subtracts 1.3 parts of Z^0.9 from 1.3 parts of 1/Z, then adds 1/C, resulting in a scene on the verge of evaporation. Indeed, if the value of the imag(p3) parameter, which sets the bailout radius, is increased, the image soon breaks into scattered fractal debris, and then goes totally blank, changing into an evaporated all-inside image that can be seen only by using an inside fill something like bof61. Curiously, if imag(p3) is decreased, the image also goes blank, though in this case the image consists of flat outside material. The parent fractal of today's image consists of a very distorted Mandeloid with an open eye, perhaps the all-seeing eye of you-know-what, lying just to the right. The scene itself lies in a valley that is not really a valley, which separates the Mandeloid from the eye. I originally intended to rate today's image a 7, but upon re-viewing it after a restful night, I decided a 6 would be more appropriate. I named the image "Autumnal Equinox", and why not? The equinox is but a few hours away, and at least in the northern hemisphere, the leaves are starting to turn colors. The 20-minute render time drags, but as always, the completed GIF image is or soon will be available on the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather Saturday was partly cloudy and humid, with a temperature of 88F 31C. Showers threatened in the afternoon, but never moved in. The fractal cats, being intrepid, ignored the threat of rain, and had a pleasant afternoon in the yard, doing little but sitting and thinking. As for me, it's Sunday morning and all is well. If I simply relax and let nature have its way, things could remain well all day. The next FOTD will appear on Tuesday the 24th. Until then, take care, and don't lose your way in the valley of the lost fractals. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Autumnal_Equinox { ; time=0:20:20.72--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.07306512309502931/-0.035159792779246\ 05/9.071547e+007/1/5/-2.20061751078637347e-007 params=-1/0.9/1/-1/0.3/100 float=y maxiter=2500 inside=0 logmap=363 periodicity=10 colors=000nAIpA9rA1oD7lGCiJIfLNcOS`RYYTbVWhSZmQ`rT\ asVbsXct_dtaetcfuefuhgujhvlivojvqkwslwulwsltqlrolo\ mlmkljilhhlfflcdlablZ`lXZlUYlSWlQUlNSlLQlIOlGNlELi\ DKgDJdDIbDH_CGYCFVCETCDQCBOBALB9JB8GB7EB6BA59A46A3\ 4A22A35D48F5BH6DJ7GL8JN9LPAORBRTCTVDWXEZ_F`aGccHfe\ IhgJkiKnkLpmMsoNvqOxsLolIfeFYZCPS9GL68ECBFHDGMFGRH\ HWKI`MIeOJjQKoSKnUJnVJnWInXImZHm_Hm`GmaGmbFldFleEl\ fElgElhDkjDkkCklCkmBknBjpAjqAjr9js9jt9hoEfjIeeMcaQ\ bXU`SY_NaYJeXEiV9mU5qV7mW8jW9gXAdXCaYDZYEVZFSZHP_I\ M_JJ`KG`LDZMFYMHXNIWNKVOLTONSPORPQQQRPQTOQUMRWLRYK\ SZJS`ITaGTcFUdEUfDVgCViBVjAWiAYhAZh9`g9af9bfFYdKTc\ QOaKJKXIbZIc_IdaIeZIaaIefIhhIiiHjkHkmHlnHmpHnrHosH\ puHqvHruGpuGnuGmtGktGjtGhsGgsGesGcrGbrG`rG_rGYqGXq\ GVqGTpGSpGQpGPoGNoGMoGKoGJkOFgVBcU7_UZYUcXUhVUmUSt\ SNwRJzQFzSEzUDzVCzXCzYBz_Az`Azb9zc8ze7zf7zh6zi5zk5\ zl4zn3zo2zq2zr1zg9zi9zlAz } 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 20-09-02 (Red-Green-Blue [7])
by Jim Muth 20 Sep '02

20 Sep '02

FOTD -- September 20, 2002 (Rating 7) Fractal visionaries and enthusiasts: To produce today's image I took 1/10 part of 1/Z and subtracted 1-1/10 parts of Z^1.1 from it. The resulting fractal consists of two distorted Mandelbrot sets sitting side-by-side in the upper half of the screen. The two sets are distorted in different ways. The set on the left lacks a prominent period-2 bud, while the set on the right has its period-3 buds shifted almost into East Valley. There are mathematical reasons for these distortions, which are beyond the scope of this discussion, (meaning I don't know the reasons), but the inner details of the two sets are much the same as the familiar M-set. To find new and interesting types of midgets, one must get away from the familiar. Checking today's parent fractal, I noticed that a large quantity of fractal debris is scattered between the two large Mandeloids. Today's scene is located in this debris. I named the image Red-Green-Blue, since it has large quantities of these primary colors in it. The blue midget is surrounded by a reddish aura, which in turn is surrounded by a field of greenish stars against a black background. The whole thing could be worth a rating of 8, but, looking at the result, I get the impression that I tried too hard on the coloring. The actual rating of an above-average 7 seems just about right. The render time of 7 minutes is acceptable, though still a bit slow. As always, the completed GIF image will soon be available on the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> I am considering whether to resume posting the FOTD images and discussions to: <alt.binaries.pictures.fractals> I realize that posting to usenet is an invitation to spammers, but every spammer on earth must already have my address, and the most it can mean is a few more strikes of the delete key. Besides, my FOTD-CD will soon be ready, and I'll need to give it a little publicity. The weather Thursday here at Fractal Central was unnotable . . . except to the dynamic cats that is. The cloudy skies, tempera- ture of 79F 26C and the moderately high humidity were a bit too much for their comfort. They would have preferred drier air, more sun, and a temperature a few degrees cooler. But despite their discomfort, they managed to spend over an hour in the yard, watching the squirrels gathering nuts and remembering the days when they had the energy to actually chase and maybe even catch a squirrel. As for me, I definitely have the energy and the work to expend it on. But if I don't get started, I'll never finish. So until next FOTD, which will arrive in two days on Sunday the 22nd, take care, and don't have an out-of-fractal experience. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Red-Green-Blue { ; time=0:07:23.47--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.57333997680331930/+0.623010026257395\ 70/2.47078e+009/1/-67.5/-0.000842505711319684047 params=0.1/-1/-1.1/1.1/0/0 float=y maxiter=1000 inside=0 logmap=152 periodicity=10 colors=000Dj3Cg3Cc4BZ5BV5AR6AN69D703800800900900B0\ 0C00DN7FQ7GU7HX7J`7Kc7Lf8Sh9XkA_mBcpChrDluEqwFwtEs\ rDooCkmBhjAeh9be8Yc7P`6MZ5JMEZ9MmITpR_r_ethlvqsxzz\ zmiwbUuUXXQUcMRiIOoEMuFKsGIrHGqHEpICoJAmK8lK6kL4jM\ 2iM0hL2jK4kJ5mI7nH9oGAqFUzEUzDWzCHvBIwDGpEFiFDcGCX\ HAQ0000000000000003CX7BZBA`E9bI8dM7fP7hT6jX5la4of3\ sk2wo2zl8znDzgJmdOUZUNTZHQdAOi4MgCKeJIcRGaYE`dKWaQ\ RZWMXaHUgCRm8PkAMiCKgEIeGGcIEaJC_LAYN8WP6URUSTWQUY\ ST_ifalbcoZerVgoTilSkiQmfPocNqaMsZKtWJuTHvQGwNExLD\ yMFzMGzMHzMJzMKzMLzMMzNOzNPzNQzNSzNTzNUzNVzMazLgzK\ kzKizGdzHbzIazI`zJ_zKYzKXzLWzLVzMTzNSzNRzOQzPOzPNz\ QMzQLzTMzVMzXMzZMz`MzbMzdMz2qz3lz3gz3bz4Yz4Tz4Oz4J\ z7Kz9KzBKzDKzFKzHKzNLzTMzZNzcOziPzoQztQzrOzpNznLzl\ KzjIzhHzfFzdEzbCz`Bz_AzZDzZGzZJzYMzYPzYSzXVzXYzX_z\ W`zVazVazUbzTbzTczSczRdzRdzQezPezPfzOfzNgzNgzLezKd\ zJczIazH`zG_zFZzJUzMPzPLz } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] FOTD 18-09-02 (Difficult to Color [5])
by JimMuth＠aol.com 19 Sep '02

19 Sep '02

Deborah Schambe wrote: >Is your glass half empty or half full? >Apparently it's half empty, because you've already drunk the first half. >Wednesday + 2 = Friday. :) I goofed. It's the cats' fault!! Jim M.

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FOTD 18-09-02 (Difficult to Color [5])
by Jim Muth 19 Sep '02

19 Sep '02

FOTD -- September 18, 2002 (Rating 5) Fractal visionaries and enthusiasts: Today's image came on with much fanfare. When I saw it in thumb- nail size, I expected another 8-rater. But when the time came to apply the color, things did not go as planned. Try as I might, I could not get the colors to go onto the image smoothly. The reason is that the iteration count of the bands jumps around haphazardly, making smooth coloring almost impossible. In the end, I decided to let nature take its course and let the image appear in its natural form. To remind myself of the coloring problems, I named the image "Difficult to Color". The formula behind the image takes plain Z and adds 12 times as much 1/Z to it before adding 1/C. The resulting figure is a large fan-shaped bay edged by many tiny round mandel-shaped bays. Today's image is located in one of the arms of a many- pointed star associated with one of these small bays. The render time on my machine of 1/100 second short of one full hour is excessive for such a mediocre image, which I can rate no higher than a 5, but as always, relief is at hand at the FOTD web sites in the form of the completed image, which will soon be ready for download. The two FOTD web sites are located at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather here at Fractal Central on Tuesday was so close to perfect that the minor shortcomings can be ignored. The cats were happy, and that's all that really matters. For humans who might be curious, the temperature reached 82F 28C under partly sunny (or was it partly cloudy) skies. Another day has now begun -- one that promises to be a near repeat of yesterday. If all goes well, the cats will be happy again, and if the work goes well, I'll be happy. Until next time, which will arrive on Saturday the 20th, take care, and be liberally conservative with your fractals. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Difficult_to_Color { ; time=0:59:59.99--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.45800919027048830/+0.420562881994095\ 90/1.168692e+008/1/72.5/-8.86262575897078797e-008 params=1/1/12/-1/0/0 float=y maxiter=9000 inside=0 logmap=1360 periodicity=10 colors=000RNeSOfTPgUQhVRiVSjVTkVUlVVmVWnVXoVYpVZqW\ _rW`sUZqTYoSXmSWkSViSUgTSeTRcTQcTPcTOcTNcTLcSKcRJc\ QIcPHcPFcOEcNDeMCgLBiKAkJ8mI7mH6mG5lF4lF3lG6iH9gHC\ eIFcJIaJLZKOXLRVLUTMXRN_PNbMOeKPhIPkGQnEOo9QpCSqFU\ qIWrKYrN_sQasSctVetYgu`iubkvemvhowjqwmrwptxtrvsjkr\ zqvnkpnnoopootnotmnslmrklrjlqjkpijphioghnfgmegmefl\ dekcdkbcjabi`cjadkabi`_g_YeZVdXTbWQ`VOZULYSJWRGUQE\ SPAQNCRODSOESOFTPGTPHUPIUPKVQLVQMWQNXROXRPYRQYRSZS\ TZSU_SV_SW`TXaTYaT_bU`bUacUbcUcdVddVeeVgfXfeWfeVfd\ VfdUfcUfdTfdTeeSeeSefReeReeQedQedPdcPdcOdbOdbNdaNd\ aMd`Mc`Lc_Lc_KcZKcZJcYJcYIbXHbXHbWGbWGbVFbVFbUEaUE\ aSDaSDaQCaQCaPBaOB`NA_NAZM9YK9XJ8YJ8XI7VI7UH6TH6SG\ 5VG5_F4dF4cG5cH5ZI6YJ6YK7YL7XM7XN8XO8WP9WQ9WR9VSAV\ TAVTBVUBUVCUWCUXCVYDWZDX_EY`EZaE_bF`cFadGbeGcfFdgG\ ehHfiHgjIhkJilJjmKknKloLmpMnqMorNpsBqt6ru9svBtwEux\ GvyJwzLxzOyzQzzTzzVzzYzz_ } 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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Borland C 3.1 Compiler
by Newman Chakerian 19 Sep '02

19 Sep '02

I have managed to compile and run fractint using Borland C 3.1 IDE My problem is that I cannot step through the code. When I try to 'step into' I get a popup message saying: ' WARNING: no debug info. Run anyway ? ' If you select Yes it just runs the whole program. Thanks, Newman

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FOTD 14-09-02 (X Marks the Spot [8])
by Jim Muth 17 Sep '02

17 Sep '02

FOTD -- September 16, 2002 (Rating 8) Fractal visionaries and enthusiasts: The fractal for today is a winner, a little gem that honestly earns its immodest rating of 8. It was created with my little- used MandelbrotMix3 formula, which combines four different powers of Z but leaves finding a critical point up to the user. Luckily, I have another formula which finds the critical points graphically, so this is not too much of a problem. Today's image is partially evaporated, consisting as it does of 80 percent inside and 20 percent outside. The greatest surprise came when, trying different inside fills, I found that the < zmag > fill gives the most pleasing results. Normally, this fill results in too chaotic an effect, but in today's already- chaotic scene, it works to near perfection. The straight criss-crossing ridge-like areas that fill the background are most unusual. They appear to have been intro- duced artificially, but they are quite natural. A midget of sorts lies at the center of attention, where the most prominent ridges cross. The midget is not really all there, but its strange energy field is very much present, being revealed by the inside fill. Since the image is filled with X's, I named it "X Marks the Spot". One glance at the image will show that the rating of 8 is fully justified. The 37-minute render time however is a bit trying, but the wait can be eliminated by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather Sunday here at Fractal Central was cloudy and muggy with occasional showers of rain. The temperature of 79F 26C fell in the comfort range of the fractal cats, but the wet grass and drippy trees kept the dynamic duo confined to the indoors through most of the afternoon, where they expressed their dis- pleasure by making themselves obnoxious. It's cloudy again this morning, but with a forecast of a drying trend starting this afternoon, the cats should have a better day. My day will turn better once I have finished the work before me. Until next time, take care, and be careful around those dangerous fractals. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ X_Marks_the_Spot { ; time=0:37:57.10--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3 function=recip passes=1 center-mag=-0.3480403693685333/0/728.2051/1/180 params=1/-1.5/0.2/-2/0.15/2/2/0.6/2.11537091657/52\ 5 float=y maxiter=1200 inside=zmag symmetry=xaxis periodicity=10 colors=000QAGN6KK2NJDIJNEvrjkhlaZnS\ PpIFrMChMCkGFhAIe5Lc2kQzBApH8fN6XS5NY3Db2RK4d15T93\ HH25O1S2tPApNHlLPhJWdGc`EjXCrTAyP1hn3fg5da7cW9aPB_\ JDZDNSBWLAdE9m78v17rAFnJNjRVf_bbgjZprWxyTpwRiuPbtM\ VrKOpIHo4rRAnQGkPLhOReNWbMa_LfXL_WITWGMWEFWC8WA9YC\ 9ZDA_EA`FAaGPLQb5_XHWSTTNdQIpNQnUXl`dkfkimrhsneqkb\ og`mdYlaVjYThVQfSOeRK`RGWQCRQ8MQ5HN6KK6MI6PF6RC6UA\ 6W76Z56`IGTVPLgYDsf5lZ9eSDZLGSEKM7NJCMHGMELMCPMATL\ 7YL5aL3eL7`MBWNFRNIMOMHPQCPU7QX3QQ7LKBHEFC8J82N4DT\ FOZQZd`ijkspvolnlhgid_faTcYL`UEYR7XNCXKGXHKXEOWBSW\ 8WW5_W2cSAfPIiMQlJXnIRiHLeGFaF9YF4UKCYOJaSQeWXi_cm\ cjqjknpkk4YOAh3C`4DT5HQAKOEOMIRJNVHRYFV`IPIt1RuM_v\ fhwzbsyXoyRlxLhxGexHXnHPeIHXI9OI1FaoS_pWYp_XqcVqgT\ rkSroUkhWebX_XZTQ`NKaHECJYJOWPTVWYUabTggSk_OnSLrKI\ uCFx4Ct5Gq6Jn7Mk8Pg9SdAVaBYZC`HlYIjZIhZIfZId_Ib_I`\ _PYYWWWcSdjPmqMvqIoqFiqCbq9Xq6Rh9M`CHTFC } frm:MandelbrotMix3 {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END 20.0 PAR-FORMULA FILE==================================

2 1

FOTD 16-09-02 (X Marks the Spot [8])
by Jim Muth 16 Sep '02

16 Sep '02

FOTD -- September 16, 2002 (Rating 8) Fractal visionaries and enthusiasts: The fractal for today is a winner, a little gem that honestly earns its immodest rating of 8. It was created with my little- used MandelbrotMix3 formula, which combines four different powers of Z but leaves finding a critical point up to the user. Luckily, I have another formula which finds the critical points graphically, so this is not too much of a problem. Today's image is partially evaporated, consisting as it does of 80 percent inside and 20 percent outside. The greatest surprise came when, trying different inside fills, I found that the < zmag > fill gives the most pleasing results. Normally, this fill results in too chaotic an effect, but in today's already- chaotic scene, it works to near perfection. The straight criss-crossing ridge-like areas that fill the background are most unusual. They appear to have been intro- duced artificially, but they are quite natural. A midget of sorts lies at the center of attention, where the most prominent ridges cross. The midget is not really all there, but its strange energy field is very much present, being revealed by the inside fill. Since the image is filled with X's, I named it "X Marks the Spot". One glance at the image will show that the rating of 8 is fully justified. The 37-minute render time however is a bit trying, but the wait can be eliminated by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather Sunday here at Fractal Central was cloudy and muggy with occasional showers of rain. The temperature of 79F 26C fell in the comfort range of the fractal cats, but the wet grass and drippy trees kept the dynamic duo confined to the indoors through most of the afternoon, where they expressed their dis- pleasure by making themselves obnoxious. It's cloudy again this morning, but with a forecast of a drying trend starting this afternoon, the cats should have a better day. My day will turn better once I have finished the work before me. Until next time, take care, and be careful around those dangerous fractals. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ X_Marks_the_Spot { ; time=0:37:57.10--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3 function=recip passes=1 center-mag=-0.3480403693685333/0/728.2051/1/180 params=1/-1.5/0.2/-2/0.15/2/2/0.6/2.11537091657/52\ 5 float=y maxiter=1200 inside=zmag symmetry=xaxis periodicity=10 colors=000QAGN6KK2NJDIJNEvrjkhlaZnS\ PpIFrMChMCkGFhAIe5Lc2kQzBApH8fN6XS5NY3Db2RK4d15T93\ HH25O1S2tPApNHlLPhJWdGc`EjXCrTAyP1hn3fg5da7cW9aPB_\ JDZDNSBWLAdE9m78v17rAFnJNjRVf_bbgjZprWxyTpwRiuPbtM\ VrKOpIHo4rRAnQGkPLhOReNWbMa_LfXL_WITWGMWEFWC8WA9YC\ 9ZDA_EA`FAaGPLQb5_XHWSTTNdQIpNQnUXl`dkfkimrhsneqkb\ og`mdYlaVjYThVQfSOeRK`RGWQCRQ8MQ5HN6KK6MI6PF6RC6UA\ 6W76Z56`IGTVPLgYDsf5lZ9eSDZLGSEKM7NJCMHGMELMCPMATL\ 7YL5aL3eL7`MBWNFRNIMOMHPQCPU7QX3QQ7LKBHEFC8J82N4DT\ FOZQZd`ijkspvolnlhgid_faTcYL`UEYR7XNCXKGXHKXEOWBSW\ 8WW5_W2cSAfPIiMQlJXnIRiHLeGFaF9YF4UKCYOJaSQeWXi_cm\ cjqjknpkk4YOAh3C`4DT5HQAKOEOMIRJNVHRYFV`IPIt1RuM_v\ fhwzbsyXoyRlxLhxGexHXnHPeIHXI9OI1FaoS_pWYp_XqcVqgT\ rkSroUkhWebX_XZTQ`NKaHECJYJOWPTVWYUabTggSk_OnSLrKI\ uCFx4Ct5Gq6Jn7Mk8Pg9SdAVaBYZC`HlYIjZIhZIfZId_Ib_I`\ _PYYWWWcSdjPmqMvqIoqFiqCbq9Xq6Rh9M`CHTFC } frm:MandelbrotMix3 {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 14-09-02 (The Root is Square [7])
by Jim Muth 14 Sep '02

14 Sep '02

FOTD -- September 14, 2002 (Rating 7) Fractal visionaries and enthusiasts: I guess I must apologize for the pathetic discussion I wrote for the most recent FOTD, which appeared on Sep 12. The reason was my angry mood. While being fully reminded of what happened last Sep 11, I heard that my childhood football hero, John Unitas, had just died. As a result, my mood was such that if I had written what I felt at the time, someone would certainly have been offended. Today however, my mood is a bit better, though still not up to average. One thing that helps is that I have found a way to greatly reduce the annoyance of the junk e-mail that floods my jamth mailbox. The technical help department at Mindspring, which is actually Earthlink, told me a way to read the subject lines of my mail without downloading it, and delete the unwanted mail directly from the server. I should have thought of it myself. It doesn't eliminate the spam, but it does eliminate the wait of up to 15 minutes to download stuff that will be deleted immediately on my own machine. Today's image comes from 6 levels down the infinite spiral of the Z^(sqrt(2))+C fractal. I don't know exactly what that means, but the real(p2) parameter of today's formula is set to -6, so it must mean something. The parent of today's picture is a rather ordinary Mandeloid fractal with a main bay and, on the south side of the bay, off the screen, a large bud. A long filament meanders south from the bud. Today's scene, with its tiny midget, is located on this filament, rather near to where it joins the bud, in an area rich with semi-organized chaos. A far larger midget lies near today's scene, not far out the filament. This larger midget is not quite as worthy as the one in today's image. I named the image "The Root is Square" because although the number 2 has an infinity of roots, only the square one is involved in today's picture. Then I gave the image a rating of 7. I kind of enjoy the electric-arc effect of the scene. The 7-minute render time of the parameter file is acceptable to all but the busiest fractal fans. Those without the time to run the parameter file may pick up the completed image on the internet at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Friday here at Fractal Central was near perfect for the fractal cats, though a little too warm for me. The cloudless skies brought pleasure, but the temperature of 86F 30C was more appropriate for early August than mid September. At least the humidity remained relatively low, making for a day that rated a 6 on my scale of weather worth. Now it's Saturday morning, and the day promises to be a near- repeat of yesterday. There is some yard work to be done, which can be avoided if I'm clever enough. But it's a no-win situa- tion. If I skip the work, I'll feel guilty; if I do the work, I'll miss a chance for a totally relaxing day. I'll probably do the work. It's always better to be dis-satisfied with no work waiting to be done. So before I get started, take care, and once a fractal is born, it's always a fractal. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ The_Root_is_Square { ; time=0:07:42.25--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-0.202571534275736/-1.669100436259464/9\ 3199.8/1/-30/2.57370867673412107e-010 params=1.414\ 213562373/0/-6/0 float=y maxiter=1800 inside=0 logmap=250 periodicity=10 colors=000lgzldwiatfZqcWn`TkZRhWOeTLbQI_NFXLDUKADK\ ADKAEKAEKAIKALKAPKBSHCWFDZCEbAFe8Fh7Hi7Jj6Lk6Ml5Om\ 5Qn4Ro4Tp3Vq3Xr2Ys2_t1au1bu8_sEXqKUoRRmXOkbLigCihJ\ ghQehXdRXe9XeCUeFReIOeLLeOJeRGeUDeXAe_7eb5ec7ac9Zd\ BWdDTeFQeGNfIKfKHgMEgOBcN9gP8WR8KT87W78V89V9AV9AVA\ BVBCVBCVCDUDEUDFUEFUFGUFHUG5_DHUGSPJUKMUFPUARNtrMs\ sMssMssMrsMrsMrsMqsMqsLqsLpsLpsLpsLosLosLosMyoLosU\ rYKfwIbvHZuGVtFStEOsCKrBHrADq99p86p6Pd7Ob8O`9OZANX\ BNV2ROBNUKK_SGe`DkhAqlInpPltWjxbhucgsdfqdeoeemfdkf\ cigbghbehaci`aj__j_YkZWlYZo_UlYPjXKhWFfUAdT5bS0`R3\ aO6bM9bKCcIEcFHdDKdBNe9Jh4Pe7VcA`aDfZGlXJtRKrVLpZL\ naLleLjiMhlMfpMhq3dsMZvh`udbt`csXesTgrPhqLjpHlrAkp\ EjoHinKimNhlQgkTgjWfhZegadfddegcdjbcmagwbbpcYidTbm\ UPdXXW_dNblAeuEhtIksMnrQqqUtpYwoaznezmhzlgzlfziezf\ ezcdz`dzZczWbzTbzQazNazL`zI_zF_zCZz9Zz7ezIkzTrzcxz\ mwzuqzolzjRzASzBSzBTzCTzC } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END 20.0 PAR-FORMULA FILE==================================

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FOTD 10-09-02 (Not at all Deep [6])
by Jim Muth 13 Sep '02

13 Sep '02

FOTD -- September 10, 2002 (Rating 6) Fractal visionaries and enthusiasts: At first glance, today's image gives the impression of a scene lying deep in the range of arbitrary precision math. But the impression is not accurate. A glance at the parameter file will reveal a magnitude of only 5x10^5, and arbitrary precision math doesn't even work with 'type=formula' fractals. The effect of great magnitude is created partly by the nature of the image itself and partly because the parent fractal, which resembles a lacework doughnut, is grossly enlarged. The large size of the parent fractal means that the scene in effect actually lies somewhat deeper than the magnitude indicates. The name I gave the image, "Not at all Deep", was inspired by this illusory impression of great magnitude. The midget at the center of today's image lies in the remote suburbs of a larger midget located in the northern part of the bloated doughnut area of the parent fractal. The formula, which combines iterated portions of Z^(-2) and (1/Z), is quite simple, but as I have often stated, in the world of fractals, simple formulae sometimes create incredible images. The rating of 6 appears about right for this image, which impresses me as being just the slightest bit above average. And as always, the 7-minute render time can be avoided by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Monday here at Fractal Central was once again perfect, with a temperature of 88F 31C and all other things that go with weather perfection. The intrepid house cats, Thomas and Tippy, behaved perfectly as they passed the afternoon in their lounge chairs on the porch, wishing only that it had been a few degrees less warm. I'll be perfectly happy only when I finish some work that now lies in semi-disarray on the shelf beside me. So until next FOTD on Sep 12, take care, and see you then. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Not_at_all_Deep { ; time=0:07:32.09--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+126.9237024889527/+137.1000969757893/5\ 30479.5/1/62.5/6.90942504423530668e-006 params=1/\ -2/0.3/-1/98/525 float=y maxiter=900 inside=0 logmap=156 periodicity=10 colors=000UhfRjePleMneJpeHreEteCue5x24v64t93rC3pG2\ nJ2lM2jQ1hT1fW0d_0bb0`eCYXOVP_SHjQ9`XARcBIjCJfDJcE\ J`FJYGJUHJRIJOJJLKJHLJEMJBNJ8OJ5PS8M`BKiDIrGGzIEzP\ GzVHz`IzfJzlKzrLuqJppIkoGgnFbmDYlCTkBPj9Ki8Fh6Ag56\ g47f58e69d6Ac7Bb8Ca8D`9E_9FZAGYBHXBIWCJVDKUDLTEMTE\ ORJPQNQORRNWTL_UKcVIhWHlXGpVJlULhTOeSQaRTYQVVPYRO_\ NNaKO`MP_OQZQRYSSXUTXWUWYVV_WUaXTcYTeXTfWUgWUgYXdZ\ _a_aZadWbgUciRelOfoLgqJUcRGRZ3Ee4Hd4Kc5Mb5Pb6Ra6U`\ 7W_7Z_8aZ8cY9fX9hXAkWAmVBpUBrUDoYEmaGjdHhhJelKcoM`\ sNZvQWtTUrWRqZPoaMndKlgIkfKgeMddNacPZbQWaSS`UP_VMZ\ XJYYG_ZEa_Cc`Aea8gb6ic4kd3kc8kbCkaHk`Lk_QkZUkYZkXb\ kWgkVkkVohPlfKjdFgbAe`5cZD_XLWVTSU`OShKQpGPxCOtGOp\ KOmOOiSOfVObZObbOcfOdjOemXftRgiLV_FcQGteKrgNqhQpiU\ njXmk_lmcjnfioihplgqhehec`aaTZhLWiDUjFTkHSlJQmLPoM\ OqONsQLuSKwUJyVIzXGzZFz`EzbDzcaznRzmHzmJzWKzELzGMz\ INzKOzMPzOQzQRzSSzUTzWUzY } 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==================================

3 3

FOTD 12-09-02 (A Somber Minibrot [7])
by Jim Muth 12 Sep '02

12 Sep '02

FOTD -- September 12, 2002 (Rating 7) Fractal visionaries and enthusiasts: Today's discussion will be brief. When one is in as sour a mood as I am, it's better to remain silent than to speak out and risk offending. Today's fractal is another of my evaporated ones. I colored it with a palette of dark blues and indigo, and named it "A Somber Minibrot". The rating of 7 might be a bit over-optimistic, but who cares. The outzoom will reveal a horseshoe crab floating in a lagoon -- but what the heck. The render time of 15 minutes is tiresome, but the download from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> is far more reasonable. The weather here at F.C. on Wednesday was sunny and pleasant enough, with a temperature of 81F 27C, but the high winds from a hurricane just off the coast made things too hectic for the fractal cats, who took a brief glance outdoors and promptly retired testily to their sofa beds. Now, there's work to be done, so before I get myself into any more trouble, take care, and keep your cool. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Somber_Minibrot { ; time=0:15:45.75--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+3.97716686787938/+0.408927981791538/3.\ 114496e+007/1/12.5000011564625524/-9.1327179283368\ 0873e-006 params=1/-1/0.1/-2/9/1e+100 float=y maxiter=350 inside=bof61 periodicity=10 colors=000xQQIJD2O26L48J69G8BE9DBB000G6EI4EJ2GL0IN\ 0JO0LQ0NR0OT0QV0QI9V4X_0sb0pf0ng0ki0ik0gl0dp0bq0as\ 0YzL`z1VxBQXLN4OIBEEGDBL98R62X40a10g00l00q00n20l60\ i92gD6fG8bJBaNE_QIXTLVXNR_QQbTOfXLi_JlaIkfLiiNilQg\ pRftVfxXdzYbzabzbazf_zg_zixzRzzBzzOzp_zaksOwpTxlXx\ k_xgdxdgzbkz_pzYszVwzRzzQzzNzzLzzRzzYzxbxwitwnqttl\ sziszdqzapzYpzXnzXnzVlzVlzVlzTkzTkzTkzRizRizQgxQgw\ QgtOfsOfsOfxN_zNTzLOzJIzIBzI6zYBznEzzJzzNzzLzpLz_L\ zLLz6LzBJzGJzJJzOJzTJzXJzaJwfJsiJpnJlsJiwJfzJbzJ_z\ JbzLfzNizNkzOnzQqzQtzRwzTzzTzzVzzXQd6Tb8Va8kgNzn_z\ slzpgznbzk_ziVzfQzdNzYLwTLnOLdJJXEJN9JE4Jb0Iz0GTL4\ 0k00n00q00t20x40z80z91xB1sB1nD1iD1dD1_E1VE1RE0OEzz\ zzzzixzRfg8NL0404NBIbNVsYbzRizLqzExz90xD6q9Bk8Gd6N\ Y2RR1XL0dd0kx0qz0zz4zxIznVzdgzVtzRtzOtsLtgItXEtLBt\ 98t06t29x8DzBGzGJzLNzOQzTTzXVzL_z9dz0iq0nk1qgDtfOx\ d_zbkzawz_zzYVz9bpEigIqYN } 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 08-09-02 (Bluebrot [6])
by Jim Muth 08 Sep '02

08 Sep '02

FOTD -- September 08, 2002 (Rating 5) Fractal visionaries and enthusiasts: Blue and orange -- my old high-school colors -- that's the color scheme of today's image, which adds just a bit of Z^3 to Z before adding C. It's not that I'm trying to regain some of that long-gone school spirit; it's that these particular colors make the most of a routine image of just another midget. The exact amount of Z and Z^3 is determined by the real(p3) parameter, and is extremely critical. The formula, like many formulae created by M-Mix4, actually behaves as though the real(p3) parameter brought the formula near an asypmtotic point, where the fractal undergoes a sudden drastic change. The name "Bluebrot" was not named after my high-school football team, which was called the "Engineers", and usually whipped the starch out of their rival team down the road, which went by the name of the "Knights". The image's name is simply the shortest and most appropriate descriptive name I could come up with after a few minutes pondering the image. I wish I could rate the image something above a boringly average 5, but honesty prevails here at Fractal Central, and I always give the images a rating that reflects my degree of satisfaction or dis-satisfaction. If the parameter file ran in a minute or two, the rating might have been higher. As it is, the 36-minute render time is a bit much for such a mediocre image . . . except for the curious, that is. But relief in the form of the completed GIF image is at hand. The image will soon be available on the two FOTD web sites found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather Saturday here at Fractal Central was perfect, with not a cloud in the sky and a cat-pleasing temperature of 84F 29C. The cats in question were appropriately pleased. Tippy, the long-tailed tabby, actually thanked me for the wonderful day he had spent in the yard. Thomas, the overweight yellow-orange, said nothing, assuming that I already knew he was thankful. As for myself, it's once again Sunday, and I'll be pleased if I can get through the day without doing any serious work. But regardless, I'll still have a pleasant day. Until next FOTD on Sep 10, take care, and don't let a blue fractal give you a case of the blues. P.S. -- And don't forget that soon-to-appear FOTD CD! Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Bluebrot { ; time=0:36:11.98--SF5 on a P233 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.25621249906585860/+6.284024255056992\ 00/2.779084e+008/1/-112.5/-3.06632516054589077e-005 params=1/1/0.03/3/-0.003/0 float=y maxiter=6000 inside=0 logmap=698 periodicity=10 colors=000K0RM0UO0ZQ0cS0hU8mSIrSSwSazSizSszSzzSzzS\ zzSzzSzzIzz8sk0YL0B0000000000000100600B00G00L00P00\ U00_00d00i00n00s00p00n03n3DkINkYYfaUdfUakU_pUYuUUz\ SSzSPzSNzSLzSIzSfzSzzPzz3zz0xz0sz0nz0iz0dz0_z8UzIP\ zSLz_GziBzs6zp3sf0a_0_30_0Pz0sz0uz0uz0uz0uz0uz0uz0\ uz3xzBxzIxzNxzUxz_xzfxzkszipzinzfkzfizdfzddzaazafz\ YizSkzNnsIpiDs_8uP3d83P03L08G1DD3GD1DD1DD1DSz0Pz0N\ z0Lz0Ix0Nz0Sz0Yz0az3fzGkzSpzduzpzzzzzzzzzzzzz_zx8z\ u6zu3xs1ps1kp0dp0Yn0Sn0Lk0Dk08d0DY0GP0IL0LD0N60P00\ U00Y00_00a00d00f00a08_DLUSYSfiNuuLzzIPzsNxpNuzLskL\ niIifIfdIaaG__GUYDSUDNSBLPBGNBDLBDLDBLDBIDBID0zD0z\ D0zD0zD0zD0zD0zD0zD0zD0uD0sD0pD0kD0iD0fD08D0dD0_D0\ YD0UD0PD0ND0LD0GD0DD0BzfUzdSzaSzaSz_PzYPzYPzUNzSNz\ SNzPLzNLzNLxLIsIIpIInGGiDGfDGaBDYDLSGSNI_ILfDNn8Pu\ 3Sz0Uz0Yz0_z0_z0_z0Yz0Yz0Yz0Yz0Uz0Uz0Uz0Uz0Sz0Sz0S\ z0Sz0Pz0Pz0Pz0PzDSzGPzINz } 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 06-09-02 (Quatrain [6])
by Jim Muth 06 Sep '02

06 Sep '02

FOTD -- September 06, 2002 (Rating 6) Fractal visionaries and enthusiasts: Before posting my FOTD's, I always check the attached parameter files to see that they work. Almost without exception the files run as they should. However, when posting the most recent FOTD, the one for Sep. 4, I neglected for some reason to check the parameter file before clicking the send button. This oversight gave Murphy's law the chance it needed to work its mischief. When I finally did check the file later in the day, I found that a backslash was missing from the end of a broken line, causing an error message to appear when the file was run. My apologies for any inconvenience. Today's attached parameter file most definitely will run. The image it will draw will take 7 minutes to complete, and hope- fully will be worth the time spent. The image that will appear lies in the fractal that results when -1.1 parts of Z are com- bined with -1.1 parts of Z^20 before adding C. This parent fractal is actually a classic Mandelbrot set caught in the act of morphing into the Z^20 Mandeloid. Today's scene lies in a curving valley at the mouth of a small bay on the east edge of the distorted M-set. I named the image "Quatrain", though I can't say why. A quatrain is a four-line stanza of a poem. Maybe I noticed the nearly square olive-green feature around the obligatory central midget. Regardless, it's a striking image, which looks as good from a distance as it does up close. Not wanting to appear boastful, I rated it a 6, which is above average, though not by much. The trip back out of the parent fractal is interesting also. Those with a little time to spare might wish to change the logmap to 0, the passes to G and make the journey at thumbnail size. As always, the completed GIF file of the image will soon be available on the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Thursday here at Fractal Central was perfect beyond description, so I won't try to describe the indescribable other than to say that the temperature of 83F 28C pleased the cats so much that their sour dispositions turned cheerful after a couple hours in the yard. As for me, I've got a couple hours of work ahead of me, and my disposition won't improve until the work is behind me. The solution . . . get the work started. Until next time on Sunday the 8th, take care, and double check your figures. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Quatrain { ; time=0:07:30.39--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+1.57055877097165100/+0.538927007893349\ 20/4.321429e+007/1/15/3.82882488214608685e-007 params=-1.1/20/-1.1/1/0/0 float=y maxiter=1500 inside=0 logmap=132 periodicity=10 colors=000nOEqPBtR8vS5uV9pZDlaHgdKcgOZjSVlVQiUMfTH\ dTDaS8ZR4XR4UPTMlKOrBPx9Mw7Iw5Fw3Bw18w05w02wtnSoiP\ jeNeaLaYIXTGSPENMBJO9EQ79S4AU2SYDQWCPUBNSAMQAKP9JN\ 8HL8GJ7EH6DG6BE5AC48A47835724522311100Pe0IV0CL06Aj\ KTdHPZFLTCINAEH7AB57523G09D07B06905603402201qLTRG7\ PF6`iWakWcgYedZfa_hZ`iWakTbmPdnMepJfqGgsDhtAi100q9\ fn9dk8bh8_e7Yb7W`6TY6RV5PS5NP4KM4IJ3GH3DE2BB298165\ 14202I3pG2kE2fD2aB1X91S81O61J40E309104ij7fg6de6ab5\ _`5XY5VW4TT4QR4OO3LM3JJ2GH2EE2CC1991771440220xttuq\ qroopllmjjjggheeebbb```YYYWWVTTTRRQOONMMLJJIHHFEED\ CCA99777544222n0Yk0Wi0Uf0Td0Ra0P_0OY0MV0LT0JQ0HO0G\ L0EJ0CH0BE09C08906704403201V5bT4`c4Zc4Xc4Vc3Tc3Re3\ Qg3Oi2Mi2Ki2Ii2Gi1Ei1Di1Bi19q07z05z03z01xR1zD0zKUz\ YZzZHhcNNhLMmKLrJKvIIzHHzGGzEFzDDzCCzBBzAAz98z87z6\ 6z55z43z32z21z12zX1zT1zP1zM1zI0zE0zB0z70z3xzjkz`_z\ SOzICz95zcEzTKzQQzNWzKbzH } 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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Repost FOTD 04-09 Parameter file now runs
by JimMuth＠aol.com 05 Sep '02

05 Sep '02

FOTD -- September 04, 2002 (Rating 6) Fractal visionaries and enthusiasts: The parent fractal of today's image mixes some Z^3 with some Z and produces a Mandelbrot set with a new open area caught in the act of opening on the X-axis some distance to the west. (This new area is quite sensitive to small changes in the real(p3) parameter.) The Mandelbrot set part of the parent holds pretty much the same features as the classic M-set, but the newly-opened area to the west contains some entirely new features. One of these new features is a double valley. In the classic M-set, Double valleys usually indicate a non-critical environment, but in the world of the M-Mix4 formula there are no hard and fast rules, so I decided to take a look into one of the several arms in this double valley, where I found an interesting environment, better viewed than described. Today's scene is located in the suburbs of a larger midget near the end of a filament in the double valley. The trip down, which is rather interesting, can be seen in reverse by changing the logmap setting to 0 and doing multiple outzooms. Unlike I do in most of my FOTD's, I did not rotate today's image to the normal position, with the main stem of the midget facing west. The reason is simple -- though I know it is there, I have never seen the midget at the center. Unfortunately, the midget is beyond resolution. The invisibility of the midget inspired the name "The Unseen Midget". The rating of 6, based on the pattern around the midget alone, seems fair. All is not lost however, for as the pattern indicates, today's midget lies in the suburbs of a larger midget, and this larger midget is nearly exactly the same as the unseen midget in today's image. (I can tell by the pattern.) So a trip out to see the larger midget will give a good idea of the appearance of today's unseen midget. The drawback to all this exploration is the slowness of the image, which takes nearly an hour to render on my machine, but if the passes is reset to <g> and the exploration is done at thumbnail size, the trip is do-able. As always, the completed GIF image will soon be available on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Tuesday was summer-like here at Fractal Cen- tral. The hot sun and temperature of 88F 31C kept the dynamic cats satisfied, though not as active as they still occasionally are. In the evening, I found the remains of a half-eaten bird at the foot of the porch stairs. Both Thomas and Tippy pleaded innocent, so I have no idea how the bird got there. But I have a very good idea of how I'll get from busy to idle -- and that is to finish the work that needs to be done. And if I hope to finish, I must begin. So until the next FOTD on Friday September 6, take care, and accept no FOTD substitutes. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Unseen_Midget { ; time=0:55:10.80--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.00245214023728272/+1.268076105879121\ /1.714617e+011/1/90/3.88578058618804789e-016 params=1/3/1/1/-0.195/0 float=y maxiter=3600 inside=0 logmap=-1138 periodicity=10 colors=000H0_F0aD0cA0e80g60i80kA0mB0oD0qE1sG2uH3wJ\ 4yL5zM5zO4zP4zR3zS3zR6zRAzRDzRGzRKzRNzRQzRTmQXeQ_Y\ QbWQeTQiQQlNQoKQrIToGVmFXkEZhCafBcdAea8g_7jY6lV4nT\ 3pR2YhQ_gNagRehUhr_yzDxwGxwJxrMwmPwhSwcVvZYvU`vPcu\ KdtFesFfrIgqKhpNioPjnSjmVklXlk_mjanidohfpgiqfkq`gm\ WdjQ`fLYcGV`FS_EPZDMYCKXBHWAEV9CU89T76S74R95SB6TD7\ UF8UH9VJ9WLAXMBXOCYQDZSD_UE_WF`YGa_Hb`Hb_Ga_Ga_G`_\ F`_F__F__EZ_EZ_EZZGXZIWZKVZLTYNSYPRYRPYSOXUNXWLXYK\ XZJW`HWbGWdFWeER`HMXJHSMDOO8NR4NU0NW3PV6QV8SVBTUEV\ UGWUJYTMZTO`TRaSUcSWdSSeVOeYKf`GfcCgf8gi4hl1ho2di2\ ac2YZ2VT2RN2OI2KC2H62E1EQGQ`UalhlwvdtlXrbPpTHnJAl9\ FiJKgSPdaUbjZ`sKj`5sI8tLBuNDvPGwRIwTMtVPrWSoXVmZYj\ _ah`debgccj`dmZel`bka`jbZidXheVhfSggQfiOejMdkKdlIN\ h1KaX8YLbeE`bH_`JZZLYXNWUQVSSUQUTOWRLZQJ`PHbOFdMCg\ LAiK8kJ6mDNb7bS1rH3lK5gN6aP8XS9SUBMXDH_EBaG6dH1fLd\ SSgQYjPVgTTdWRaZOZaMWdKTg } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 04-09-02 (The Unseen Midget [6])
by Jim Muth 04 Sep '02

04 Sep '02

FOTD -- September 04, 2002 (Rating 6) Fractal visionaries and enthusiasts: The parent fractal of today's image mixes some Z^3 with some Z and produces a Mandelbrot set with a new open area caught in the act of opening on the X-axis some distance to the west. (This new area is quite sensitive to small changes in the real(p3) parameter.) The Mandelbrot set part of the parent holds pretty much the same features as the classic M-set, but the newly-opened area to the west contains some entirely new features. One of these new features is a double valley. In the classic M-set, Double valleys usually indicate a non-critical environment, but in the world of the M-Mix4 formula there are no hard and fast rules, so I decided to take a look into one of the several arms in this double valley, where I found an interesting environment, better viewed than described. Today's scene is located in the suburbs of a larger midget near the end of a filament in the double valley. The trip down, which is rather interesting, can be seen in reverse by changing the logmap setting to 0 and doing multiple outzooms. Unlike I do in most of my FOTD's, I did not rotate today's image to the normal position, with the main stem of the midget facing west. The reason is simple -- though I know it is there, I have never seen the midget at the center. Unfortunately, the midget is beyond resolution. The invisibility of the midget inspired the name "The Unseen Midget". The rating of 6, based on the pattern around the midget alone, seems fair. All is not lost however, for as the pattern indicates, today's midget lies in the suburbs of a larger midget, and this larger midget is nearly exactly the same as the unseen midget in today's image. (I can tell by the pattern.) So a trip out to see the larger midget will give a good idea of the appearance of today's unseen midget. The drawback to all this exploration is the slowness of the image, which takes nearly an hour to render on my machine, but if the passes is reset to <g> and the exploration is done at thumbnail size, the trip is do-able. As always, the completed GIF image will soon be available on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Tuesday was summer-like here at Fractal Cen- tral. The hot sun and temperature of 88F 31C kept the dynamic cats satisfied, though not as active as they still occasionally are. In the evening, I found the remains of a half-eaten bird at the foot of the porch stairs. Both Thomas and Tippy pleaded innocent, so I have no idea how the bird got there. But I have a very good idea of how I'll get from busy to idle -- and that is to finish the work that needs to be done. And if I hope to finish, I must begin. So until the next FOTD on Friday September 6, take care, and accept no FOTD substitutes. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Unseen_Midget { ; time=0:55:10.80--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.00245214023728272/+1.268076105879121 /1.714617e+011/1/90/3.88578058618804789e-016 params=1/3/1/1/-0.195/0 float=y maxiter=3600 inside=0 logmap=-1138 periodicity=10 colors=000H0_F0aD0cA0e80g60i80kA0mB0oD0qE1sG2uH3wJ\ 4yL5zM5zO4zP4zR3zS3zR6zRAzRDzRGzRKzRNzRQzRTmQXeQ_Y\ QbWQeTQiQQlNQoKQrIToGVmFXkEZhCafBcdAea8g_7jY6lV4nT\ 3pR2YhQ_gNagRehUhr_yzDxwGxwJxrMwmPwhSwcVvZYvU`vPcu\ KdtFesFfrIgqKhpNioPjnSjmVklXlk_mjanidohfpgiqfkq`gm\ WdjQ`fLYcGV`FS_EPZDMYCKXBHWAEV9CU89T76S74R95SB6TD7\ UF8UH9VJ9WLAXMBXOCYQDZSD_UE_WF`YGa_Hb`Hb_Ga_Ga_G`_\ F`_F__F__EZ_EZ_EZZGXZIWZKVZLTYNSYPRYRPYSOXUNXWLXYK\ XZJW`HWbGWdFWeER`HMXJHSMDOO8NR4NU0NW3PV6QV8SVBTUEV\ UGWUJYTMZTO`TRaSUcSWdSSeVOeYKf`GfcCgf8gi4hl1ho2di2\ ac2YZ2VT2RN2OI2KC2H62E1EQGQ`UalhlwvdtlXrbPpTHnJAl9\ FiJKgSPdaUbjZ`sKj`5sI8tLBuNDvPGwRIwTMtVPrWSoXVmZYj\ _ah`debgccj`dmZel`bka`jbZidXheVhfSggQfiOejMdkKdlIN\ h1KaX8YLbeE`bH_`JZZLYXNWUQVSSUQUTOWRLZQJ`PHbOFdMCg\ LAiK8kJ6mDNb7bS1rH3lK5gN6aP8XS9SUBMXDH_EBaG6dH1fLd\ SSgQYjPVgTTdWRaZOZaMWdKTg } 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 02-09-02 (What Me Worry [4])
by Jim Muth 02 Sep '02

02 Sep '02

FOTD -- September 02, 2002 (Rating 4) Fractal visionaries and enthusiasts: Fractal buds come in all shapes and sizes, enclosing, as they do, areas of a particular periodicity. Most buds are of the quadratic variety, and therefore nearly circular, but some buds are true oddballs, such as the bud that appears in today's image. Today's bud is shaped more like a bowling pin than a Mandelbrot bud. And instead of smaller buds around its perimeter, it has various bits and pieces of entire M-sets. The apparent head of the bowling pin is actually a distorted and incomplete M-set, which is connected to the body of the bud. The connection forms the neck of the pin. The overall appearance of the distorted bud creates a feeling of humorous goofiness, much as does the face of the cartoon character who speaks the words that are the name of today's image -- "What Me Worry". The rating of 4 is a bit below average, because the image isn't really that great. But the image is a real curiosity, and if it is not quite worth the 1/2-hour render time from the parameter file, it is at least worth the download from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> As always, give Paul and Scott a chance to render and post the image before visiting their FOTD sites. The weather Sunday here at Fractal Central featured steady rain and a temperature of 65F 18C . . . if such conditions can be considered a feature that is. The cats certainly did not enjoy their forced indoor confinement, and loudly let me know their displeasure. A treat of left-over turkey breast only partially relieved their distress. Today promises to be a far better day, with far less rain. On days such as this, it's best to do as little work as possible, so I'll make that my goal. Until next FOTD on Wednesday the 4th, take much care but not too much care. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ What_Me_Worry { ; time=0:28:19.89--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident center-mag=+0.38671183426525360/+0.415903832256643\ 20/4381.013/1/87.5/-8.77794364972928065e-012 params=1/5/1/2/0/0 float=y maxiter=16000 inside=0 logmap=86 symmetry=none periodicity=10 colors=00051L62M73N94NA5OB6PC7PD8QF9RGARHBSICTJDTL\ EUMFVNDVOBWQ9VPAWPAXPBXPBYOCZOCZOD_OD_NE`NEaNEaNFb\ MFcMGcMGdMHdLHeLIfLIfLJgLJgKJhKKiKKiKLjJLkJMkJMlJN\ lINmIOnIOnIOoHPpHPpHQqHQqGRrGRsGSsGStFRuGStGSsGSsG\ TrGTrGTqGUpGUpGUoGUoGVnGVmGVmGWlGWlGWkGWjGXjGXiGXi\ GYhGYhGYgGYfGZfGZeGZeG_dG_cG_cG_bG`bG`aH``Ha`Ha_Ha\ _HaZHbYHbYHbXHcXHcWHcWHcVHdUHdUHdTHeTHeSHeRHeRHfQH\ fQHfPHgOHgOHgNHgNHhMHhLHhLHiKHiKHiJFkJHiJIhJJgJLfJ\ MeJNdJPcJQbJRaJT`JU_JVYJXXJYWJZVJ`UJaTJbSJdRJeQJfP\ JhOJiMJjLJlKJmJJnIJpHJqGJrFJtEJuDJvCJwBJvCIvDIvEIv\ EHvFHvGHvHGvHGvIGuJFuKFuKFuLFuMEuMEuNEuODuPDuPDtQC\ tRCtSCtSBtTBtUBtUBtVAtWAtXAsX9sY9sZ9s_8s_8s`8sa8sa\ 7sb7sc7rd6rd6re6rf5rg5rg5rh4ri4ri4rj4qk3ql3ql3qm2q\ n2qo2qo1qp1qq1pr0qs1qt1qu1qv2qw2rx2sy3tz3uz3vz4wz4\ xz4yz5zz5zz5zz5zz6zz6zz6zz7zz7zz7zz8zz8zz8zz9zz9zz\ 9zz9zzAzzAzzAzzBzzBzzBzzC } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 30-08-02 (Curlers [7])
by Jim Muth 31 Aug '02

31 Aug '02

FOTD -- August 30, 2002 (Rating 7) Fractal visionaries and enthusiasts: Checking my e-mail box this morning, I found 23 messages, 18 of which were junk. I am not particularly annoyed by this junk mail, some of it is actually fun, especially those blatantly scam letters from the families of assassinated leaders I have never heard of in some unlikely African nations, who want to give me 8-million U.S. dollars if I send them my bank account number. And there is also the "very excite game" family of junk, which I have received hundreds of times, and delete immediately because they contains a virus. I simply delete most of this junk automatically. This morning however, when it took 20 minutes to download my queue of e-mail, I realized that things might be getting a bit out of control. I'm even getting undeliverable messages returned to me that I never sent. If the present trend continues, I might need to change my e-mail address in the not-too-distant future. But for the present, I'll stick with the 6-year-old 'jamth' address. Today's image existed for all eternity before I stumbled upon it yesterday afternoon. It is a scene in the fractal that results when 0.1 part of Z^12 is subtracted from Z^1.2 and 1/C is added. The fractal consists of a two-lobed Mandeloid with its main filament curling off to the east. The curl in this filament inspired the name "Curlers". Today's FOTD pictures a point far out on this curling filament, where a tiny midget lurks. Most of the impact comes from the coloring, on which I spent a few extra minutes. Thanks to the strong colors, the image, which otherwise would have rated a 6, rates a 7. The parameter file is unusually fast, running in the one-minute range on most machines. It will probably take longer to go online and download the completed GIF image file. But for those who will enjoy the trip, the completed image may be found online at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather Thursday here at Fractal Central was of the fractal variety, as most everything in nature is, including the fractal cats, who endured 2 outdoor hours of heavy clouds and a tempera- ture of 70F 21C before surrendering to their need for food and coming in from the yard. As for me, I'd best get busy doing the things that need to be done here in the fractal shoppe. And that means work. So until the next FOTD three days from now on Sept 2, take care, and be of sound mind and nominally unsound fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Curlers { ; time=0:01:25.91--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.42455251587505830/+0.001585523072115\ 22/4.121986e+008/1/102.499999815637167/6.040707956\ 06759248e-008 params=1/1.2/0.1/12/0/0 float=y maxiter=280 inside=0 logmap=25 periodicity=10 colors=00000000000000000000000FA1KK5ON9RREUPIKXNNc\ SPjXSqaWyfXzl`zqaWzpZzjazecy`fwXjuSlsNpsKqqFupByn8\ zl3zj0zj0se5haEXZNNWXCSf3Pq0Lz3WzCczLnzWwzezzezzez\ wezpezhezaezWezPezIezCez6ez1ez0ez0ez0ez0In00P602K0\ 9N0FP0LR0SS0ZU0eW0lX0sZ0z`0za0zc1zZ6zWCzRIzNPzKWzF\ azChz9fzBezCczCazE`zEZzFXzFWzHUzISzIRzKPzKNzLLzLXz\ RfzWqz`zzczyfywhwujusnsqpqpqpnsnnwllyjjzhhzffzeezc\ czcczhflljRpn6sq0pn0nj0jf3hc8e`EcXI`UPZRUWN`UKeSFl\ RCsR9zP6zP3zW9zaFnhKapRRwXFza5zh0zn0j0FX6EKLC8`B0q\ 90z80yC0qF6jKEcNLXSURWaK`jEcnKhqRluWpyauzfyznzzszz\ wzsywnzqfzn`zhWze0hy0ls0pn0sh0wc0z`0zW0zR1zL2zH2zE\ 8zKEzRKzWRzaXzhcznjzuqzzlzzhzzczz`zzWzzSzzNzzKzzFz\ zCzz8zz5zz1zz0zz0zz0zz0zs0zl0zf0z`0zU0zP0zR0zS0zU0\ zW1zX2zZ3z`6z`8za9zcBzeEzfFzhHzjIzjNzhRzhUzhXzh`zh\ czffzfjzfzzfzzfzzezzezzezzezzezzZyzUuzPpzKjzEfz9az\ 5Xz1Uz0Nz0Iz0Ez09z05z00z0 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

2 1

FOTD 28-08-02 (A Thorny Issue [8])
by Jim Muth 30 Aug '02

30 Aug '02

FOTD -- August 28, 2002 (Rating 8) Fractal visionaries and enthusiasts: The parent fractal of today's image is closely related to the parent of the image of Aug 26th. Negative portions of Z^(-2) and Z^(-3) are combined before (1/C) is added. The resulting fractal consists of a large central bay with a non-critical cloverleaf-like island at the center. This cloverleaf holds little of interest, but the western shore of the bay features a very prominent sub-bay, with critical buds and filaments. The filaments are not the simple jagged lines of the M-set filaments, but are twisted into loops and rings that hold countless midgets. Today's midget lies in a branch of a tiny ring near the tip of a filament. Actually, the midget is not there at all, for the escape radius of a full googol has totally evaporated the outside material, leaving only a blank inside of trapped points. But all is not lost. The inside fill of bof61 has revealed the ghost of the midget that once was there but now has gone. Curiously, the bof61 inside fill is the only fill that produces such a fine image. I think the bof61 fill colors the inside points according to which iteration comes closest to the origin, but I'm not sure. Regardless, the image rates an exceptional 8, which is the highest rating in several months. The name I gave to the image, "A Thorny Issue", is totally whimsical. The phrase simply came into my head as I studied the scene. (I'll bet a psych-something or other could learn a lot about my secret unconscious life from the titles I sometimes half-consciously give to my FOTD's.) The 3-minute render time of the parameter file is fair enough. A download of the finished image is even fairer. The completed image may be found on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather here at Fractal Central on Tuesday featured morning sunshine followed by increasingly thick afternoon clouds and a high temperature of 86F 30C. The duo of fractal cats must have approved, for they spent several hours prowling in the holly thicket at the bottom of the back yard, cleverly avoiding the burdock burrs and thistles that, despite all attempts at eradication, still grow there. And if I'm to avoid a late start in the morning, I must soon shut down the fractal shoppe and call it a night. Until the next mind-boggling FOTD appears on Friday the 30th, take care, and be as happy as the fractal duo. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Thorny_Issue { ; time=0:03:39.15--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-6.779241253387853/+2.975306275944614/2\ .396909e+008/1/-87.5/-1.68222442726295718e-005 params=-0.5/-2/-0.1/-3/0/1e+100 float=y maxiter=295 inside=bof61 logmap=40 periodicity=10 colors=000hhzhhzhhzhhzlRrU_EPV9TRARRASKAPGATDAaPJi\ _Srj`zuiirVUpHM_XYlcirjuwpnrlhmhahdWc`QZXJUTDPP7LM\ I`wSbs`dojfksghreeqcbpa`o_YnYVmWTlVQkTNjRLiPIhNFgL\ DfJAeH7dG5cFAbEEaDJ`CN_BSZAWY9`Y8dX9eX9fXAgXAhXBiX\ BjXCkXClXDmXDnXEoXEpXFqXFqVy4Xw8ZvC`uFatJcsNerQgqU\ hpYjo`lndnmholkmihmgemebmc`maYmZVmXSmVQmTNmRKmOHmM\ FmKCmI9mG6mE4mG5mI6mK6mM7mO8mQ8mR9mTAmVAoXBqZzs`zu\ bzwczx`zxYzyVzySzyPzzSzzVzzSzzPzzNzzKzzHzzFzzCzz9z\ z7zzCzzGzzKzzPzzTzzXzz`zzezzizzmzzqzzhzz`zzTzzUzzV\ zzWzzWzzXzzYzzZzzZzz_zz`zzazzazzczzezzgzzizzezzazz\ YzzUzzRzzNzzJzzFzzCzz6zz1zzFzzSzzPzzNzzLzzOzzRzzTz\ zWzzYzz`zzbzzezzhzzjzzmzzozzrzztzzwzzyzzuzzrzzozzl\ zzizzfzzczz_zzXzzUzzRzzOzzLzzIzzFzzGzzGzzGzzHzzHzz\ HzzIzzIzzIzzIzzUzzUzzUzzVzzVzzVzzWzzWzzWzzWzzXzzXz\ zXzzYzzazzYzzYzzZzzZzzZzzZzz_zz_zz_zz`zz`zz`zz`zza\ zzazzazzbzzbzzbzzbzzczzcz } 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==================================

3 3

Last word on dead issue
by Jim Muth 29 Aug '02

29 Aug '02

At 07:29 PM 8/23/02 -0700, Ken Childress wrote: <I wrote> >>and the 'I'm an artist' crowd left the Fractint list >>to flock to the other program. > <Ken replied> >This sounds derogatory. Is that what you meant? To begin, I mentioned no program and no author, though the program to which I was referring was obvious, and I did comment that the program in question was a fine program. I did not state that the Fractint code had been stolen, though I did comment that some of it it might have supplied ideas, and in that way, have appeared in modified form in the other program. Finally, by my 'I'm an artist' comment, I implied that IMO it takes more than knowing how to use a computer program to be considered an artist. The word 'artist' implies creativity and originality. It does not imply doing the same things that the rest of the crowd is doing. Such people are better considered skilled craftsmen, which is what I consider myself. If you find this derogatory, I'm sorry. Jim M.

5 7

FOTD 26-08-02 (The Web of Terror [7])
by Jim Muth 26 Aug '02

26 Aug '02

FOTD -- August 26, 2002 (Rating 7) Fractal visionaries and enthusiasts: The midget at the center of today's image is located on the X-axis of its parent fractal, which has X-axis symmetry. This is demonstrated not only by the coordinates in the parameter file but by the straightness of the arms radiating from the midget. The 180 degree rotation of the image does not change the east-west orientation of the X-axis, so why do 2 out-zooms reveal a north-south oriented axis? The mystery is not very deep, a few more out-zooms reveal the true situation -- the X-axis is not continuous. Actually, only one out-zoom reveals an interesting scene -- a near-perfect array of square figures that almost made it as FOTD. The choice between the squares in the out-zoom and the octagons in today's image was a toss-up. The squares lost only because one of the two images had to lose. The generating formula subtracts 0.2 part of Z^(-3) from Z^(-2) before adding 1/C. If I had added the 0.2 part of Z^(-3) rather than subtract it, the resulting parent fractal would still have had X-axis symmetry, but its overall shape would have been totally different, and of course, today's image would not have existed. (More accurately, it still would have existed but it would never have been found.) I used the MandelbrotMix2 formula to find today's image. This formula works the same as the overworked MandelbrotMix4 formula, except that it includes the capability to change the starting point of Z. This capability is not used in today's image. The name of the image, "The Web of Terror", which sounds like the title of a horror movie, has no connection whatever to the appearance. I might have had a fleeting impression of a spider's web, but if so, I can no longer see the resemblance. The rating of 7 seems fairly accurate, and those who spend the 3 minutes to run the parameter file will not be disappointed. Those who download the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> will not be disappointed either. The Sunday weather here at Fractal Central was perfect for most anything, with blue skies, puffy white clouds, gentle breezes, low humidity, and a temperature of 86F 30C. The fractal duo were happy all day, which is a rare event for them. My happiness however depends on finishing the work I now find before me. If I start now, I can be finished by 3pm. If I wait an hour, I will not finish before 4pm. If I put off some of the work until tomorrow, I can be finished by noon. Most likely, I'll choose the first option. Until next FOTD, which will arrive in all its glory within 48 hours, take care, and beware of fractals lurking in dark corners. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Web_of_Terror { ; time=0:03:13.01--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+7.662161881652889/0/1.171407e+011/1/180 params=1/-2/-0.2/-3/0/0/0/0 float=y maxiter=500 inside=0 outside=tdis periodicity=10 colors=000z8z89S8AR9AP9BOACMADLADK9CJ9BI8AI89H78G7\ 8G77F66E65E54D53C53CB7EGBFLEHRIIWLJ`PLeSMkWNqZPwbQ\ zeRxcSrbSn`Sk_SgYScXS_VSXUSTSSPRSLPSIOSEMSALS6JS3I\ S4KQ5LP6MO6NM7OL8QK9RI9SHATGBUECWDCXCDYAEZ9F_8F`7I\ b6Kc6Md6Pe6Ug6ch6mi6wj6wl6wm6wn6mo6cjA`fDZbHWZKTUO\ RQROMVMIYKKVILSHMQFONDPLCQIARG8TD7UB5V84W6KdKZlXYj\ YXhYWgYWeYVdYUbYUaYT_YSZYSXYRWYQUYQTYRVXSXVTZUU`SV\ bRWdPXfOYhMZjLZkKWeOT_RQUUNOYKI`ICcJH_KMXKQUJSWJTX\ JVZJW_IX`IZbI_cI`dIbfHcgHdhHfjHgkHhlPilWilcjljjlqj\ leZgUObIDY62TEFPMRL8tF9qKAoOBmSBkWCi_DfdDdhEblF`pF\ ZtH`sIarJcqKdpMeoNgnOhmPilQkkSljTmiUohVpgWqfVpcVpa\ Vo_VoYVoWUnUUnSUnQUmNUmLTlJTlHTlFTkDTkBTk9ShASeARb\ BR`BRYCQVCQTDPQDPNEPLETJDWHD_FCbDCfBBi9Bm7Ap5As3Ap\ 6Cm9DjCFgEGdHHaKJZNKXPL_OIbNFeNDXMrYNsmL5lQAkVEj_J\ idNhiSgnWgq_eoaclcbhe`egZaiYZkWVmVSnWRpXQqYPsZOtZN\ uSWsMdrGmpAvoe1hO4b66X77V } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

1 0

Compiling the sources?
by Marc Schreier 26 Aug '02

26 Aug '02

Hi, did anyone managed to compile the Fractint sources with Visual Studio 6? The Fractint homepage points to a port - work in progress - but still not available. Regards Marc

2 1

FOTD 22-08-02 (Square in Sight [7])
by Jim Muth 25 Aug '02

25 Aug '02

FOTD -- August 22, 2002 (Rating 7) Fractal visionaries and enthusiasts: Checking the fractal gossip lines, I see that a new version of the fractal generating program preferred by the trendy fractal crowd has just been released. I already have the previous version of the program, though I rarely use it, so I may or may not eventually pick up this newest version, for which the program's author is charging a nominal upgrade fee. In any case, I'll wait until a debugged version appears. I have nothing against the performance of this other program, it's a fine fractal generator, but I remember several years ago, when the Fractint list was receiving queries from the author of the other program, asking questions about the operation of the Fractint code. Shortly thereafter, the other program appeared on the scene as a shareware product, and the 'I'm an artist' crowd left the Fractint list to flock to the other program. So far, so good, but I wonder how much of the original Fractint code now resides in slightly modified form in the other program, which is being sold for profit. Something not quite ethical appears to have happened somewhere along the line, but neither I nor apparently anyone else can pin it down. Well, I guess it's time to move on from ethics to today's fractal, which was generated by the old-fashioned Fractint program aided by the MandelbrotMix4 formula. The expression 6Z^(-0.7)-0.12Z^(2.2)+(1/C) was iterated to create the parent fractal, which consists of a large double-lobed Mandeloid with a smaller satellite Mandeloid just to the east. Today's midget lies deep in the main valley on the east side of the large Mandeloid. I named today's image "Square in Sight". No square features actually exist in the image, but the coloring gives the appearance that the midget lies in the center of a square. This illusory square inspired the name. I feel that the rating of 7 is justified in light of the fact that the pattern around the midget is different enough to warrant notice. The render time in the 4-minute range is short enough to make running the parameter file practical and long enough to make it interesting. As always, those who would rather avoid parameter files may download the completed image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather was typical mid-summer fare here at Fractal Central on Wednesday. The high temperature of 88F 31C was just about average; the moderately high humidity and stagnant air were also average for mid-summer. The fractal cat duo had an average day -- one hour outdoors lounging in the shade, 22-3/4 hours indoors lounging on the floor, 1/4 hour eating. With another day's work before me, I'd best get busy without delay. Until the next glorious FOTD appears on August 24, take care, and remain steadfast. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Square_in_Sight { ; time=0:04:16.99--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.42420968295669740/-0.001119486396590\ 06/4.82806e+009/1/-70/2.93649964008824149e-006 params=6/-0.7/-0.12/2.2/0/0 float=y maxiter=750 inside=0 logmap=81 periodicity=10 colors=000M0aO0cP0dQ0eS0eT0fV0fX0gY0i_0j`0la1mc3od\ 4pf6rg7jf9cd6Xg4Qj3Lm3Fp19s03vF0yM0zT0rM0jF6cMFVSP\ O`YGif7rp0uy`zz0zz0zz1xy4uv7rsAorDloGilJfiMcfP`d_P\ jiDos1uz0yx0vs3soArjGodOm`TjX_gSffMlcIsaDy_9sYCoiD\ _uFJzAMu7Ol3Qa0ST0YX0cj0_l0Vl0Sm3Om6LmAGoDDoI9oM4p\ P1pT0pX0r`0rc0rf0si0sl0sm0sp0ss3uu4ux7uzAuzCuzDpzD\ mzDizDfzDazD_yFXyFSyFPyFLyFIyFFsIDmJCiLAcO9_P9TQ7P\ S6JV4DX39Y33`10a00c00d00`6AXDMSLXOQgJYrFdzAlz7rzAs\ zDuzGvzJxyLxvOysQzpTzoVzmYyl`xjcuifsgirflofmmdplcs\ iavg`yf_zcYzaYz`0r00m00h30eA0cG0fM0iT0l_0of0rl0ur1\ sm9rjGpgOodVma`l_cgXfcTi_QlVOoQLrMIuKFrPCmUAhZ3cc0\ Zh1Ym4Yr7XvCXvFXvIVuLVuPVuSTsVTsYTsaSudSvgSxjPyiOz\ gLzgJzfGzfFzdCzdAzc7zc6za4zaazmzzxzzpzzjzzczzYzzQz\ zLzzDzz7zz1zz7zzCzzGzzLzzPzzTzz_zzczzgzzlyzpxzuvzy\ xzzxzzyzzyzzzzzzzzzzzzzXzz0zz0vz4lzAczGTzMLzQPzOSz\ LXzI_zFXzDVzCTzCSzAuzszzx } 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==================================

5 5

FOTD 24-08-02 (Sliced Melons [7])
by Jim Muth 24 Aug '02

24 Aug '02

FOTD -- August 24, 2002 (Rating 7) Fractal visionaries and enthusiasts: Today's image is named "Sliced Melons". If the first three letters of the second word are reversed, the title becomes "Sliced Lemons". But there is nothing sour about the image, which uses the < tdis > outside coloring option. In fact, after careful consideration, I rated the image at a 7. The parent fractal combines portions of Z^2 and Z^3. The whole- number exponents result in a fractal that has no branch-cut discontinuities when calculated with the outside set to display the standard equal-iteration bands, but the < tdis > outside- coloring algorithm used in today's image introduces the disconti- nuities that are visible in the image. The parent fractal is a distorted Mandelbrot set rotated 180 degrees, with lots of interesting activity on its negative (in this case, positive) stem. East (in this case, West) valley of the parent fractal is also decorated with interesting spurious activity, though I did not explore this area. With a render time of 6 minutes on my humble fractal machine, today's fractal is a bit slow, making a download of the completed image the marginally better choice. The download is available on the W.W.W. at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Friday here at Fractal Central was overcast and very humid -- wet enough to swim in. The temperature of 86F 30C was about average. A few drops of rain fell in the after- noon, which is too bad, since we're in a rather severe drought. The fractal cats finished their outdoor activity before the raindrops appeared, so, unlike the local farmers, they were not displeased. With thunder-showers prowling the area this morning (Saturday), and some real rain hopefully soon to occur, I'd best wrap up this edition of the FOTD and see whether I can console the dynamic duo. Until next FOTD on Monday the 26th, take care, and be serendipitous. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Sliced_Melons { ; time=0:06:12.34--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=ident passes=1 center-mag=+2.943452875421294/+0.00522078768874016\ /1.530056e+012/1.0002/177.5/0.00916304379004028585 params=1/2/-0.2/3/-0.25/0/0/0 float=y maxiter=1000 inside=0 outside=tdis symmetry=none periodicity=10 colors=000RmRUmUXnX`n`cocgofjpjnpmqqptqsrnpqknpiln\ fimdglaejZciX`hUZfSXePVdMSbKQaHO`FMZINYLOXOPWQPVTQ\ TWRSYRR`SQcTPeTNbSM_SLXSJVSISSHPSGMSEKRDHRCERBBR99\ R86R73R61R7GM8UH9gCAu7IkEQaKYSQdIWUOVKTUAZT0cS4fW7\ h_BkcEmgHojHniHngImfImdIlcJlaJk`Jk_Ml`Pl`Sm`UmaXna\ _naaobdobgobipclpcoqcqqdtrdwrdyrdldX`RPbVMcYKd`Iec\ GffEgiBhl9io7jr5ku3lx1jy2hy3fy3dy4by4`y5Zy5Yy6Wy6U\ y7Sy7Qy8cz8Zt9Qp9VjJV_TKKKcElg3uf8sfCreGpeKoeOmdTl\ dXjc`icdgchfdj`ekWflQgmLhoGipAjq5jr0kp3ln5ll7mj9mh\ BnfDndFobHp`KpZMqXOqVQrTSrRUsPWsNYpMZmLZjKZhK_eJ_b\ I__H_YH`VG`SF`QF`NDRKBHH98RKK_UWicgrmsolklldjlXglQ\ elJdgEccAb_6bW2_Y6YZAW_DTaHRbLPcOMeSKfWIgZFibDjfBk\ iAjj9ij8hj8gj7fj6ej6dk5ck4bk4ak3`k2_k2_k7blBdlGflK\ hmPjmTlmQciOWfLOcJG`KFZLEXMDVNCTPBRUAPZ9Oc8Mh7Km6I\ r5Gm4Eh3Cc2BZ1HU1MJ1SF1XB1b81g72d72a72Z62W62T62Q52\ N52L52I42F42C429326323321 } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

1 0

Recent Newton_elliptic formulae.
by Morgan L. Owens 24 Aug '02

24 Aug '02

So I spent ten minutes just looking. SkeinedSpire { ; Colours by Mark "Bud" Christenson ; Version 2001 Patchlevel 8 reset=2001 type=formula formulafile=newton_e.frm formulaname=newton_elliptics_3 center-mag=-0.558014/0.500417/12.69162 params=0.1/0.5/-1/0 float=y maxiter=1023 inside=255 periodicity=0 colors=FMUGLUILUKKU<5>NL`OMaPMc<2>RNfSOhSOh<9>ZUo_Up_Vp<2>bXscYtc_t<3>fd\ wffwggxgixhjy<3>nqzprzrtz<3>zzz<27>C__AZZ8YY<3>0UU<10>M_NO_MQ`MS`LUaK<4>\ abFbbEdaC<3>ja8k`6m`5<2>q`2s_0s_0<24>xt0xu0yv0<2>yy0zz0xy0<15>HW0EU0BS0<\ 2>3M00K00L0<36>0u00v00w0<2>0z00z00y0<7>0q00p00o0<2>0l00k00j2<7>0ZI0XK0VM\ <2>0RS0PU1PU<7>DNU } SmallInfinities { ; A Mandelprobe disrupted by a nearby singularity ; SkeinedSpire Closeup ; Colours by Mark "Bud" Christenson ; Version 2001 Patchlevel 8 reset=2001 type=formula formulafile=newton_e.frm formulaname=newton_elliptics_3 center-mag=-0.58718581135681620/+0.45507375059740630/147.577 params=0.1/0.5/-1/0 float=y maxiter=1023 inside=255 periodicity=0 colors=FMUGLUILUKKU<5>NL`OMaPMc<2>RNfSOhSOh<9>ZUo_Up_Vp<2>bXscYtc_t<3>fd\ wffwggxgixhjy<3>nqzprzrtz<3>zzz<27>C__AZZ8YY<3>0UU<10>M_NO_MQ`MS`LUaK<4>\ abFbbEdaC<3>ja8k`6m`5<2>q`2s_0s_0<24>xt0xu0yv0<2>yy0zz0xy0<15>HW0EU0BS0<\ 2>3M00K00L0<36>0u00v00w0<2>0z00z00y0<7>0q00p00o0<2>0l00k00j2<7>0ZI0XK0VM\ <2>0RS0PU1PU<7>DNU } JuliaImpactFeature { ; When it hit the ground, it hit the ground hard. ; Another SkeinedSpire Closeup with a colour scheme ; from the ever reliable selection by Sylvie Gallet ; Version 2001 Patchlevel 8 reset=2001 type=formula formulafile=newton_e.frm formulaname=newton_elliptics_3 center-mag=-0.58741182340086060/+0.45145680389088130/6416.391 params=0.1/0.5/-1/0 float=y maxiter=1023 inside=255 periodicity=0 colors=000UUZ<15>jjlkkmllm<6>rrssstttu<2>wwwxxxxxv<3>xvmxukxthxtfxsdyra<\ 9>ylLykJyjH<2>yhCxgAxgA<11>nW2mV2lU1<4>fQ0eP0dO0bN0aM0`M0<3>VI0UH0TG0<10\ >B60950740<2>210001112<8>5AE6BF6CH7DI7EJ8FL<10>BJSBJTBJU<3>DLWEMXGNY<6>T\ YfV_hX`i<2>aemcgocgo<9>lmpmnpnopooppppqqq<4>llnkkmjjliikhhjggj<39>55E44D\ 33C<2>00A00A11B<28>TTZ } frm:newton_elliptics_3{ x=real(p1) y=imag(p1) A=real(pixel) B=imag(pixel) phi=tan(real(p2)) t=imag(p2) z=x+flip(y) : oz=z x=real(z) y=imag(z) d=2*y*phi-(3*sqr(x)+A) f=(sqr(x)+A)*x+B-sqr(y) g=phi*x+t-y nx=x-f+2*y*g ny=y-phi*f+(3*sqr(x)+A)*g z=nx+flip(ny) |z-oz|>0.0001 }

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Re: [Fractint] FOTD 22-08-02 (Square in Sight [7])
by Rupert Millard 23 Aug '02

23 Aug '02

Hi Jim, >So far, so good, but I wonder how much of the original Fractint >code now resides in slightly modified form in the other program, >which is being sold for profit. Something not quite ethical >appears to have happened somewhere along the line, but neither I >nor apparently anyone else can pin it down. It's an intersting question but my answer is "probably none." Ultra Fractal is written in Delphi and Fractint in C. The Fractint compatibility formulae are written in Ultra-Fractal's formula language. The source of these is available and IMHO it is indiscernable from the fractint code. Plenty of other programs implement the same forumlae as fractint and many of these are hard-coded in C - I think these are more questionable. btw: can someone give me a link to the old fractint archives from the majordomo days? From, Rupert _________________________________________________________________ Join the worlds largest e-mail service with MSN Hotmail. http://www.hotmail.com

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Re: [Fractint] Extended Fermat's Last Theorem - Slightly Off-topic
by Andrew Coppin 23 Aug '02

23 Aug '02

IIRC, a pair of Japanise (?) students proposed that all elliptic curves are also modular forms. Someone else pointed out that, assuming Fermat was wrong, his equation x^n + y^n = z^n would be an elliptic equation, and the corresponding modular form is decidedly weird. Yet ANOTHER mathematition later proved that this modular form is in fact too weird to actually exist. In other words, assuming that EVERY elliptic curve REALLY IS a modular form, Fermat's Last Theorum MUST be true. Andrew Wiles proved that elliptic curves ARE modular, and as a side effect proved Fermat right. Andrew. PS. I've read the book. And I'm kinda bored today... >From: "Morgan L. Owens" <packrat(a)nznet.gen.nz> >Reply-To: fractint(a)mailman.xmission.com >To: fractint(a)mailman.xmission.com, fractint(a)mailman.xmission.com >Subject: Re: [Fractint] Extended Fermat's Last Theorem - Slightly >Off-topic >Date: Mon, 19 Aug 2002 13:43:43 +1200 > >At 01:09 19/08/2002, dirving(a)box.net.au wrote: >>"Ricardo M. Forno" wrote: >> > >> > Does someone in the list know if the following conjecture, that >>includes as >> > a particular case Fermat's Last Theorem, has ever been posed, and >>proved >> > false or true? >> > x[1]^p + x[2]^p + ... x[n]^p = z^p, for x[i] > 0 and 1 < n < p, has no >> > integer solutions. >> > TIA. >> > >> > _______________________________________________ >> > Fractint mailing list >> > Fractint(a)mailman.xmission.com >> > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >> >>I would conjecture ... no. > >Reasonable: a proof of this extended conjecture would in turn provide an >alternatve proof of FLT as a special case. > >So if there has been a proof, it has been found more recently than (and >probably develops the ideas of) Wiles' tour de force. > > >Morgan L. Owens >"Yes, Andrew; a corollary :-)" > > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com

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Re: [Fractint] Extended Fermat's Last Theorem - Slightly Off-topic
by Franktal Gallery 22 Aug '02

22 Aug '02

Morgan, thanks for the explanation and the link ! Regards, Miguel >From: "Morgan L. Owens" <packrat(a)nznet.gen.nz> >Reply-To: fractint(a)mailman.xmission.com >To: fractint(a)mailman.xmission.com, fractint(a)mailman.xmission.com >Subject: Re: [Fractint] Extended Fermat's Last Theorem - Slightly >Off-topic >Date: Fri, 23 Aug 2002 00:48:14 +1200 > >At 23:46 22/08/2002, Franktal Gallery wrote: >>Could you please explain the "semistable" concept ? > >Oof. Where to start (and where to finish?) > >See http://mathworld.wolfram.com/Semistable - following is a paraphrase. >[snip] >[snip] >[snip] _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com

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Re: [Fractint] Extended Fermat's Last Theorem - Slightly Off-topic
by Franktal Gallery 22 Aug '02

22 Aug '02

Could you please explain the "semistable" concept ? Thanks, Miguel >From: "Morgan L. Owens" <packrat(a)nznet.gen.nz> > >[snip] > >The two theorems run: >If FLT is false, then y^2=x(x-z^n)(x+y^n) is semistable, but not modular. >(Conjectured in 1982 by Gerhard Frey; proven in 1986 by Ken Ribet via >Jean-Pierre Serre). > >and > >All semistable elliptic curves are modular. (Conjectured by Yutaka Taniyama >in 1955, later generalised by Goro Shimura and Andre Weil by dropping the >"semistable" bit; proven in 1994 by Andrew Wiles). > _________________________________________________________________ Send and receive Hotmail on your mobile device: http://mobile.msn.com

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FOTD 20-08-02 (Fractal Kernels [7])
by Jim Muth 20 Aug '02

20 Aug '02

FOTD -- August 20, 2002 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal image is corny. This does not mean that it is trite and old-fashioned, it means that it is filled with corn kernels. The corn in the image appears in neat rows, almost the way corn kernels grow on the corncob. This corniness inspired the name "Fractal Kernels". The effect of corn kernels is produced by iterating the formula Z^(-2)-0.01(Z^2)+(1/C), and doing the calculation with the bailout radius set to 99.999, (which is critical), and the outside set to < fmod >. The small range of colors in the image was not intentional. It exists because the image uses only a small part of the 256-color palette. Unwilling to have yet another consecutive 6-rated FOTD, I rated today's image at a rather liberal 7. Perhaps a 6-1/2 would have been more appropriate, but my rating scale does not have half- step increments. The 4-minute render time is acceptable, but downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> is more acceptable. The fractal weather Monday here at Fractal Central was hot and humid enough to keep the fractal cat duo housebound. The high temperature reached 97F 36C at 4pm, and as is usually the case these days, the promised cooling showers once again failed to appear. One thing that had better appear however is the work that's due, and the only way to finish the work is to start it. So without further fanfare, I'd best get started. Until next time, on the 22nd, take care, and watch your bailout. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Kernels { ; time=0:04:00.35--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-4.43910986029936400/-5.965792592977377\ 00/1.175254e+008/1/-42.4999968823281691/-4.8222949\ 2321933906e-006 params=1/-2/-0.01/2/0/-0.001 float=y maxiter=1000 inside=0 proximity=0.5 outside=fmod logmap=yes periodicity=10 colors=000vtzvtztszqrzqqzopznoznozlnzilzgkzeizegzd\ gzafz_dz_czYazXazV_zTZzTXzQVxOTvMTqMQoKOnIOlHMgFKe\ FKdDIaBHY9FX9FV7DT5BO3BM29K27I07F05D03B03905H27S39\ Z5Bc7Df9FiBHkDIzFKzHMzIOzKQzKQzKQzKQzKTzKTzKTzKTzK\ VzKVxMVvMVqMXoMXnMXiMXgMYeMYaMY_MYYKX_KX_IXaIXaHXd\ HXdFXeFXeFXgDXgDXiBXiBXl9Xl9Xn9Xn7Xo7Xo5Xq5Xq3Xt3X\ t3Xt5Yq7Yo7Yn9YlB_iB_gD_gF_eF_dHaaIa_IaYKaXKaXMdVO\ dTOdQQdOTeMTeKVeKXeIXeHYgFYgD_gBagBag9di7ei5ei3gi2\ il0il0ll0ll0nl0on0on0qn0tn0tn0vo0xo0xo0zo0zo0zv0zz\ 0zz0zz0zz3zz7zzBzzDzzDzzFzvFzoHtiHndHgXIaQIXKKQDKK\ 7MF2M90MH3KM9KTFKYMIdTIiYIoeHvlHzqHzzFzzFzzFzz7zz0\ zz0zz0nz0vz_zzazxdzxdzzatzaaz_Kz_5z_IqQVgIeX9tM2zB\ 0z20z00zT3zO5zM7zK9zI9zHBxFDqDFlBFTIDBQB0X93_IDaTM\ d_VeidgqnizvlzzIzz0zz0zv0zzIzzVzzezzqzxzzqzqlziezd\ dviaIoqD_z7Kz37z7FzBMzFVvI_oMgiQodVx_YzOizDtz2zz0z\ z0zz0zz0zo3ze5zV9zKBzBxtz } 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] Extended Fermat's Last Theorem - Slightly Off-topic
by Rupert Millard 19 Aug '02

19 Aug '02

Ricardo, >Does someone in the list know if the following conjecture, that includes as >a particular case Fermat's Last Theorem, has ever been posed, and proved >false or true? >x[1]^p + x[2]^p + ... x[n]^p = z^p, for x[i] > 0 and 1 < n < p, has no >integer solutions. >TIA. Yes, this conjecture was made by Euler in 1769. He conjectured "it is impossible to exhibit three fourth powers whose sum is a fourth power, four fifth powers whose sum is a fifth power, and similarly for higher powers." This was first disproven in 1966 by L.J.Lander & T.R.Parkin with: 27^5+84^5+110^5+133^5 =144^5 The first found with fourth powers was done by Noam Elkies in 1988 and is: 20615673^4 = 2682440^4 + 15365639^4 + 18796760^4 Then Roger Frye found: 422481^4 = 95800^4 + 217519^4 + 414560^4 which is the smallest solution for fourth powers. From, Rupert _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com

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Extended Fermat's Last Theorem - Slightly Off-topic
by Ricardo M. Forno 19 Aug '02

19 Aug '02

Does someone in the list know if the following conjecture, that includes as a particular case Fermat's Last Theorem, has ever been posed, and proved false or true? x[1]^p + x[2]^p + ... x[n]^p = z^p, for x[i] > 0 and 1 < n < p, has no integer solutions. TIA.

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FOTD 18-08-02 (Iterative Teardrops [6])
by Jim Muth 18 Aug '02

18 Aug '02

FOTD -- (Rating 6) Fractal visionaries and enthusiasts: It's Sunday mid-morning here at Fractal Central, and all is well. I have just finished emptying my e-mail box of two large undeliverable e-mails that were returned to me. This is well enough, except for the fact that I never sent the letters in the first place. It's probably another virus, and a clever one at that -- one that works like sending a letter via normal mail with no postage and writing the name of the address you want it delivered to in the 'from' space. Then when the post office 'returns' the letter for lack of postage, they are actually delivering it. I also feel a bit cruel about failing to reply to Baerbel's request for information about unsubscribing from the Fractint list. But it's a bit amusing to see such a request (from someone who already knew how to subscribe) appear three lines below the unsubscribe information in the letter's header. As for today's fractal, (which I have rated at a harmless 6), it's a scene in the fractal that results when 0.01 part of Z^2 is added to Z^(-2), and (1/C) is added to the combination, then the whole thing is iterated with a bailout radius of 100. That 0.01 part of Z^2 is not much, but it makes a world of difference in the final fractal. The parent fractal, which is enclosed in a circle, looks surprisingly like a fractal planet. Changing the logmap of today's image to 0 and doing about 10 out-zooms will reveal this planet in its full glory. As is the case with most fractals that contain a negative exponent of Z, the bailout radius has a great effect on the appearance of the fractal. With the parent fractal on the screen, redraw the image with imag(p3) set to 2400. A totally different image appears. I named today's image "Iterative Teardrops" because of the teardrop shape of the elements surrounding the central midget. These disconnected elements are typical of fractals whose formula contains negative powers of Z. The rating of 6 equals a little above normal on my rating scale -- about the mildest praise I could give to such a mundane image. The redeeming feature is the render time of 6 minutes, and the fact that the completed GIF image file may be downloaded from either of the following web addresses: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Saturday here at Fractal Central was uneventful. The partly cloudy day with a temperature of 95F 35C and moderately high humidity was notable only because it continues the warmer and drier than normal pattern that has prevailed most all summer. Also it was the fourth day in a row on which the weather experts had predicted showers, and the fourth day in a row on which the predicted showers failed to arrive. Those experts are far better at explaining why something did not happen than forecasting what will happen. The fractal cats, who are unconcerned with weather experts, passed the day doing what cats do best -- lazing around the fractal grounds. As for me, it's Sunday morning, and if I really work hard, I might find a way to get through the day without working. And don't laugh. After all, working to avoid work is no more anti- productive than fighting for peace. Until next time, on the 20th, take care, and don't be too lazy. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ IterativeTeardrops { ; time=0:06:12.45--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+3.31533979732890300/+3.380854530622418\ 00/2.718068e+010/1/17.4927412805414235/0.007870415\ 83158384211 params=1/-2/0.01/2/0/0 float=y maxiter=1000 inside=0 logmap=130 periodicity=10 colors=000GLKFNKNUTV`WbgZjnhtml90M_pwcipgbgkWZnPQe\ TNXXKOXHRbJTecVhLfkm_nNmqOctPzvQYqRQlSIgTBcUFdXJe_\ NfbRgeVhhTqpSYwRZwQOwbzocmidhcdcZe0TeUO_TPVTQPTRKT\ SFRTnGwjJtgMndPhaSbZVXWYRT`LQcGWaOa`WgZclYjghsbrwn\ auzLpjKmVJkFIi0Ig6RoBZvHmwMnwJcwHTwFIwD8wSCgfGTuJE\ tLFsMFsOGrPGrRHqSHqTH9WbDYeG_gJajMblPdnSfqVhsYiurk\ wzhtseiscZtf_pdbmbej`gg_jdYlaWoZVqWTtTRwQPwNOwKMwH\ KwEJwDIwCHwBGwAFw9Eu8Ds7Cp6Bm5Ak49h38e38cBDfVEkWCp\ XAuX9wO5pG2gK9lNGpQMtUTwXZw_ewbkwb_wbOwbCwb1wd2we3\ wf4wg5wh6wj6wk7wl8wm9wnAwoAwjRtegjaxadscfnehigjdil\ _knVmpQorLqtGsvBux6wz2wrDujOqbZnVijNsgQUwNWwKYwI_w\ FawDcvAet7gs5ir2kq0lp4fs7`uAVwDUwGVwJWwMXwPYwSZwU_\ wW`wZaw`bwbcwedwgewifwlgwnhwpiwsjwukwwlwymwvnwtowr\ pwpqsnrnlsiitdgu`evWcwRaxM_yIYzMWzQUzTSzXQz_OzcMzg\ LzjJznHzqFzuDzwBzw9zw8zwJzwUzwdzwozwnzwnzwnzwnzwnz\ wnzwnzwozwpzwpzspzopzkpzg } 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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(no subject)
by Baerbel Strauch 18 Aug '02

18 Aug '02

how can i stop getting e-mails about fracint? _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com

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Fractal Tone-Poems (music?)
by Bill Jemison 17 Aug '02

17 Aug '02

Thanks Miguel! I remember that you had posted some music pars a while ago, in fact I have them saved in a special directory. so please do post some more. I like Nocturn as well. the orbits are rather hypnotic along with the music. Lotus is probably my favorite, due to the way that the unfolding of the "petals" follows the tonal patterns. It's not particularly "melodic" but I feel that it has merit anyway. That's why I am inclined to call them tone poems rather than music, although one might be able to argue that there isn't much difference. Bill

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Re: [Fractint] Fractal Tone-Poems (music?)
by Franktal Gallery 16 Aug '02

16 Aug '02

Bill, I believe Nocturn is one of the best music PARs I ever heard ! I used to post music PARs a couple of years ago, and I'll do it again when inspiration strikes me... ;-) For those of you who may never heard them, here's a link to my music PAR collection : http://www.geocities.com/franktal2002/sounds.html Regards, Miguel >From: Bill Jemison <fishburnIII(a)compuserve.com> >Reply-To: fractint(a)mailman.xmission.com >To: fractint(a)mailman.xmission.com >Subject: [Fractint] Fractal Tone-Poems (music?) _________________________________________________________________ Send and receive Hotmail on your mobile device: http://mobile.msn.com

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Fractal interstellar gas
by David Jones 16 Aug '02

16 Aug '02

Fractal interstellar gas at end of a star's life: http://hubblesite.org/news_.and._views/pr.cgi.2002+15 David gnome(a)hawaii.rr.com

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Re: [Fractint] FOTD 08-08-02 (Odd Mandelbrot [5])
by gnome＠hawaii.rr.com 16 Aug '02

16 Aug '02

I firmly believe that cat fur is fractal - explains why such small animals can shed so much fur everywhere without visibly losing any fur. ;-) David gnome(a)hawaii.rr.com >>On Tue, 13 Aug 2002 19:07:34 -1000, David Jones wrote: >> >>>Besides, some of us think that Jim is really just a virtual >>> identity of the cats. >> >>You mean a fractal manifestation? >> >>:-) >> >>John >>-- John Lewis, jlewis(a)clara.net on 08/14/2002

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FOTD 16-08-02 (Papillon [6])
by JimMuth＠aol.com 16 Aug '02

16 Aug '02

FOTD -- August 16, 2002 (Rating 6) Fractal visionaries and enthusiasts: Having posted several consecutive FOTD's that were faster than the speed of light, I now post one slower than...well...a fractal cat. The slowness is a result of the magnitude of the image, which takes us into the realm of arbitrary precision math. It's a slow trip into the Mandelbrot set to the location of today's image, but a trip well worth taking, for the midget in the image is unlike any I have previously seen in a fractal as mundane as the M-set. The scene pictured in the image is located in a remote valley of the largest midget on the west branch of the filament extending from the large period-3 northern bud of the M-set. I named the picture "Papillon", which is the French word for 'butterfly'. While studying the image, I saw purple butterflies all through it, but since I have used this name several times in the past, I decided to use the French word for that insect instead. The rating of 6 is nominal. The scene displays a curious mixture of total chaos and areas of organization, which is rather unusual for at least the lower magnitudes of the M-set. A rough version of the image can be seen in 3 minutes by striking the < g > key and entering the command < mathtolerance=/1 > before running the parameter file. This will force the program to calculate the scene using conventional math. But to see the image in its fully-resolved glory, a wait of 5 hours will be required. All is not lost however, for the completed and fully-resolved image will soon be available on the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Thursday here at Fractal Central was once again warm and humid -- the kind of day that brings out the laziness in cats. The temperature of 95F 35C kept the not-very- dynamic duo confined to quarters until the sun went down, and even then, they ventured out only briefly. Luckily for me, modern science has provided relief from the heat in the form of air-conditioning, which I took advantage of all day as I tended to the work that needed to be done. Tomorrow promises to be a bit cooler, with at least a chance of showers, another ideal day for working. So until next time, which will arrive on Sunday the 18th, take a moderate amount of care, but not so much care that life ceases to be fun. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Papillon { ; time=4:56:06.77--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-0.1534230146723439126/1.03855500630879\ 9133/9.504526e+013/1/-27.3516134375319133/3.885780\ 58618804789e-016 params=0/0 float=y maxiter=30000 bailout=6 inside=0 symmetry=none periodicity=10 colors=000gCcgAff7hf5jg8kgBkgDkgGkgIkgLkgOlgQlgTlg\ VlgYlg_ljT_mNOpHCqIBrJArK9sL8tM7tN7uO6vP5vQ4wR3xS2\ xS2wU3vV4uW5tX6sY6rZ7q`8pa9ob9ncAmdBleCkfCgUAcH8`4\ 6_39_3B_3E_3G_3J_3L_3O_3Q_3T_3V_3X_2`_2b_2f_2h_2k_\ 2m_2q_2s_2v_2x_2zZ3wZ3tZ4qZ4nY5kY5hY6eY6bX7_X7XX8X\ X8UVASUBRTDQSEORGNPHNOJNNKMMMMLNMJPLIQLHSLGTLFVKDW\ KCYKBZJA`J9aJ8bJBaID`IF`IH_IJ_HMZHOYHQYHSXGUXGWWGZ\ VG`VGbUFdUFfTFiSFkSEmREoREqQEsQEoTGkVHhXJdZKa`MYbN\ VdPRfQNhSKjTGlVDnW9pY6rZBm`GhaLccQZdUUeZPgcKhhFjmA\ kq6lkEneMocLpaKq_JqYJrWIrVHsTHsRGtPFuNFuMEvKDvIDwG\ CwEBxDBxJGqOLjUQcZVXd_QidJnhDleGkbIj_KiXMhUPgSRfPT\ eMVcJYbG_aEa`Bc_8fZ5hY2jX0lW3jW5iV7hV9gUBfUDeTFdTI\ bSKaSM`RO_RQZQSYQUXPXVPZUO`TObSNdRNfQNhPPiORjOSkNU\ kNWlMXmMZmL`nLaoKcoKepJfqJhrIjrIksHmtHotGpuGrvFsvF\ mtGhrHcqHZoIUmIPlJKjJFhKAgK5eL0dL0bI0aGEFvDKrCOoBS\ lAWh9_e8cb7g_Dd`JbaO_aUYb } END PARAMETER FILE=========================================

1 0

Fractal Tone-Poems (music?)
by Bill Jemison 15 Aug '02

15 Aug '02

<<Oh, no colourmap, then :( :)>> Never will be from here, but sometimes I do use colormaps ;}. However, as I said, some of these have no image, so there's not much need for any colors <g> Bill

1 0

Fractal Tone-Poems (music?)
by Bill Jemison 15 Aug '02

15 Aug '02

<<Your waterfall par was truncated.>> Indeed! Sorry 'bout that. Here is the correct version, complete with omited "}" ********************************* Waterfall { ; Music par Copyright (c) Bill Jemison [70400,2537] 1999 ; Fractal Tone-Poem ; OPL3 (most SB compatibles - NOT SBLive!) ; add Concert Hall reverb if possible reset=2000 type=chip passes=1 video=SF7 center-mag=0/0/0.001754386 params=-15/-19/1 float=y viewwindows=12/0.75/yes/0/0 hertz=-100 sound=x/fm/quant polyphony=3 decay=8 sustain=14 srelease=10 scalemap=1/3/5/6/8/10/12/1/3/5/8/10 orbitdelay=1000 showorbit=yes } *********************************

2 1

Re: [Fractint] FOTD 08-08-02 (Odd Mandelbrot [5])
by Jim Muth 14 Aug '02

14 Aug '02

Morgan Owens wrote: <much snippage> >I agree completely, [that the science-religion conflict is >off-topic on this list] so why do you keep [broaching the >topic here] especially when you said you'd stop? IMO, the non-problem lies not so much in the fact that I keep posting off-topic letters, but rather in the nature of fractals themselves, which invite and almost demand philosophical (and yes, mystical) speculation. This, in large part, is what makes fractals so fascinating to both skeptics and the less skeptical. Check the original FOTD for August 8, which started this thread. In that letter I mentioned the four-dimensional nature of the Julibrot, which I often mention, and pointed out that the world we live in has only three dimensions, with no place for a four-dimensional object. I mentioned nothing about religion or the philosophy of science. As I recall, someone else posted a justified and IMO on-topic reply speculating about the nature of numbers and mathematics, and the mini-debate progressed from there. I have no idea where or how the topic of the conflict between science and religion entered the discussion. >So I take it you waited a while so that people who might want >to see your reply would've had time to subscribe before you >posted it? Most of the delay in my replies is due to the time difference between New Zealand and the east coast of the USA. And yes, I did post the notice to this list so that those who might want to see my reply would know where to find it. My message might even have resulted in a few additional subscribers to the under- manned philofractal list, where posting a letter is often like talking to oneself. >I have a suggestion. I'm suggesting it here 'cos it could >impact on the other readers of this list. Start yourself a >weblog. Then you can post whatever you like whenever you like... I've been thinking of doing things like this for years. It's a nice idea, but I don't see how I could find the time. As a final remark, I wonder why no one ever complains about the really off-topic things I write, such as the weather report and activities of the cats. All the off-topic complaints seem to come when I connect fractals to metaphysical things such as spiritual reality, a connection which is only slightly if at all off-topic. To me, fractals are spiritual (non-material) realities and their existence lends credence to the claims of other spiritual realities, such as the claims of religion. I cannot honestly ignore the fact that fractals lead in this direction. Jim (still controversial) M.

10 9

Vignette with Preamble, still...
by Morgan L. Owens 14 Aug '02

14 Aug '02

The Morse-Thue Floor. I think about eight iterations should be enough to give an idea... MorseThue-2c{ Axiom i Angle 4 i=[c6@i2[f[+@4f]f[+@4f]f[+@4f]f]+f[-@4f]f[-@4f]f[-@4f]f] i=[[ij]+g-ji]gg j=[c44@i2[f[+@4f]f[+@4f]f[+@4f]f]+f[-@4f]f[-@4f]f[-@4f]f] j=[[ji]+g-ij]gg f=gg g=gg }

1 0

Fractal Tone-Poems (music?)
by Bill Jemison 14 Aug '02

14 Aug '02

Jim Wilson wrote this, though I couldn't read it...must be some sort of mime-thing, which I have long forgotten. >You know, when I first started to read this "Vignette" my first thought >was that this had no business being in the Fractint forum. However, >reading on, I became quite impressed by this verbal fractal Most posts >are graphics pars or formulae, can't remember if,or when, anybody offered >a music par. This is a something different...now if only Morgan could >incorporate some verbal recursion, this might constitute a new Fractal >form, requiring a different type of formula. Could we soon be posting >.vig files? If so, then nobody woud feel the need to plead for >brevity After all, what is a brief fractal? Anyway, I have a few music pars, or as I prefer, fractal tone-poems, which I have been reluctant to let see the light of day - especially since our beloved par-rater extrordinaire once declared that *any* music par had a maximum possible rating of 2. I won't bother trying to rate them...Lee Skinner says that Fugue_on_y_minor sounds like "farts" on his speakers and Chaos_City hurts his ears. A couple of them may have been included in a version of Fractint...if so, sorry for the duplicate. There are a few idiosyncrasies involved with sound pars. Resolution often affects the sounds, so most of these pars force one of the standard Fractint video modes, SF5(640x480), SF7(1024x768), and one SF9(1280x1024). If SF9 gives you a problem, use 1280x1024x256 disk video. If you have changed your config file, choose your corresponding res for each par, please. Some of these are "multimedia" ie. the image is part of the show - Lotus, for instance, (usually and good image is just an accident)...others either have no image or are drawn so slowly that there might as well not be one. Lastly, but very important. These are OPL3 chip compatible. That includes most soundcards, but *NOT* the SBLive!, which has an EMU10K chip. Other SB cards, or SB compatibles will give the proper sounds as far as I know. Often the SBLive will indeed play something from these pars, but it is totally different in most cases. I do have some SBLive! compatible pars if someone wants. Oh yeah...some of these get to a point where they are no longer interesting or repetitious but others get more interesting later in. Be sure to let Boo! and Lotus run to conpletion though. Bill Jemison ************************************* BOO! { ; Image&Music (c) Bill Jemison 2000 ; Fractal Tone-Poem ; OPL3 (most SB compatibles - NOT SBLive!) ; playtime~00:00:35 reset=2000 type=threeply passes=1 video=SF5 center-mag=-25.6682/-4.28027/0.001124723/0.4739/-85/-55.646 params=-165/-17/126 float=y maxiter=13 viewwindows=1/0.75/yes/0/0 cyclerange=1/15 hertz=-1000 sound=x/fm attenuate=mid polyphony=2 attack=8 decay=5 sustain=14 srelease=10 orbitdelay=400 showorbit=yes colors=000zzz<253>000 } Chaos_City { ; copyright (c) Bill Jemison 1999 ; Fractal Tone-Poem ; OPL3 (most SB compatibles - NOT SBLive!) ; add Concert Hall reverb if possible ; must use 1024x768x256 video mode reset=2000 type=mandel passes=d video=SF7 center-mag=-0.21515300000000000/+0.64304200000000000/1354.084/0.1539/-7.\ 496/-51.993 params=0/0 float=y maxiter=1000 fillcolor=0 inside=0 outside=0 viewwindows=19/0.75/yes/0/0 cyclerange=1/1 hertz=0 sound=x/fm polyphony=2 wavetype=7 attack=3 decay=5 sustain=15 srelease=8 orbitdelay=1500 showorbit=yes colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzzzLzzz000555<3>HHHKKKOO\ O<3>ccchhhmmmssszzz00z<3>z0z<3>z00<3>zz0<3>0z0<3>0zz<2>0GzVVz<3>zVz<3>zV\ V<3>zzV<3>VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3>hzh<3>hzz<2>hlz00S<3>S0\ S<3>S00<3>SS0<3>0S0<3>0SS<2>07SEES<3>SES<3>SEE<3>SSE<3>ESE<3>ESS<2>EHSKK\ S<2>QKSSKSSKQSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS00G<3>G0G<3\ >G00<3>GG0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG8AG88G\ 8<2>8GE8GG8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>BGFBG\ GBFGBDGBCG000<6>000 } Chop_schtiks_SF7 { ; Copyright 2000 by Bill Jemison ; Fractal Tone-Poem ; OPL3 (most SB compatibles - NOT SBLive!) ; add Concert Hall reverb if possible reset=2000 type=frothybasin passes=1 video=SF7 center-mag=0.877039/-0.240632/1.465201 params=1/0/2.028713768218725 float=y maxiter=647 bailout=1 symmetry=none periodicity=0 viewwindows=8/0.75/yes/0/0 hertz=-50 sound=z/fm/quant polyphony=9 scalemap=1/3/5/6/8/10/12/1/5/8/1/5 orbitdelay=750 showorbit=yes } Crystal { ; copyright (c) Bill Jemison 1999 ; Fractal Tone-Poem ; OPL3 (most SB compatibles - NOT SBLive!) ; add Concert Hall reverb if possible reset=2000 type=threeply passes=1 video=SF7 center-mag=-25.6682/-4.28027/0.001127669/1.2175/-174.164/11.757 params=55/1/42 float=y maxiter=48 viewwindows=1/0.75/yes/0/0 hertz=50 sound=y/fm attenuate=mid polyphony=2 attack=8 decay=5 sustain=14 srelease=10 orbitdelay=1000 showorbit=yes colors=000zzz<253>zzz } Cycle-o-rama { ; Image&music (c) Bill Jemison 2000 ; Fractal Tone-Poem ; OPL3 (most SB compatibles - NOT SBLive!) ; add Concert Hall reverb if possible ; playtime 0:08:22 reset=2000 type=threeply passes=1 video=SF7 center-mag=6.091/19.6806/0.01024156/2.6547/171.252/24.801 params=22/0.4/-1.8 float=y maxiter=32 viewwindows=2/0.75/yes/0/0 hertz=0 sound=y/fm attenuate=mid polyphony=9 wavetype=5 attack=10 sustain=10 srelease=10 orbitdelay=400 showorbit=yes colors=000zz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL000\ 0<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e00L00zz\ LzL0000<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e0\ 0L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2\ >z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzz\ ezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2\ >0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL0zL0cc\ c<24>ccc<4>ccc00L00e00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzze } Fugue_on_y_minor { ; copyright (c) Bill Jemison 1999 ; Fractal Tone-Poem ; OPL3 (most SB compatibles - NOT SBLive!) ; add Concert Hall reverb if possible ; must use 1024x768x256 video mode reset=2000 type=mandel passes=d video=SF7 center-mag=-0.21515300000000000/+0.64304200000000000/1354.084/0.1539/-7.\ 496/-51.993 params=0/0 float=y maxiter=1000 fillcolor=0 inside=0 outside=0 viewwindows=19/0.75/yes/0/0 cyclerange=1/1 hertz=50 sound=y/fm/quant polyphony=2 wavetype=7 attack=3 decay=5 sustain=15 srelease=8 scalemap=1/4/8/1/1/8/4/1/4/1/8/12 orbitdelay=1500 showorbit=yes colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzzzLzzz000555<3>HHHKKKOO\ O<3>ccchhhmmmssszzz00z<3>z0z<3>z00<3>zz0<3>0z0<3>0zz<2>0GzVVz<3>zVz<3>zV\ V<3>zzV<3>VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3>hzh<3>hzz<2>hlz00S<3>S0\ S<3>S00<3>SS0<3>0S0<3>0SS<2>07SEES<3>SES<3>SEE<3>SSE<3>ESE<3>ESS<2>EHSKK\ S<2>QKSSKSSKQSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS00G<3>G0G<3\ >G00<3>GG0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG8AG88G\ 8<2>8GE8GG8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>BGFBG\ GBFGBDGBCG000<6>000 } Lotus {; copyright (c) Bill Jemison 2000 ; Fractal Tone-Poem ; OPL3 (most SB compatibles - NOT SBLive!) ; add Concert Hall reverb if possible reset=2000 type=threeply passes=1 video=SF7 center-mag=-25.6682/-4.28027/0.001124723/0.4739/-85/-55.646 params=-55/-1/-42 float=y maxiter=49 viewwindows=1/0.75/yes/0/0 hertz=-50 sound=y/fm attenuate=mid polyphony=9 attack=8 decay=5 sustain=14 srelease=10 orbitdelay=1000 showorbit=yes colors=0000Lz0ez0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e0\ 0L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2\ >z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzz\ ezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2\ >0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<2\ >00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL\ 0000<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e00L0\ 0zzLzL0zL0<25>C4HA4H83I<2>21K00L00e00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<\ 2>00z } Pod_Racers { ; Copyright (c) Bill Jemison [70400,2537] 1999 ; Fractal Tone-Poem ; OPL3 (most SB compatibles - NOT SBLive!) ; add Concert Hall reverb if possible reset=2000 type=mandelcloud passes=1 center-mag=-0.5/0/0.6666667 params=50 float=y maxiter=500 viewwindows=12/0.75/yes/0/0 hertz=512 sound=x/pc/fm polyphony=3 wavetype=1 decay=8 sustain=14 srelease=10 orbitdelay=1000 showorbit=yes } Nocturn { ; copyright (c) Bill Jemison 1999 ; Fractal Tone-Poem ; add Concert Hall reverb if possible ; must use 640x480x256 video mode reset=2000 type=mandel passes=d video=SF5 center-mag=-0.215153/0.643042/1354.077/0.1539/-7.499/-51.994 params=0/0 maxiter=1000 fillcolor=0 inside=0 outside=0 viewwindows=19/0.75/yes/0/0 hertz=0 sound=x/fm/quant polyphony=8 wavetype=4 scalemap=1/4/8/1/1/8/4/1/4/1/8/12 orbitdelay=4000 showorbit=yes colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzzzLzzz000555<3>HHHKKKOO\ O<3>ccchhhmmmssszzz00z<3>z0z<3>z00<3>zz0<3>0z0<3>0zz<2>0GzVVz<3>zVz<3>zV\ V<3>zzV<3>VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3>hzh<3>hzz<2>hlz00S<3>S0\ S<3>S00<3>SS0<3>0S0<3>0SS<2>07SEES<3>SES<3>SEE<3>SSE<3>ESE<3>ESS<2>EHSKK\ S<2>QKSSKSSKQSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS00G<3>G0G<3\ >G00<3>GG0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG8AG88G\ 8<2>8GE8GG8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>BGFBG\ GBFGBDGBCG000<6>000 } Rainforest { ; copyright (c) Bill Jemison 2000 ver=20 ; Fractal Tone-Poem ; OPL3 (most SB compatibles - NOT SBLive!) ; add Concert Hall reverb if possible ; requires 1280x1024 res...use diskvideo if necessary reset=2000 type=formula formulafile=1c3145.par formulaname=carr3145 passes=1 video=SF9 center-mag=-0.00150344575698622/-0.29691627188504780/823280.3/1/139.999 params=200/300/400/550 float=y maxiter=647 symmetry=none periodicity=0 viewwindows=2/0.75/yes/0/0 hertz=0 sound=x/fm orbitdelay=400 showorbit=yes colors=000000<3>C04005I06<3>U0B<3>i04m02m68<3>pUWq_asee<3>zzs<3>alGWi6Vg\ 6<3>T_8SY9SW9<3>POBGI87B56AA<3>152040AAG<2>0Qc<5>5Zf6`g7ag<3>BhiBjjClk<2\ >Fpl<3>jvqrwrzyt<3>zsZyqUyoOynJylDxj2wiK<3>vc4ua0ub3<3>vhJviNvjPwkR<2>xo\ a0qe<11>cQTfOSjLQ<3>wCM<3>bADXABS99M96H84<6>872772672<2>160<5>572672772<\ 3>A93B94C94DA5EA4FB3PG3<3>jY1ob1uf0zk0<3>0kk<2>WgD<3>CXF<3>GVEHUEITEJTDK\ SDLSDMRCOQBORA<3>OH7OE6NB5<4>YH8_I9aJ9cKAeLAhMB<3>mTInVJpYH<2>vdByg8yh5y\ i3<3>ya4y_4yY4<3>yR4yQ5yO5<3>zG6zE6uH8qKBlNDgQFeNDbJA<12>F73 } frm:Carr3145(YAXIS){;Modified Sylvie Gallet frm. [101324,3444],1996 ; passes=1 needs to be used with this PHC formula. ; Converted to IF..RLSE logic by Sylvie Gallet, 11/30/97 pixel = -abs(real(pixel)) + flip(imag(pixel)) c0 = (-0.7456,-0.132) - 0.0025/pixel if (whitesq) c = (-0.0466,-0.00825) + c0 z = zorig = |pixel|*pixel*pixel + conj(0.10/pixel) else c = (0.0466,0.00825) + c0 z = zorig = - sqr(|pixel|*pixel*pixel + conj(0.10/pixel)) endif imagp1 = imag(p1) , imagp2 = imag(p2) , bailout = 16 , iter = 0 : if (iter == p1) z = 0 , c = 0.09375*cabs(zorig) + c0 elseif (iter == imagp1) z = 0 , c = 0.140625*conj(zorig) + c0 elseif (iter == p2) z = 0 , c = 0.2109375*flip(zorig) + c0 elseif (iter == imagp2) z = 0 , c = 0.6328125*abs(zorig) + c0 endif iter = iter + 1 z = z*z + c |z| <= bailout } Waterfall { ; Copyright (c) Bill Jemison [70400,2537] 1999 ; Fractal Tone-Poem ; OPL3 (most SB compatibles - NOT SBLive!) ; add Concert Hall reverb if possible reset=2000 type=chip passes=1 video=SF7 center-mag=0/0/0.001754386 params=-15/-19/1 float=y viewwindows=12/0.75/yes/0/0 hertz=-100 sound=x/fm/quant polyphony=3 decay=8 sustain=14 srelease=10 scalemap=1/3/5/6/8/10/12/1/3/5/8/10 orbitdelay=1000 showorbit=yes *********************************************

2 1

FOTD 14-08-02 (Superstrings [6])
by Jim Muth 14 Aug '02

14 Aug '02

FOTD -- August 14, 2002 (Rating 6) Fractal visionaries and enthusiasts: Today's fractal, which illustrates a scene in the fractal created by the formula Z^(1.15)+C, reminds me of superstrings, those theoretical infinitesimal multi-dimensional abstractions that we hope will help us find the theory of (almost) every- thing. Thus, I named the image "Superstrings". The resemblance of the twisting filaments in the image to actual superstrings is a total fantasy on my part. Actual superstrings would be so far removed from the intuitive world of everyday ex- perience that they would not have the attribute known as appear- ance. Nor would they have color or any of the other attributes that make the world we live in so familiar. The actual strings, if they exist, would twist and vibrate in a space of 10 or 26 dimensions. And of course, if the strings were ever actually found, and the super-math made to add up, the question of what the strings are composed of would immediately arise. Consider- ing this last question, I suspect that a successful theory of (almost) everything is safely out of reach. Turning to the fractal image of the day, the midget at the center lies on a grossly enlongated, wildly twisting filament extending from the parent fractal. The abundance of filaments surrounding the midget is a result of the many branch-cuts and discontinuities. Calculated at such a low power of Z, the actual shape of the midget is oval, with only the slightest hint of buds -- a shape that mirrors the shape of the parent fractal. The borders of the midget consist of fragments of the most bizarre kind, but in this close-in area the calculation time becomes unacceptably long. If I find a few spare hours, I might do some exploring around the edges of the midget, but don't hold your breath waiting. Perhaps the most satisfactory aspect of today's image is its speedy render time. The image requires only 1-1/2 minutes to render in its full glory from the attached parameter file at SF5 resolution. SF6 resolution takes only 2-1/2 minutes, and the higher resolutions, proportionally longer. For those for whom rendering fractals is not a cup of tea, the image will soon be posted to the FOTD web sites of Paul and Scott. Paul's site is at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's site is at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Tuesday here at fractal HQ was hazy, hot and humid, with not a hint of a breeze. After all, it is the hottest time of the year, so why shouldn't it be 100F 38C. The dynamic fractal duo passed the day in the coolest location they could find -- plopped on the tile of the bathroom floor. They stirred only to fill their empty stomachs. It's going to be hot again tomorrow, so the day will likely be a repeat of today. But at least the work will be lighter. Until next time, on Friday the 16th, take care, and work on those extra dimensions. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Superstrings { ; time=0:01:39.86--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-10.13707406873212000/+17.3412503504878\ 6000/6814.379 params=1.15/0/50.65/1500 float=y maxiter=600 inside=0 logmap=44 periodicity=10 colors=000QOiGMc6LY0LT4JODJJMIDTI9aI4jG0sG0zG0z_0z\ rAzlDvgFscGo_JlTLgPMdLP`GQYCSVGTSJVPMXMPYJT_IX_F_`\ Caa9fc6id3lf1of4ld6jc7ia9gaAf`Cd_Dc_FaYI`XJ_XLYVMX\ TOVTPTSQSQSQQTPPVOOXMMYLL_JJ_IJ`GIaFGcDFdCDfACfAC`\ 7FX6IS4LO3OI1QD0T90X40_00`00a00a03c04c06d09d0Af0Cf\ 0Fg0Gg0Ii0Li0Mj0OjAVcJaYSiSapMjxGszArxGprMplQofXm`\ amVfMIu04zD7uV9gjAV0zoVjVzVCzY7z_4ya0uc0rf0og0g0z_\ 0zS0zJ0zC1x33v04u04s69XC3YI0_M0`Q0VT6PXCJ_IDcO7fT1\ i_0ld0fc0aa4Y`CT_IOYOJXVFV`AVfS_Oga4xd0og0gj0_m0Sp\ 0Ls4Cv74yC0zF6mQDa`MPlTDv`1z_9zYFzXLzVQzTYzSczQizQ\ ozXcz`SzdGzi4zm0zo3zoCzpMzpVzpczfozXyzMzzTvz_jzd_z\ lOzrCzx0zPTz0vz0lz0cz0Tz3Lz4Cz6Jz6Qz_Sz`PzaMzaJzcG\ zcDzdAzd9z`6zX4zS1zO0zJ0zF0zA0z60z43z4Dz4Oz4Yz4gz4\ pz3pz3rz1rz1rz1sz0sz0uz0uz0uz0vz0vz0vz0yz0xz0xz0yz\ 0yz0yz0zz0zz0zz0zz0zz0zz0zz07z0Iz0Sz0`z0jz0uzzJzzL\ zzMzyOzvPzuPzsQzpSzoTzmVz } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] FOTD 08-08-02 (Odd Mandelbrot [5])
by Jim Muth 13 Aug '02

13 Aug '02

Morgan Owens wrote: >You know (you should, I think I pointed this >out last time) that (a) people not on the >philofractal list won't see the reply, and... I consider the science-religion conflict to be off-topic on this list. Those who wish to see the reply, which is the introduction to a book about the conflict, should go to the philo- fractal list, where such wisdom (or blather) is right on topic. >...(b) people on the philofractal list don't >need the announcement. Which is why I posted it only to the Fractint list. Jim M.

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FOTD 12-08-02 (The Richest Fractal [7])
by Jim Muth 12 Aug '02

12 Aug '02

FOTD -- August 12, 2002 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal image, which rates a 7, is named "The Richest Fractal". Yes, I realize that the Mandelbrot set is in all likelihood the overall richest fractal, but in the M-set (and the Julia sets) it is not possible to illustrate much of the overall variety in a single image. However, in today's image, which is a scene in a valley of the Z^1.555+C Mandelbrot fractal, much of the variety does appear in a single picture. This is possible because the branch cuts have thoroughly scrambled the original fractal into an omelet of which today's image is a small sample. As is almost always the case in my FOTD fractals, there is a midget at the center. And there are midgets also lurking near the top and bottom of the image. This abundance of midgets is quite unusual in this exponent range, and, combined with the overall variety, makes the image one of the richest of all time. The rating of 7 might be a bit liberal, but a liberal view makes one feel better, so a rating of 7 it is. Enjoy the fractal scene! The render time on my tired old P200 machine is 9 minutes. On a state-of-the-art screamer it will be notably less, but not 1/10th the time. Apparently, the screaming machines with 10 times the cycles per second do less fractal calculation on each cycle. The wait-to-see can be reduced even further by visiting the web site of Paul at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or of Scott at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> and downloading the completed GIF image from there. But allow a few minutes for the image to be posted before visiting. The fractal weather Sunday here at Fractal Central was typical summer fare, with hazy sunshine, a temperature of 93F 34C, and moderately high humidity. The dynamic fractal duo passed the day alternating between the cool indoors and the rather uncomfortable (for humans) outdoors. As for this human, he's about ready to pass the day changing the work to be done into work done. The task will take about 6 hours, so until next time, which will be on the 14th, take care, and keep searching. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ TheRichestFractal { ; time=0:09:15.03--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=+0.66148150361188480/+0.368251074896650\ 90/798.3305/1/107.5/2.71022093656370089e-012 params=1.555/0/-4.64/0 float=y maxiter=8000 inside=0 logmap=110 periodicity=10 colors=000wMUtLTqKToKSlJSjJRgIRdIQbHQ`DNaHQbLSbPUd\ SXeWZg_`ibckfeljgnmjoqlqunrxpstnsplsljshhsdgs`esXc\ tUatQ_tMZtIXtEVtATt6Ru2Rt3Qs3Pr3Or3Oq3Np3Mo4Lo4Ln4\ Km4JlGIoIDlKIiMMfOQcQVbSZcUadWeeYhf_kganhcqietjgwi\ fugdsfcqdboc`ma_k`Zh_XfYWdXVbVT`USZSRXRPVQOSONQNLO\ LKMKJKIHIHGGGFEKIKOKPRMUVPZZRdaTieWniYshGyl_xtwyps\ wmpujmtgjrdfpacoZ`mWYkTVjQRhNOfKLeHIcCDcEFbGGbHHbJ\ IaLKaMLaOM`QN`RP`TQ`VR_WS_YU__VZ`WZbXZdZYe_Yg`Ymc_\ haYc_WZYVUWTQUSLSQGQPBON7RM9UUAa`8leBhgDehFbiHZjJW\ kLTmNPnPMgRJeUFhTGqSGqRHrRHrQIsPItPJtOJtNKuNKuMLvL\ LvLMwKMwJNxHMzJNxKOwLPvMQuNQtORrPSqQTpRUoSUnTVmUWk\ VXjWXiXYhYZgZ_f_`d``caabbbacc`dc_edZeeZffZggYhgYih\ XjiXkjXlkWmlWnmVonVnoWonVonUonTonSonRpnRpnQpnPpnOp\ nNqnNqnMqnLqnKqnJrmJrmIrmHrmGrmFsmFsmEsmDsmCsmBtmB\ tmAtm9tm8tm7tm7sl9rlBqlDpkFpkHokJnjLmjNljPliRkiTji\ VihXhhZggahh`hi`hj`ik_il_ } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] FOTD 08-08-02 (Odd Mandelbrot [5])
by Jim Muth 12 Aug '02

12 Aug '02

At 12:31 AM 8/12/02 +1200, you wrote: >I'm not the one who said there was a [science-religion] >conflict. I'm the one who keeps pointing out the >narrowness of the views of those who insist on it. <snip> See my reply on the philofractal list. Jim (the narrow-minded?) Muth

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Vignette with Preamble
by Morgan L. Owens 12 Aug '02

12 Aug '02

So there I was, putting off working, one hand doing a landed fish impression on the keyboard, a coffee-cup in the other. I shifted my attention into neutral and let just whatever turn up, eyes focussed in the middle distance, coffee approaching the optimum temperature for swigging. Idly flipping over a mental loose rock, something caught my mental eye. Merely through the act of coming into the focus of my consciousness, it was immediately bolstered by the increased attention paid to it; so important to be noticed, it obviously warranted having more thought applied in fleshing it out. By the time I was consciously aware of it, it was effectively what I've written. I jotted it down. I made one or two quick passes over the result for the sake of such things as grammatical cohesiveness; and in one or two transitional points I had to add a few words so that they'd be at least vaguely referenced, rather than utterly obscured. But the detail given was all there at the time - I almost got the impression that there was a swarm of stagehands just out of shot scrambling about readying things Just In Time. (Kind of like an ad that used to be on TV for a range of printers.) While I wrote it all down at the time, some bits I only recognised (like the caramel floor) or understood (like the name) later. All this is said in apology for the condition of what follows. There's no plot or other context that serves to frame or border it - hence "vignette". Character development is basically not present. And (something which annoyed me slightly at the time) virtually no soundtrack whatsoever. I can say that the setting is "in space" (not that that narrows things down much: I'm figuring it must be interplanetary), and that the shuttle features the ellipse as a major design element. (I've just realised where I saw the main window before - Arthur C. Clarke's _Against the Fall of Night_ - only it was a video display there. So much for originality.) Oh, and why I'm posting it? Well, I flatter myself to think that it might give some people ideas for images - there are more fractals in it than meet the eye. Myself, I came up with a new kind of abstract machine that could be modelled as an n-unsigned counter machines with an unorthodox repertory of operations (and verified that it's equivalent to a Turing machine). But that reminds me: time to get back to work. Morgan L. Owens "A man is a small thing. And the night is very large and full of wonders." -{*}- There was a shaft of light shining from floor to ceiling beside the window - or was it ceiling to floor? At neither end was there any visible light source, just a bright spot as if it were the target of the beam. The real give-away of course was the fact that it violated the truism about the invisibility of light: it was able to shine with a milky glow without any assistance from anything in the air to scatter it. She figured the effect could be achieved by some sort of standing wave effect: elaborate radio-frequency fields generated at points unknown around the cabin, interfering with each other to dump all their energy into this one narrow region, harmonising to produce the visible range of frequencies. She thought she could see it wriggle slightly in response to her movements. The shaft of light spoke; well, if the builders could manage it with light, then sound shouldn't have been too much trouble. All it said was "Your destination," brightening briefly at the same time. Outside she could see what the beam was probably referring to. She tried on a few descriptive comparisons: a cartoon cloud, or a bunch of grapes with pearls instead of grapes. "K'," the shaft said. She looked at it, for lack of anything more appropriate to focus on. "Its name is K'. You are unable to pronounce it." "Kih?" "K'." "K." "K'." "K'." "K'." She gave up. They had drawn nearer. A sculpture of a bunch of grapes perhaps - sculpted in opal. The overall greyness was resolving into something less easy to characterise. The sweeps and blurs of colour gave the impression of being layered, as if the apparent surface allowed partial views into deeper parts. They were more than just sweeps and blurs, however. As the shuttle continued to approach, shifting perspectives told her that they represented elaborate structures, tangled branchings, clumps of woolly cables, (more) bunches of grapes. But nothing was so straightforward to be one particular colour, and some shifted both in response to changing angle of view and internal changes of their own. She was also gaining an idea of the size of K' - at least a dozen kilometres in length. Not all of what she saw was attached to the main body, she saw. Almost every structure was accompanied by a swarm of objects of bewildering variety, from sizes that would dwarf their shuttle (and festooned with their own elaborate structures and escorts) down to the limit of visibility. Things would attach themselves to the main body; attachments would break off and move freely. She didn't see the entrance ahead: her eyes kept snagging on one detail after another and there was too much for her to assimilate. Nevertheless, before too long she realised that their view was no longer shifting, and that the surface like a broken rockface before her, decorated with bursts of capillary piping, could be called a wall. What got her attention was the shuttle being opened. The shuttle wasn't opening. Instead, it was being swiftly dismantled around her. The shaft of light had already vanished without her noticing. Starting with the largest components in the shuttle's design, psychedelic shrubbery of various proportions and assisted by clouds of insect-like things, from the size of small birds down to gnats, would separate each part from its neighbours and then dismantle each. In some cases, the process was so thorough that pieces would effectively dissolve before her eyes into the haze of midges enveloping them. Everything seemed to ignore her as she stepped aside for the floor to be chewed up. Otherwise she wouldn't still be standing. She looked down between her feet at a string of beads that was being drawn out from somewhere underneath the shuttle. About half a metre away, a bundle of straight wires about ten centimetres long was hovering horizontally just above the floor and engaged in a rapid dance about each other. Every time a bead passed underneath one of the wires would drop down and slice it in two. The wire would return to the bundle, the two pieces of the bead would be carried away through one hole in the wall or another, and the thread on which it had been strung would be drawn further into a puckering in the floor. The wires were about the simplest things she saw there. Then without warning one of the wires leapt up out of the bundle, crumpled in on itself like a protein finding its tertiary structure, and threw itself to the floor; this extended a pseudopod and drew it in. As the pseudopod collapsed back (the wire within dissolving), ripples of density spread outwards through the floor and interfered with other ripples passing back and forth from other events in the floor (not all of them apparent). The floor itself had the appearance of glitter and grit suspended in acrylic. It was difficult to tell, given the back-and-forth swaying that was the rippling effect, but the individual flecks appeared to be moving about. She had no idea how deep it was, and nothing caught her eye that didn't demand her fullest attention. Was that a cluster of pipes down there or just a denser-than-average accumulation of grit? Now the swirl of activity developed a focus on her, though there was no specific indication to the effect. Instead, she found herself nudged and guided out of the room by passing objects, each apparently by complete accident as it raced off to carry out some far more important task, toward a short corridor lined with more of the piping that had been scattered on clumps on the wall. Here, they made up the wall. "Piping" didn't do them justice. Every pipe was thickly carbuncled with tiny opalescent stacks of thin plates of various diameters. Mites were clambering from plate to plate, trekking from stack to stack. Spindly spiders clambered above, disassembling, reassembling and shuffling whole stacks. Spots of diffuse brightness moved along the pipes, as if shining things were flowing within at different speeds and in different directions. They provided the only illumination in the corridor but it was quite sufficient, as any given tube was lit along at least half its length by these spots. Refracted sparkles from the stacks provided another layer of illumination. Out of the corner of her eye, they appeared to combine to form elaborate signs, but she couldn't parse any meaning. The corridor was only a few metres long, and she arrived in a small room. The floor was a smooth caramel hue, while the ceiling glowed softly in a shifting arrangement of colours, like coloured oils swirling on a light box. The colour of each of the walls wasn't fixed either; being one tint directly before of her, and shading into another as the angle the wall made with her gaze narrowed. Not only that, but she was sure the colours themselves were shifting up and down the spectrum, just too slowly for her to apprehend. She had already mislaid the corridor. Close up, the walls appeared to be obsessively grooved in a rectilinear labyrinth, with antlike dots of at least two different sizes crawling along in the grooves. Sometimes when two dots met, they'd both reverse directions; other times only one would do so. Larger and smaller dots could apparently pass over or through each other. In short, it was much more understated than the (shuttlebay?) she'd just left. To say that she was overwhelmed by this stage would be an extreme understatement. There was literally so much going on around her that she could feel her brains starting to leak out of her ears. Whatever she glanced at screamed its significance and activity. Sitting exhaustedly on the floor, she shook and bowed her head. She made the mistake of allowing her eyes to focus on what she was sitting on. It wasn't a single colour. Instead, it was divided up into a grid of brown and yellow squares, each roughly a millimetre on a side. She couldn't help but try and determine the pattern, but if there was one it always just barely eluded her. There was definitely one there: it was certainly not just a random arrangement of noise - she searched in vain for three consecutive brown or yellow squares (except diagonally, but even then only as part of a longer row) - but nor was there any periodicity she could put her finger on.

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Re: [Fractint] Vignette with Preamble
by Jim Muth 12 Aug '02

12 Aug '02

At 10:35 AM 8/11/02 -0700, John Wilson wrote: <snip> >...now if only Morgan could incorporate some verbal >recursion, this might constitute a new Fractal form, >requiring a different type of formula.... Computer generated prose (and poetry) created with fractal algorithms is being done. Here is a two- paragraph sample. The sentence structure is pretty much correct, but the whole thing equals nonsense. Apparently, fractals have quite a way to go before they write their first interesting short story. BEGIN FRACTAL GENERATED PROSE========== Rose, have a wide dryer. You won't shout it. If the elder tailors can converse stupidly, the smart book may measure more satellites. We sow solid frames alongside the sad outer camp, while Norman finitely answers them too. Some coconuts comb, kill, and clean. Others sneakily dine. Who creeps wistfully, when Pauline departs the cosmetic bandage in back of the hallway? Where will you order the closed noisy dusts before Terry does? Both pouring now, Russell and Ronnie help the handsome oceans brave the tight smog. Where did Harry climb at all the walnuts? We can't laugh billiards unless Ann smartly moves afterwards. Will you look at the fog, if George seemingly believes the bush? We tease the rich diet. What doesn't Russel recollect fully? To be stupid or angry will fear dry ulcers to nearly excuse. Don't mould a shirt! While weavers usably smell pools, the plates often play through the stale carpenters. END FRACTAL GENERATED PROSE============= Jim M.

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Re: [Fractint] FOTD 08-08-02 (Odd Mandelbrot [5])
by Jim Muth 11 Aug '02

11 Aug '02

At 05:11 PM 8/10/02 +1200, Morgan Owens wrote: >At 03:02 10/08/2002, John Wilson wrote: > >>Whoah! That's a real blow below the belt. I am anxiously awaiting >>replies from the mathematicians, but shouldn't this be in the Philofractal >>list?. >> >>John W. > >Perhaps, but Jim would probably complain that it's not "irrationally >mystical" enough. It's the Philofractal list after all, not the >"scientifractal" one. This topic *should* be on the philofractal list, but I suspect that Morgan no longer subscribes to that list. Can't take irrationality and mysticism, I assume. Jim M.

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Hypergeometry
by Andrew Coppin 11 Aug '02

11 Aug '02

Hi folks. I realise that this subject is perhaps *a little* off topic, but I'm posting it here in case anyone else is interested. Jim's talking about the 4th dimension got me thinking... I want to do projections and slices of 4D shapes. But I don't have the software... A while back I managed to write a program to do wireframe projections of 4D figures. It wasn't all that good really! So I sat down and wondered if I could adapt my raytracer to draw 3D slices... But today I managed to get good old POV-Ray to draw it for me! Just took a bit of algebra shifting! A hypercube is the intersection of 8 hyperplanes. Each one is given by ax + by + cz + dw - e <= 0. To convert these into standard POVRay planes (ax + by + cz - f <= 0), just select a value for W, then f = dW + e. Now do a CSG intersection of all 8 planes and bob's your uncle! (Actually my uncle's name is John, but hey...) As I type this I'm doing some animations of various slices. This is where I need some help... I can get the slices to look like ordinary cubes (which vanish/appear at certain W values), but that's not vary exciting. If you cut a normal cube across a corner, you get a triangular section (rather than square). I managed to get a prism-shaped cross section out of my hypercube (by doing a 45 degree YW rotation), but how do I rotate the hypercube so that one of its corners faces along the W axis? (The hypercube starts out aligned to the coordinate axies.) Secondly, what other interesting 4D polyhedrons (?!) are there, and how do I construct them? Thanks folks! Andrew. PS. I say again, if anyone wants to see the POVRay files or just chat about the math, feel free to email me off list (or on list if enough people are interested...) PPS. I'd love to post pictures, but A) no binaries on a mailing list, and B) the animations are a tad TOO BIG to be emailing around anyway! _________________________________________________________________ Send and receive Hotmail on your mobile device: http://mobile.msn.com

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FOTD 08-08-02 (Odd Mandelbrot [5])
by Jim Muth 10 Aug '02

10 Aug '02

FOTD -- August 08, 2002 (Rating 5) Fractal visionaries and enthusiasts: Today's image is a scene in that great abstraction known as the Julibrot. The iterated formula is Z^2+C, which draws our old friend the first fractal of all, the Mandelbrot set. But the same formula also draws a horde of Julia sets, which might have come first, and though they are not as well known, a horde of perturbed Mandelbrot sets can also be drawn by the simple formula. But wait, that is not all. The Z^2+C formula also draws families of sets which have no official names, though I call them Oblate, Parabolic, Elliptic, and Rectangular sets. These six families of fractals represent the six mutually perpendicular orientations through the four-dimensional object known as the Julibrot. Yes, I realize that a four-dimensional object is an absurdity. Such an object could exist only in a space of four dimensions, and a quick glance at the world shows that there is no room for a fourth dimension. Our three familiar dimensions take up all the space that exists. If anyone doubts this, I challenge the doubter to go out to an open area and point his arm to a direction that is not one of our familiar 3-D directions. Yet, the Julibrot figure does not know that it cannot exist, because it is there and it will not go away. I know it is there because I can calculate and then see slices through it, and I can rotate those slices in most any direction I desire. Today's image for example is one of a midget on a filament in the east suburbs of the large midget at -1.75 on the negative stem of the M-set. But it does not look like a Mandelbrot midget. Nor does it look like a Julia set for that matter. In fact, it is none of the four other types of sets either. It is a nothing set -- a slice through the Julibrot at the point of the Mandelbrot midget, in a totally oblique direction. But sometimes, even nothing can be something, and today's nothing set makes a picture which contains much of the character of the Mandelbrot midget of which it is an odd slice. Because it is an odd slice of a Mandelbrot midget, I named the image "Odd Mandelbrot" The rating of a 5 seems about right, and the render time of under one minute is certainly right. As always, the completed GIF image ia available on the WWW at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Wednesday was almost perfect. The blue skies, gentle winds, and temperature of 80F 27C kept the fractal duo outdoors for a good part of the day. And when it was finally time to return indoors, they did so reluctantly. I now find myself with a moderate amount of work that needs to be done. Since it's always better to have work behind one rather than before, I'll have to get the work behind me. Until next FOTD on Aug 10, take care, and prosper. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Odd-Mandelbrot { ; time=0:00:50.09--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new center-mag=-0.00000\ 000000474777/+0.00000000001270966/3.405492e+010/0.\ 1549/64.5600772360675847/76.4411018546430654 params=45/-45/2/0/-1.746325272478873/0.00829666984\ 6033399/-1.746325272478873/0.008296669846033399 float=y maxiter=1500 inside=0 logmap=132 colors=000c83d82e82fB5gD7gG9hICiKEiNGjPIkRLkUNlWPl\ ZRm`UnaWncYod_mebkgdihfehfbg`_eTWcMI`IGZEEWACU6AS3\ HO4NK5UG6_C7f88l59i68g68e67c77a76_76Y85W85U84S84P9\ 4N93L93JA2HA2FA1DB1BB09B07B0BI2FO3JU4N_6Re7Vk8Vo8S\ jCSjCPeGNaKKXOHTSFOWCK_9Fc7Bg46k22o76kC9gHDdLG`QKX\ VNU_RQcUMhYJm`FqcCeWCUOCIGC69CM5E`1Fh3Dp4Bw5Ar4Bn4\ Ci4Ce4Da4DX4ET4EO4FK4FG4GB4G74H34H78JBBKEFMIINMLOP\ PQTSRXWT_ZUcaVgeXjhYnl_ro`urarp_ooZlnYjmXglWdkVajU\ _hTXgSUfRReQPdPMcOJbNHaML_LOYLRXLUVLXUL_SLbRLePKhO\ KkMKnLKqJKtIKwGKzFKyGMxHNwIOvJPuKQtKRsLTrMUqNVpOWo\ PXnPYnOZoNZoM_pL_pK`qJ`qHarGbrFbsEcsDctCdtBduAeu9e\ v8fv7fw7gx6hy6iz6jz6kz6lz5mz5nz5oz5pz5qz5rz4sz4tz4\ uz4vz4wz4xz3yz3zz3zz3zz3zz2zz2zz2zz2zz2zz2zz1zz1zz\ 1zz1zz1zz1zz0zz0zz0zz0zz0zz9zz8zz8zz8zz8zz7zz7zz7z\ z7zz7zz6zz6zz6zz6zz6zz5zz5zz5zzdzzczzbzz`zz_zzZzzY\ zzWzzVzzUzzSzzRzzQzzPzzNz } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 10-08-02 (Levanter [6])
by Jim Muth 10 Aug '02

10 Aug '02

FOTD -- August 10, 2002 (Rating 6) Fractal visionaries and enthusiasts: Today's image is named "Levanter". If I remember correctly, a levanter is a strong wind on the Mediterranean Sea. I have no idea why I gave today's rather harmless fractal such an unlikely name. I guess I simply liked the sound of the word. Actually, when I began trying to think of a name, my thoughts were of politics and had drifted to the Middle East. I had done a lot of thinking earlier Friday, trying to convince myself that the U.S.A. is not about ready to launch a war in the Middle East, the purpose of which would be to secure the oil fields in an effort to boost its lagging economy. I might be imagining all this neo-imperialism, but the older I get, the more I realize that the only problem with my cynicism is that I'm usually not cynical enough. Remembering my resolution never to discuss politics, I will now confine my comments to the fractal at hand. The iterated formula, Z^(10)-10(1/Z)+C, is another whimsical expression I entered into the M-Mix4 formula at random. It draws a tiny M-set far beyond the right edge of the default screen. This M-set is surrounded by even tinier cut-off M-sets, like our galaxy is surrounded by globular clusters. Today's scene, with its obviously cut-off features, reveals one of these tinier 'globular' M-sets. When calculated with the normal equal-iteration bands on the outside, today's image was dull and flat. To add a little life, I re-calculated the scene with the outside set to <tdis>, and tweaked the colors a bit. The resulting picture improved from a 4 to its current rating of a 6. Perhaps the best feature of the image is its super-rapid render time of 44 seconds. Even the download of the completed image file from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> can't beat that time. The fractal weather Friday was wonderful here at Fractal Central, with a temperature of 86F 30C, sapphire blue skies decorated with cottonpuff clouds, low humidity and a gentle breeze. The fractal duo approved heartily by actually romping in the yard a few times in between their bouts of sleeping on the porch. They are indeed in touch with their inner kittens. As for me, I'd best get in touch with the work that needs to be done. I know it's Saturday, and Saturday is supposed to be an off day, but when a job comes in on Friday afternoon and needs to be delivered Monday, it means working on the weekend, especially since the customer is paying extra for rush service. So until next time, which will arrive on the 12th, take care and for peace's sake, avoid politics. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Levanter { ; time=0:00:44.65--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+11.48064466578638/-2.778123424321501/2\ .234309e+008/1/15/-0.000284086357036986148 float=y params=1/10/-10/-1 maxiter=270 inside=0 outside=tdis colors=000MnzMmzMlzMkzMjyNixNhwNgzNfyOexOdw000MHRV\ KPbOMmQJzUHpPKlLMkHPjDRi9TaJaVSiNaqGjyMixShwYhwcgv\ ifunfuofupfupguqgurhushushuritqitpitojtnjtnjsSpmmj\ slkskksjksilsilrhlrglrfmremrdmrdnqcnqbnqanq`oq_oq_\ opZppYppXppWppVqpVqoUqoTroSroRrotvvquunutktshtsetr\ bsq_sqXrpUrojVxiWwiWwhXwhXwgYwgYvgZvfZvf_ve_ve`ue`\ udaudaucbucbucctbctbdtadtaetaes`fs`fs_gs_gsZhsZhrZ\ irYirYjrXjrXkqXkqWlqWlqVmqVmqVnpUnpUopTopTppTpoSqo\ SqoRroRro5T46U67V78W98XA9YCAYDAZFB_GC`ICaJDaLEbMEc\ OFdPGeRGeSHfUIgVJhXJiYKj_Lj`LkbMlcNmeNnfOnhPoiPpkQ\ qlRrnd36c58c69c7Ab8Bb9CbADaCEaDFaEG`FH`GI`HJ_JK_KL\ _LM_MNZNOZOPZPQYRRYSSYTTXUUXVVXWWWYXWZYW_ZV`_Va`Vb\ aVcbUecUfdUgeThfTigTjhSliSmjSnkRolRpmRqnPAIQGNQMRQ\ RVQXZRbcRggRmkD2oE3oE4oE5oE6oF7oF7oF8oF9oFAoGBoGCo\ GCoGDoHEoHFoHGoHHoHHoIIoIJoIKoILoJMoJMoJNoJOoJPoKQ\ oKRoKRoKSoKToLUoLVoLVoLWo } 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 06-08-02 (Blackberries [6])
by Jim Muth 06 Aug '02

06 Aug '02

FOTD -- August 06, 2002 (Rating 6) Fractal visionaries and enthusiasts: Fractal Central has suffered two more power failures since I posted my most recent letter. (But still the fractals keep coming.) This most recent outage was the tenth since Saturday morning. I know this to be an accurate count because every time the power cuts off and comes back on, my fax machine spits out a 5cm strip of paper. There are 10 strips now lying beside the fax machine. The local electric utility, always with a handy excuse, claims that broken trees are continuing to fall. This is well and good, except that they also advertise their professional tree- trimming program which they claim is designed to prevent such outages. The newer suburban subdivisions in the area are being constructed with the power lines underground, which does cut back on the number of outages, but this creates another problem. Fractal Central lies in a lightning-prone area, and the above- ground power grid acts as a rather effective, if unintentional, lightning rod. After almost every lightning storm, there is news of one or more of these new high-priced houses in one of these new subdivisions without overhead power lines being struck by lightning and set afire. I guess I'd rather have a few power outages per year than have my house burn down. And finally, what ever happened to those old-fashioned but effective lightning rods on the rooftops? As for today's fractal, I entered a lot of ones into the M-Mix4 formula and came up with a basket of blackberries. The fractal berries actually have me hungry. Not surprisingly, I named the image "Blackberries". It's an acceptable image, maybe a little above average. As such, it was rated a liberal 6. Spending 39 minutes to render a single 6-rated fractal is a bit much to expect of even the most avid fractalist. For increased happiness, I suggest a download of the completed GIF image file from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Monday here at Fractal Central was hot and humid, with a temperature of 95F 35C, which was just hot enough to keep the dynamic duo confined to quarters. In the evening a light shower passed over, followed by a cooling breeze to make the evening end pleasantly. Today promises to continue the cooling trend, but before I can enjoy the pleasant conditions, I must finish some work, while hoping the power stays on. And before I finish, I must begin. So until next time, (on the 8th), take care, and strive for perfection. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Blackberries { ; time=0:39:01.75--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.13984727490430700/+1.592634280290241\ 00/1.003849e+007/1/-127.499999891903641/-2.5538621\ 2705266402e-007 params=1/1/-1/-1/0.1/0 float=y maxiter=5000 inside=0 logmap=675 periodicity=10 colors=000QKibWCaZD``E_cFZeGYhHXkIWmJVpKUsLTuMSxNR\ zNOuMLqMIlMGhMDcMA_M8VM5RM2MM0IM2HP4GR5FT7EV8DXACZ\ BB`DAbF9dG8fI7hJ6jL5lM4nO3pP3rSFnUQjXagZlc`w`ctafq\ ahoaefdcYg`PjZHmMzTRuRWqP_lNdhMhcKm_IqWHoZLnaPmcTl\ fXji`ikdhnhgpkiojkoimoioohqohsoguogwofxoftmepkdljc\ hhbdgaae`Yd_UbZQ`YM_XJYWFXVBVU7UT3SS0RS2QT4QT6QT8Q\ TAQTCQTEQTGQTIQTKQTMQTOQTQQTSQTUQTVQTXURYXQ_`OadMb\ gKdkIfoGgrEivCjyBRmzQkyQixPhwPfvOduOctNasN`rNZqMXp\ MWoLUnLSmKRlKPkKOkLMjLLiLKhLJhLIgLGfLFeLEeLDdLCcLB\ cNEbOGaPI`QK_RMZSOYUQXVSWWUWXXVYZUZ`T`bSadRbfQchPd\ jOelOcjNahM_gLYeKWdJUbIS`HQ_GOYFNXELVDJTCHSBFQADP9\ BN89L77K65I54H45G65G76G96GA7GC7FD8FF8FG8FI9FJ9ELAE\ MAEOBEPBERBESEFTHFTKGTNGUQHUTHUWHUXJWXKXXLZYN_YO`Y\ PbYQcZSdZTfZUgZVh_Xj_Yk_Zm``n`ao`bq`craesafuagvahw\ djsflohnkjpglrcnt_pvXmwYjwYhwYewYcwY`xYYxYWxYTxYRx\ YOyYLyYJyYGyYEyYIsZMmZPh_ } 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: RE: [Fractint] FOTD 04-08-02 (Screw Propeller [5])
by harrybissell＠prodigy.net 06 Aug '02

06 Aug '02

Downed power line OFTEN lay on the ground sparking... The sparks may only be 10's of amps and the conductuctors are good for hundreds or thousands of amps... so there is little chance of a breaker trip unless the wires contack each other. The power supply will happily arc for days. I had a downed power line in my backyard... slowly sawing (arcing) its way through a large tree. When I called the utility... they said "Call us back when its sawing through a HOUSE.... <click>" Guess they had more important calls to make :^P ??? Harry Bissell <resume lurk> --------Original Message-------- From: schamber(a)uwm.edu To: <fractint(a)mailman.xmission.com> Sent: Aug 5 2002 08:57 Subject: RE: [Fractint] FOTD 04-08-02 (Screw Propeller [5]) >I, too, have seen a live wire on the ground. It was particularly distressing >because at the time I was living in a community house (13 people) and there >were people coming and going at all hours and no way to warn the people >coming home that the back door, which was used most often, wasn't >particulary safe. Also the power company didn't seem too disturbed by >imminent electrocution. Luckily no one was hurt. >============================================ >Deborah Schamber >UW System Institute on Race & Ethnicity >-----Original Message----- >At 14:26 05/08/2002, JimMuth(a)aol.com wrote: >>After a day without power and a live wire sparking and >>sputtering on the ground in the alley beside Fractal central, >That's something I've never understood - if that's a power line you're >referring to then in this country such an insult to the supply would cause >a circuit breaker to jump out and the whole line would've gone dead (and >the line company would be alerted). You just don't see live wires sparking >and sputtering on the ground - after all, that represents lost revenue to >the line company. >Morgan L. Owens >"Safety regulations alone demand it." >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Powered by Wild On Web: Free POP Mail Access - Access your E-mail from Anywhere in the World! http://www.wildonweb.com |Awards|Money|Bank|Credit|Dating|Games|Jokes|Vitamins|Magazines|Diet| |Bookstore|News|Babies|Cards|Homepages|Hobbies|...

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FOTD 04-08-02 (Screw Propeller [5])
by JimMuth＠aol.com 05 Aug '02

05 Aug '02

FOTD -- August 04, 2002 (Rating 5) Fractal visionaries and enthusiasts: After a day without power and a live wire sparking and sputtering on the ground in the alley beside Fractal central, the local electric utility has finally repaired the situation, and things are back to normal. (I wrote the above paragraph around 11am this morning, when I assumed things were under control. Unfortunately, the power went off again before I could post the FOTD, and just now, 10:15pm, has come back on for good . . . I hope.) With no time to search for an outstanding fractal, I had to settle on a run-of-the-mill high-iteration midget located in a remote valley of the Mandelbrot set. I named the image "Screw Propeller". I gave it this name because the elements around the midget remind me of a ship's propeller, and not as an insult to some imaginary fellow named 'propeller'. Since the scene is in the classic M-set, and the midget happens to be the first one I came to, I have rated the picture a perfectly average 5. The only really unusual feature of the image is the high maxiter of 100,000 and the logmap setting of over 13,000. Since its magnitude is still within the range of conventional math, the image renders in 10 minutes. The image will download from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> in even less time however. The fractal weather Saturday started with a violent thunder- storm with 80mph (130kph) winds, over 4 inches (10cm) of rain in one hour, hail and continuous lightning. Trees fell everywhere. The day then continued with heat, humidity and additional but less violent storms. The 95F 35C heat and thunder kept the fractal duo of cats confined to the indoors. The power failure that ensued when a tree across the alley fell on power lines kept me from fractalling and left me with no excuse to escape the task of cutting and collecting the fallen tree limbs that cluttered the front lawn. Today is just as hot, but at least no more storms are in sight. Until the next time on August 06, take care, and fractals may be the answer, but first one must know the question. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Screw_Propeller { ; time=0:10:59.00--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-0.22509332273260120/+0.758019130508034\ 70/1.25732e+010/1/14.9999752295271485/1.9313561407\ 1707207e-005 params=0/0 float=y maxiter=100000 bailout=6 inside=0 logmap=13255 periodicity=10 colors=000cvzq0Sq0Sq1Sq1Up1Vo1Xo1Zn1_n1am1cm1dl1fl\ 1hk1ik1kj1mj1ni1pi1qj3oj4mj6kj7jj9hjAfkBdkDckEakG_\ kHYkIXkKVlLTlNRlOQlPOlRMlSKlUJmVHmWFmYDmZCm`Ama8na\ 6mb7mb8lb8lb9kb9kbAjbAjbBibCibChbDhbDgbEgbEfbFfbFe\ bGebHdbHdbIdbIcbJcbJbbKbbKabLabM`bM`bN_bN_cOZcOZcP\ YcPYcQXcRXcRWcSWcSVcTVcTVcUUcUUcVTcWTcWScXScXRcYRc\ YQcZQcZPc_Pc`Oc`OcaNcaNcbMcbMccMccLaaL``L__LZZLYYL\ XXLWWKUUKTTKSSKRRKQQKPPKOOJMMJLLJKKJJJJIIJHHJGGIEE\ IDDICCIBBIAAI99I88H56I77I87J97JA7KB7KD7LE7LF7MG7MH\ 7NJ7NK7OL8OM8PN8PO8QQ8QR8RS8RT8SU8SW8TX8TY8UZ9U_9V\ `9Vb9Wc9Wd9Xe9Xf9Yh9Yi9Zj9Zk9_lA_mA`oA`pAaqAarAbsA\ buAcvAcwAdxAdyAdzAcu9cp9cl8cg8cc7cZ7cU7cQ6cL6cH5cC\ 5c85d98eABeBDfCGfDIgELhFNhGQiHSiIVjJXkK_kLalMdlNfm\ OinOlmPlmPmmQnmQomRplRqlSrlSslStlTulTvkUwkUxkVykVz\ kVzkWzjWzjXzjXzjYzjYzjYziZziZzi_zi_zi`zjazkbzlczmc\ zmczmczmczmczmczmczmczmcz } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 04-08
by Jim Muth 05 Aug '02

05 Aug '02

At 02:46 PM 8/5/02 +1200, Morgan Owens wrote: >That's something I've never understood - if >that's a power line you're referring to then >in this country such an insult to the supply >would cause a circuit breaker to jump out and >the whole line would've gone dead (and the line >company would be alerted). You just don't see >live wires sparking and sputtering on the >ground - after all, that represents lost >revenue to the line company. It was a live 4,500 volt power line sparking and smoking, not actually on the ground, but tangled in the tree which had pulled it down. I suppose the downed line was not grounded solidly enough to trip the breaker. But it was a curious sight as different parts of the fallen tree smoked and burst into flame as the current arced across the breaks in the wood. We first called the fire department, but when the company arrived they said they could do nothing about live wires. They notified the power company, which already had been notified six times. But since over 100,000 lost power in the storm, the power company was overwhelmed. It was 16 hours before the crew finally reached the scene, cut up the tree, restrung the wire and moved on to the next job. Just to keep this on topic, the lightning during the storm traced lovely fractal patterns in the sky. Jim (the enlightened) Muth

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Alibi for a late FOTD
by JimMuth＠aol.com 04 Aug '02

04 Aug '02

Due to another (no kidding) power failure at Fractal Central, the FOTD for August 4 will appear ASAP. (As Soon As Possible.) Jim (in the dark) Muth

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Fwd: Re: [Fractint] Volumetric Fractals, Julia and Mandelbrot mysteries
by Morgan L. Owens 04 Aug '02

04 Aug '02

> >This isn't from the post you're thinking of - I just lifted it from a >private email I sent in April 2000: > > >Evolution mode options: >Evolution mode: yes (of course) >Image grid size: 15 >Grout: no > >Tweak central: >Param 1 real: x >Param 1 imag: y >the rest: no Because one can't (couldn't?) save evolver screens as .pars, it had to be saved as a .gif instead. (The type was "julia", randomness was of course turned off). >I've just started wondering what would happen a formula is written to >allow a displacement parameter à la lyamandel/hypercomplex, so that some >point other than the centre of the Julia set is centred on the Julia's box. Or just use the image coordinate settings :) Any reason why the evolver's grid size might be limited to 51? >Morgan L. Owens "3*17?"

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Re: [Fractint] Volumetric Fractals, Julia and Mandelbrot mysteries (and a few railways)
by Morgan L. Owens 03 Aug '02

03 Aug '02

> At 02:39 02/08/2002, geoff stanton wrote: > >> I'm mostly interested in 3D graphics, surround sound and model >railways. > > >Fractal railways!! Now there's a project I'd love. Yes! With their dimensionality determined by boxcar counting! Morgan L. Owens "And with plenty of critical points."

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Re: [Fractint] Volumetric Fractals, Julia and Mandelbrot mysteries
by Franktal Gallery 03 Aug '02

03 Aug '02

>>>http://mschreier.tripod.com/ Marc, very interesting page... >From your page : "The Mandelbrot set is an index for Julia sets, but now it was demonstrated the Mandelbrot set is in fact a picture made of Julia sets. I swear, I didn't take a mosaic application to use Julias matching the Mandelbrot, all of it was done buy pure calculation using Fractint!!!" Yeah, we believe you ! ;-) >>>http://mschreier.tripod.com/english/jam/pic/julia_band2d.png This can be also achieved with Fractint, by using the evolver feature. I don't have it installed right now, but I remember a post a while ago with the specific instructions to get a picture just like that one. Somebody in the list will probably find out the required evolver settings, in a matter of microseconds. Best regards, Miguel Fliguer - Buenos Aires, Argentina Franktal Gallery - http://www.geocities.com/franktal2002 >From: "Marc Schreier" <marc.schreier(a)gmx.de> >Reply-To: fractint(a)mailman.xmission.com >To: <fractint(a)mailman.xmission.com> >Subject: [Fractint] Volumetric Fractals, Julia and Mandelbrot mysteries >Date: Wed, 31 Jul 2002 22:41:41 +0200 > >Dear Fractint users, > >Ever wanted to see fractals in 3D? Then use Fractint's built in stereo >support. >But there is an interesting alternative: volume rendering!!! >A friend of mine is working with volumes in his PhD thesis and I did some >nice datasets just for fun - and to explore fractals in a very different >way. >While my computer calculated lots of Julia sets I also discovered a >surprising >phenomena, but see yourself :) >You are welcome to visit my latest work, the "Julia and Mandelbrot" page, >at http://mschreier.tripod.com/ > >To my person: > >Actually I'm living in south of Germany, I'm working for a local >car supplier compagny, and just got the MSc in Distributed Computing >Systems Engineering at the Brunel University (Uxbridge, West London). >I was exploring fractals since 20 years, first on the good old C64 >(remember the Mandelbrot renderer that used also the 1541 floppy CPU?), >then with Fractx86 and later with Fractint. >I'm mostly interested in 3D graphics, surround sound and model railways. > >Best regards > >Marc > >--------------- >JX-8P Resource Center >http://www.synthzone.com/~mschreier/ >--------------- > > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint _________________________________________________________________ MSN Photos is the easiest way to share and print your photos: http://photos.msn.com/support/worldwide.aspx

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FOTD 02-08-02 (Twirling Banners [6])
by Jim Muth 02 Aug '02

02 Aug '02

FOTD -- August 02, 2002 (Rating 6) Fractal visionaries and enthusiasts: At first glance, today's image looks like an exotic midget created by the MandelbrotMix4 formula, but it is not. The image, with it's almost-disconnected appearance, is actually a scene in our faithful old friend, the Mandelbrot set. The scene is located deep on a filament in the northeast suburbs of the large midget on the negative stem of the M-set. The exact location can be found in a few seconds by outzooming. As one backs out, the magnitude soon falls within the range of conventional math, so the trip back to the surface is a fast one. Today's scene almost appears disconnected, but it is not. All parts of the Mandelbrot set, including the midgets and the elements around them, are connected to the main body of the set. The shoreline of every midget and the main body as well is a single unit. True, the connection is often made by an infinitesimally thin filament, but the connection is there. By comparison, many fractals created by the MandelbrotMix4 formula are not connected. In these fractals, there frequently is no main body, but only a cloud of fractal debris scattered around the area like ejecta around an explosion. And like at the scene of an explosion, isolated bits of debris are often found far from the center, totally disconnected from the rest of the fractal. I named today's definitely connected fractal "Twirling Banners" when I was reminded of synchronized gymnasts twirling their banners. If it were not part of the M-set, today's image might have rated a 7. As it is, a rating of a slightly-above-average 6 will have to suffice. Since the image is in the magnitude range where arbitrary precision math is required, it takes over 22 minutes to render on my P200 machine. A download of the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> will be considerably faster. The weather Thursday here at Fractal Central was of the typical high-summer variety -- a temperature of 97F 36C, blazing sun, high humidity, and light winds. In the evening, thunder clouds developed on the horizon, but never moved in. These conditions kept the fractal cats confined to the cool indoors through the afternoon. In the evening, when the sun sank low and they finally did venture outdoors, the local catbird began annoying them, apparently aware that their bird-catching days are nearly finished. And now it's Friday morning -- another hot day -- and I've got a pile of work to finish. It's time to reconfigure the fractal shoppe into a workroom and get busy. Until next FOTD on the 4th of August, take care, and fractals are too complex to be natural, yet they are not artifacts. So what are they? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Twirling_Banners { ; time=0:22:51.60--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-1.74644456175032895642/0.0051806197286\ 35784144/3.752443e+015/1/-122.5/3.8857805861880478\ 9e-016 params=0/0 float=y maxiter=6000 bailout=8 inside=0 symmetry=none periodicity=10 sound=off colors=000ho_eoXcoU`nQZnNZqNXnKWdHVVFUTFUSFURFUQFU\ PFUOFTNFTMFTKFTJFTIFTHFTGFSFFSEFSDFSCFSAFS9FR8FR7F\ R6FR5FR4FR3FR2FV5KY8O00000000000000000000000000000\ 0000000J0IJHFIEBIB8I84I51K66M7BN8GP8KQ9PSAUUBZVBdX\ CiYDn_Er`Et`Hr`Ko`Nl`Pj`Sg`Vd`Xa`__`bX`dU`gR`jP`lM\ `oJ`rG`tEVfDQTDKFDF2DH4CI6CJ8CKABLCBNEBOGBPIAQKARM\ ATO9UQ9VS9WU9XW8ZY8__8`a7ac7be7dj5cg7cd8cbAc_BcYDc\ VEbSGbQHbNJbLKbIMcENbGNaINaJN`LN`MN_ON_PNZRNZSNYUN\ YVNXXNXYNW_NW`NYbN_cNaeNcfNfhNiiNmkNplNpnNuoNzqNzr\ NzpMpoLjnKdmKalJajIbiIbhHcgGdfGfdFgcEibEjaDl`Cm_Cl\ aGkcKjdOifShhWhi_gkcfmgenkdpocrscswanp`iiZdcY_XWVR\ VQKXIBULESNGQQIOSLMUNKXPIZSGaUEcWCeZAh`8jb6ld8jcAi\ bChaDg`Ff_HeZIdYKcXMbWNaVP`UR_TSZSUYRWXQXWPZVO`UNb\ TMcSLeRKgQJhPIjOHlNGmMFoLEqKDrJCtIBvHAwG9vFBuFDtEE\ sEGrDHqDJpCLoCMnBOmBPlBRkATjAUi9Wh9Xg8Zf8`e7ad7cc7\ dd8cd9be9aeA`fA_fBZgBZgCY } END PARAMETER FILE=========================================

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Volumetric Fractals, Julia and Mandelbrot mysteries
by Marc Schreier 01 Aug '02

01 Aug '02

Dear Fractint users, Ever wanted to see fractals in 3D? Then use Fractint's built in stereo support. But there is an interesting alternative: volume rendering!!! A friend of mine is working with volumes in his PhD thesis and I did some nice datasets just for fun - and to explore fractals in a very different way. While my computer calculated lots of Julia sets I also discovered a surprising phenomena, but see yourself :) You are welcome to visit my latest work, the "Julia and Mandelbrot" page, at http://mschreier.tripod.com/ To my person: Actually I'm living in south of Germany, I'm working for a local car supplier compagny, and just got the MSc in Distributed Computing Systems Engineering at the Brunel University (Uxbridge, West London). I was exploring fractals since 20 years, first on the good old C64 (remember the Mandelbrot renderer that used also the 1541 floppy CPU?), then with Fractx86 and later with Fractint. I'm mostly interested in 3D graphics, surround sound and model railways. Best regards Marc --------------- JX-8P Resource Center http://www.synthzone.com/~mschreier/ ---------------

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FOTD 30-07-02 (Aquatic Life [8])
by Jim Muth 30 Jul '02

30 Jul '02

FOTD -- July 30, 2002 (Rating 8) Fractal visionaries and enthusiasts: Today's fractal reminds me of another real-world object. In this case, I see the graceful swaying of seaweed, a few meters under the surface near some tropical shore. The scene is also filled with schools of small, colorful tropical fish, though these are more difficult to pick out. With all this underwater activity in mind, I named the image "Aquatic Life". Then I stepped back to evaluate the result. After much mental wrestling, I rated the image a much-above- average 8. The formula of the aquatic scene is Z^(-1.1)+Z^(-11)+(1/C), a simple expression that does more than it should. But as I stated recently, it is not the formula that works the magic; it is the 280 iterations. The parent fractal of today's scene appears as a large open bay with many buds and valleys around its perimeter. Today's scene is located in the center of a blunt valley on the south shore of the main bay. The aquatic effect was achieved by rendering the scene with the outside set to the <tdis> option, followed by careful coloring. The render time of just over 1 minute makes running the attached parameter file the quickest way of seeing the seaweed. But downloading the completed GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> might be a lot more fun. The weather Monday here at the (IMO) center of the fractal world was hot, hot, hot. A breeze and slightly lower humidity made it feel less oppressive than it otherwise might have been, but 100F 38C is still hot -- there's no escaping it. The heat was so severe that it buckled the rails of a local rail line, causing a train to derail. The dynamic fractal cats avoided the excessive heat by passing the day in the air-cooled indoors, though they did check several times just to be sure it really was that hot outside. Today is Tuesday, and it's another scorcher -- a perfect excuse for me to stay indoors and get a little ahead on the upcoming convention program that needs to be finished within a week. Until next time, which will come in 3 days on August 2, take care, and why are tropical shores with all their humidity and heat considered paradise on earth?. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Aquatic_Life { ; time=0:01:27.77--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.856206964880088/-1.054799381804275/2\ 124528/1/-160/-3.37734701108538538e-008 params=1/-1.1/1/-11/0/525 float=y maxiter=280 inside=0 outside=tdis periodicity=10 colors=000z01z03y04u04o06j06f07`07X09S09M0AI0AD0C7\ 0C30D00D13I47M7CQAGTDLYGPaJTfLYiOamQfrTjvXoy_szaxz\ czzUzzKzz7zz6vz4lz3`z1Qv0Gs6FuCDvIDxOCyTAzYAz`CzcF\ zfGziIzlLzoMzrOzuQzxSzyTzxVzxXvxYrvYmv_iv`dv``uaXu\ cSudOsdJsfFsgAsg6mc9g`CcYFYVGTSJOOMJLPDIQ9FT3CX09Y\ 6C_DD_LF_SG_TI_TPcPXgLaiGikCmaJqSPu0Mz6LuAJoGGjLFd\ QD_VAT`9Pd7Jj4Do37u13y00z00z00z10z60zC0xG0sM1oQ4iX\ 7d`A_fDVjGQpJLuMGzPAzUUzc1zmYzuVzzSzzQzzOzyMzxJzvI\ zuFzsDzrAzp9zo6zm4yl1yj0xl3vl6vl9umCumFsmGroJroMpo\ PppSopVopXmrUlsUluUjuUjvUitUimUmcUqUPvCdz0sv4osCjo\ JflQaiYYddValQ_sMVzISzDPzATzMXsX`jfc`pgQzjIzgMzdPz\ cSx`Vs__oXajVdfSgaQjYYXcdIgl4lgAicGg_MfVSdQYaMc`Ii\ _DoY9uV4zT0zS0zQ0zV0z_0za0yf0vj0sm0pr0mv0jy0gz0dz0\ az0_z0Yz0Vz0Tz0Qz0Pz0Mz0Ly0JxIiTJfOJdILcDLa7M`1M_0\ OY0OX0ld3sXJzQYy6ls0yo0xl0xi0xf0va0v_3vX6uT9uPCuMF\ sJIsGLsCi09i07i0`_7zPTz9F } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 28-07-02 (The Helm [7])
by Jim Muth 28 Jul '02

28 Jul '02

FOTD -- July 28, 2002 (Rating 7) Fractal visionaries and enthusiasts: I named today's 7-rated image "The Helm" because of the resemblance it bears to a ship's wheel. Almost all my FOTD fractals are named after a resemblance they bear to a real-world object. This tendency to find the familiar in the unfamiliar is a universal human trait, perhaps best illustrated by the "faces in the clouds" illusion. No ship's wheel exists in today's image, which is merely a mapping to the screen of the number of iterations required before the iterated points of the image pass beyond the bailout radius. The coloring does not exist in the formula, but was consciously added by myself to enhance the resemblance to a wheel. Today's image is in fact nothing but one of the many ways in which the basic underlying mathematical abstraction could have been made manifest. The same formula could just as easily have created a piece of fractal 'music'. (Though I have yet to hear a piece of fractal 'music' that was worth being listened to more than once. [Or even once, for that matter.]) Today's generating formula -- 1.5(Z^1.1)+1.5(Z^11)+(1/C) -- is unusually simple. This is not surprising. When working with fractals, long convoluted formulae are unnecessary, and in fact often not worth the effort of writing them. Complex formulae are not needed, because the iterations work the magic. Great images come from skillful searching, not necessarily from 200- line-long formulae. The above statements are my personal opinion of course, especially the statement about fractal 'music' being worthless. Since beauty exists in the mind of the beholder, it may be that my mind is not tuned to the mental frequency of the appreciation of fractal 'music' and all the beauty in the music passes right through me like light through the invisible man. Forgetting the worth or non-worth of fractal music, the render time of today's image is a fast 3 minutes on my brave little P200 fractal machine. Approximately the same time will be required to download the completed GIF image from Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's FOTD site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The route to enjoyment of the image is left to the viewer. The weather Saturday here at Fractal Central was not perfect, but it could have been a lot worse. The temperature was held to a muggy 83F 28C by heavy clouds, which threatened all day but produced only a few drops of rain. The cats, who dislike high humidity, briefly checked the outdoor conditions, then decided to spend the day indoors. And I'm about ready to spend today relaxing. Until next time, take care, and where is that "Theory of Everything for Dummies" book? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Helm { ; time=0:03:11.41--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-6.14601973153377700/-1.981123197536113\ 00/1.483931e+010/1/-28.746056810576011/-0.02765394\ 21627924401 params=1.5/1.1/1.5/11/0/0 float=y maxiter=900 inside=0 logmap=63 periodicity=10 colors=0006AI7AJ8AK9APAJUBMXCNcvl4kc8UNCzu8faBTODm\ A3`B7KBBk_ocTbWNVOHNb`dVSWNJNzfvbR`labcVXWOROHLu9x\ gAhUBUOZ9KNCDwBEcDFPErCkeB`TBQg_t`TiUN_NHP80PB4LE8\ I2Y_z8cj9X`ARQBLfl1FwzGfjGRVvrt1GQ6EMBCI6Y8AQBDIDq\ 1lnkYbZRRNLkwd`fWQRNLThIM6HI9GECHtkGYVY1dP6S9iPDSK\ RPJNKHJFG9W6CP9EIC1_p5Tf9NYDHOA3HD7G4q0jFk_D`QCQWr\ 8SgAOXCKMEFYGGMFKWYILOE6zF9bGDMmYVXMNv9H6HSBELsoZi\ dU_VPQLK9YikQ3WI9T1YjhRVSL24e77XC9O0eV8QNR_rOThLNZ\ IHPKZeIRXHJOrUOkpT`bOQPJYv_TjUPZPKNK__JTRHMJG5wdBZ\ SCQJDMIEIHFEG4pd7eYAWSDLLJOCfEM69P9AMBAKEBHTaSOTNK\ KJavGUfFNRFNboA5NC7KE9HdwuYjjSZ_MNP6JxBFa9nFDVFONZ\ Vy4Uba_h4TX8MMCP4MM6KK8IIAG5wK8jIBZHENGjwlvfomiddl\ UWoJNq8OuRPxhMflJdpGesHfjIgaIhUUiWejXqkYXl`CmbroaZ\ qQ4szAub1wKzyjnzbbzVRzNqz5gz8ZzAPzDzzPbzKQz83zK7zI\ AzHDzGYzBSzDMzEDzNszH_zG2zm7zaCzQxzflz_azTRzMOzELz\ FIzFQz2Nz6Lz9IzC6ztBz_OzW } 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 26-07-02 (Quadrapod Minibrot [8])
by Jim Muth 26 Jul '02

26 Jul '02

FOTD -- July 26, 2002 (Rating 8) Fractal visionaries and enthusiasts: After a long fractal drought, we finally have a fractal that rates an 8, a rating that equals much above average on my conservative 0-to-10 scale of fractal worth. Actually, the fractal itself is quite humdrum in the mathematical sense. Most of the high rating is based on the coloring, which in a moment of excessive fractal zeal, I devoted an entire half-hour to. The parent fractal of today's scene consists of a Mandelbrot figure with several large irregular open holes at the end of some of its filaments, and strings of smaller holes at the ends of others. There is also a string of holes extending outward from the center of East Valley. Today's image lies in an isolated, cut-off feature near this string of holes. The string-of-holes nature of the area in which today's image lies is reflected in the four strings of holes radiating from the brilliant red flower around the central midget. Since there are four of these 'arms', I named the image "Quadrapus Minibrot". (I have no idea what a real 'quadrapus' might be, though the fractal cats might fit the description.) The formula of the image uses the golden ratio, 1.618..., which often appears in the designs of nature. The ratio also appears at places in the Julibrot, where least expected, but that's another story for another day. The render time of 3 minutes from the parameter file is close to the time required to go online and download the completed GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Thursday here at Fractal Central featured a pleasant break from the oppressive heat and humidity that usually plagues this part of the world at this time of year. Lots of clouds and a cool breeze off the ocean held the temperature to 79F 26C. The grass, still wet from an early morning shower, was a bit too uncomfortable for the dynamic duo, who prefer their paws dry, but they did spend a few relaxing hours on the dry porch, watching the local birds. And I'm also going to relax -- but not until I finish the work that needs to be done. Until next time, on Monday the 28th, take care, and keep the ratio golden. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Quadrapus_Minibrot { ; time=0:03:39.53--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-2.85097707624026200/-3.007861364773440\ 00/5821280/1/-115/1.56494616987412627e-008 params=1.5/1.618/1.5/16.18/0/0 float=y maxiter=400 inside=0 logmap=71 periodicity=10 colors=00020K10K00K40MBAQI9WPMcXcadt_lzZtzXlzUdvRX\ qOPlLKgIPcFU_C_W9eR7lM4sI1yE0z90zd0zZ0yS0sB0nB2gC5\ cE7XF9TFCMHEIIHCKK8KL7PH5WCBTEHRFLOFRMHXLHaIIgHIlE\ KsCKyBLz8Lz7Mz5Mz8Pz9RzCTwEUtFWoIXlKZgMadOc_PdXTeT\ UgPXiLZjI_lIZlIWlBTg4Pc0PZ0PU0tU0PW0PW0PW0PWIIa09W\ 0BW0BX0BX0CX0CX1EX1EZ1EZ1FZ2FZ2FZ2HZ2H_4I_4I_4I_5K\ _5Ka5La5La7La7Ma7Ma7Mc8Oc8Oc8Pc8Pc9Pd9Rd9Rd9RdBTdB\ TdBUeBUeCUeCWeCWeCWgEXgEXgEZgEZgFZgF_iF_iF_iHaiHai\ HdjHggIjdLnaOqZRtWUtTUtPUtITtBTt4Tt1Rt2Rt5Rt7Pt9Pt\ BPtEOtFOqIOnKMjMMgOMdRLaTLZWLWXKW_KXaK_dPacXcadd_l\ dZtdXzcWzcUycTwcTtcUscWqcWncXlcZicZgd_dd_cda_dcZdc\ XddUdeTdePddXaXdZPlWItTBwR4vT0vU0tW0tX0sZ0s_0qa0qc\ 0od0ne0ng0li0lj1jl1jn2io4iq5gs7gt8et9dt9dtBctCctEa\ tFatH_tI_tKZtKXtLXtMWtOWtPUtRUtTTtTTtURtWRtXPt_Otc\ OteMtiMtlLtoLtsLtvKtyItzKtzItzItzItzItzItzItzItzIt\ zItzItzItzItzItzItz5tq4to } 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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xfractint now available for Gentoo Linux
by James S. Martin 26 Jul '02

26 Jul '02

Folks, I took it upon myself to write an ebuild for xfractint(development version 20.02.4, no extra map files) for Gentoo Linux . After obtaining the latest updates by doing an "emerge rsync" you should be able to type "emerge xfractint" and watch it download, compile, and install xfractint for you, with your CPU optimizations. James

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Re: [Fractint] Yet another trivial...
by Jim Muth 26 Jul '02

26 Jul '02

While toying with the Lyapunov Mandelbrot formula recently posted by Morgan Owens, I noticed that the formula produces images virtually identical to those drawn by the Fractint type=hypercomplex Mandelbrot formula. I have included two parameter files, one of which uses the Lyapunov Mandelbrot formula, while the other uses the hypercomplex Mandelbrot formula, yet the two files draw identical images. Perhaps one of the math experts on the list can explain what is happening here. . . . Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Lyapunov { reset=2002 type=formula formulafile=allinone.frm formulaname=LyapunovMandel center-mag=-1.07668/7.77156e-016/1.344086 params=0/0/0/1/16/0 float=y maxiter=500 inside=0 logmap=yes periodicity=0 sound=off colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzz\ zLzzz000555888BBBEEEHHHKKKOOOSSSWWW___ccchhhmmmsss\ zzz00zG0zV0zj0zz0zz0jz0Vz0Gz00zG0zV0zj0zz0jz0Vz0Gz\ 00z00zG0zV0zj0zz0jz0Vz0GzVVzbVzjVzrVzzVzzVrzVjzVbz\ VVzbVzjVzrVzzVrzVjzVbzVVzVVzbVzjVzrVzzVrzVjzVbzhhz\ lhzqhzuhzzhzzhuzhqzhlzhhzlhzqhzuhzzhuzhqzhlzhhzhhz\ lhzqhzuhzzhuzhqzhlz00S70SE0SL0SS0SS0LS0ES07S00S70S\ E0SL0SS0LS0ES07S00S00S70SE0SL0SS0LS0ES07SEESHESLES\ OESSESSEOSELSEHSEESHESLESOESSEOSELSEHSEESEESHESLES\ OESSEOSELSEHSKKSMKSOKSQKSSKSSKQSKOSKMSKKSMKSOKSQKS\ SKQSKOSKMSKKSKKSMKSOKSQKSSKQSKOSKMS00G40G80GC0GG0G\ G0CG08G04G00G40G80GC0GG0CG08G04G00G00G40G80GC0GG0C\ G08G04G88GA8GC8GE8GG8GG8EG8CG8AG88GA8GC8GE8GG8EG8C\ G8AG88G88GA8GC8GE8GG8EG8CG8AGBBGCBGDBGFBGGBGGBFGBD\ GBCGBBGCBGDBGFBGGBFGBDGBCGBBGBBGCBGDBGFBGGBFGBDGBC\ G000000000000000000000000 } Hypercomplex { reset=2002 type=hypercomplex function=sqr center-mag=-0.5759/7.77156e-016/1.344086 params=0/0/0/0.5 float=y maxiter=500 bailout=7 inside=0 logmap=yes periodicity=0 sound=off colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzz\ zLzzz000555888BBBEEEHHHKKKOOOSSSWWW___ccchhhmmmsss\ zzz00zG0zV0zj0zz0zz0jz0Vz0Gz00zG0zV0zj0zz0jz0Vz0Gz\ 00z00zG0zV0zj0zz0jz0Vz0GzVVzbVzjVzrVzzVzzVrzVjzVbz\ VVzbVzjVzrVzzVrzVjzVbzVVzVVzbVzjVzrVzzVrzVjzVbzhhz\ lhzqhzuhzzhzzhuzhqzhlzhhzlhzqhzuhzzhuzhqzhlzhhzhhz\ lhzqhzuhzzhuzhqzhlz00S70SE0SL0SS0SS0LS0ES07S00S70S\ E0SL0SS0LS0ES07S00S00S70SE0SL0SS0LS0ES07SEESHESLES\ OESSESSEOSELSEHSEESHESLESOESSEOSELSEHSEESEESHESLES\ OESSEOSELSEHSKKSMKSOKSQKSSKSSKQSKOSKMSKKSMKSOKSQKS\ SKQSKOSKMSKKSKKSMKSOKSQKSSKQSKOSKMS00G40G80GC0GG0G\ G0CG08G04G00G40G80GC0GG0CG08G04G00G00G40G80GC0GG0C\ G08G04G88GA8GC8GE8GG8GG8EG8CG8AG88GA8GC8GE8GG8EG8C\ G8AG88G88GA8GC8GE8GG8EG8CG8AGBBGCBGDBGFBGGBGGBFGBD\ GBCGBBGCBGDBGFBGGBFGBDGBCGBBGBBGCBGDBGFBGGBFGBDGBC\ G000000000000000000000000 } frm:LyapunovMandel { narg=real(p2) nmag=imag(p2) bailout=4*(real(p3)==0)+real(p3)*(real(p3)!=0) z0=c0=pixel z1=c1=pixel+nmag*(cos(narg)+(0,1)*sin(narg)) : z0=z0*z0+c0 z1=z1*z1+c1 cabs(z0-z1)<bailout } END PARAMETER FILE=========================================

3 2

Yet another trivial messing around with the Mandelbrot set accompanied by a long-winded (yet on-topic) intro.
by Morgan L. Owens 25 Jul '02

25 Jul '02

At least there are only two formulae this time, rather than thirty-two. As you are no doubt all aware, one of the defining characteristics of chaotic systems is that they have a property known as "sensitive dependence on initial conditions". Two different starting states for a given system, however close to each other they may be initially, would eventually diverge and produce entirely different histories for the system's evolution. Equivalently, any inaccuracy in measuring or specifying the initial state of the system would eventually be magnified to the point that the inaccuracy dominates and the system could be in virtually any possible state. Usually, the rate of divergence is exponential - i.e. the difference between the two states is multiplied by some factor every iteration or unit of time. Measuring the rate of divergence hence provides a way of helping identify chaotic systems. This is the origin of the Lyapunov exponent, developed by Aleksandr Lyapunoc (or Liapunov or Ljapunov or whatever other spellings can result from a Cyrillic->English transliteration.) in the late nineteenth century. To avoid describing Jacobian matrices and characteristic values, I'll just give an explicit definition in the case of a one-dimensional system, where the state of the system at any instant is described by a single number: n L = lim (1/n)SUM log|df(x )/dx| n->inf i=1 i Where f is the dynamical rule in question; x_0 is the initial state; and x_1, x_2, ... are subsequent states. L is the Lyapunov exponent. Roughly it says we measure by how much each step magnifies (or shrinks) the divergence at the previous step and average these measurements over larger and larger numbers of iterations, continuing until the average settles down to a steady value. If L is less than zero, then the divergence becomes a _con_vergence and the system has a periodic cycle. If it's equal to zero, the system is described as Hamiltonian; an example would be the system x = x+1 - everything just cruises along. If L is _greater_ than zero - for many, the most interesting situation - then one has a chaotic situation. Higher-dimensional systems have several Lyapunov exponents, and determining them and seeing which are larger and which are smaller, which are positive and which are negative, one can learn quite a few things about the system's sensitivity to initial conditions. Interesting side note: When f is one-dimensional which depends on a given parameter a, then if there is a particular value for the parameter - call it a_inf - at which the behaviour of f becomes chaotic (i.e., where L becomes positive), it can be shown that log|2|/log|delta| L approx. |a - a | inf Where delta = 4.6692016.... Now that I've gone into all that detail about what the Lyapunov exponent is, you can safely ignore it, because most of it is purely background justification for my formulae. Someone else might like to implement the Lyapunov-calculation code in a Fractint formula, so that, e.g., one could have the pixel value specify the parameter to a function, and have Fractint colour that pixel according to the value of L; but all I do here is the perturbation thing. For each pixel, I start the usual quadratic map iteration (z->z^2+c) both for the pixel value itself and a perturbed version, the perturbation being specified in polar coordinates by p2. The bailout condition is simply whenever the two orbits diverge by a sufficient minimum amount, specified in p3 (which defaults to 4 if the user doesn't say otherwise). And as I found with my initial random explorations, they can be _very_ sensitive to different perturbations. Gee, all I really needed to write was that last paragraph; but that wouldn't have been anywhere _near_ as informative. Morgan L. Owens "As an aside, it's tempting to speculate that the generic quadratic behaviour of smooth functions ensured by Morse's Theorem accounts for the fact that almost all the basic laws of physics (conservation of energy, Fermat's principle, and the principle of least action, for example) are expressed as quadratic forms. Since it's both stable and 'typical' to be locally quadratic, it's reasonable to expect that the local laws of classical physics will also be expressible as quadratics, as indeed they are." Lyamand_1 { ; Version 2001 Patchlevel 8 reset=2001 type=formula formulafile=lyamand.frm formulaname=LyapunovMandel passes=1 center-mag=-0.162602/0.700584/5.464481 params=0/0/1/0.1/0/0 float=y maxiter=255 inside=255 logmap=5 periodicity=0 colors=000zzz<42>zzBzz9zz8<3>yy4yy4yx4<72>yX0yX0yW0<127>000 } LyapunovJulia_1 { ; Version 2001 Patchlevel 8 reset=2001 type=formula formulafile=lyamand.frm formulaname=LyapunovJulia center-mag=+0.46966854283928040/-0.00187656380316929/57.97101 params=-1/0/3.14/0.4/0/0 float=y maxiter=1023 inside=255 logmap=36 periodicity=0 colors=000<42>00s00t00v00w00x00z<41>0qz0rz0sz<3>0yz<9>bymfyljyk<3>zye<9>\ zyGzyEzyB<3>zy0<41>z80z70z50<2>z20z00y00<24>T00S00R00<3>L00<9>jaDleEoiF<\ 3>zyL<9>z_8zY7zV6<3>zK0<11>D50930520000 } frm:LyapunovMandel { narg=real(p2) nmag=imag(p2) bailout=4*(real(p3)==0)+real(p3)*(real(p3)!=0) z0=c0=pixel z1=c1=pixel+nmag*(cos(narg)+(0,1)*sin(narg)) : z0=z0*z0+c0 z1=z1*z1+c1 cabs(z0-z1)<bailout } frm:LyapunovJulia { narg=real(p2) nmag=imag(p2) perturb=nmag*(cos(narg)+(0,1)*sin(narg)) bailout=4*(real(p3)==0)+real(p3)*(real(p3)!=0) z0=pixel c0=p1 z1=z0+perturb c1=c0+perturb : z0=z0*z0+c0 z1=z1*z1+c1 cabs(z0-z1)<bailout }

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FOTD 24-07-02 (Ridges Everywhere [7])
by Jim Muth 25 Jul '02

25 Jul '02

FOTD -- July 24, 2002 (Rating 7) Fractal visionaries and enthusiasts: I am fractally annoyed. When I opened my e-mail box a few minutes ago, I found six frivolous letters, each of which had basically the same 90kb file attached. Usually I receive one or two copies of this file every day, but six is a record. I must have received two- hundred copies of this same meaningless file over the past few months. The file always has a different name, but the body, with a few variations, remains basically unchanged. The message that accompanies the file often says something such as "I now make this game for you to try. You are the first." Since the file obviously contains a virus, I have not run it, but it is amazing how long this virus has been circulating, and how pervasive it is. It is even more amazing how long the FOTD has been circulating, with no end in sight. In fact, starting in October, when the FOTD CD is ready, the ongoing FOTD will once again appear on a daily basis. Until then, it will appear on every even-numbered day. Be patient. And today being an even-numbered day, we have a new FOTD to discuss. This one once again colors the outside with the <tdis> algorithm, which creates the effect of ridges. This ridge effect is why I named today's image "Ridges Everywhere". The striking overall effect earns the rating of 7. Today's scene is part of a parent fractal created by the formula 2(Z^(0.9))+2(Z^(-0.9))+C. The parent is a distorted M-set lying in the normal orientation. Today's image lies in a spiral in the rump of an elephant on the southern shore of East Valley. The 18-minute render time can be annoying for those who lack leisure computer time. As a remedy, I suggest visiting Paul's site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> and downloading the completed GIF image from there. The weather Tuesday here at Fractal Central was of the fractal variety, with a temperature of 102F 39C at 5pm and 72F 22C at 6pm. The spectacular drop was caused by a heavy and quite noisy thunder-storm that struck at 5:30 and put a temporary end to the excessive heat. When the fractal cats came out of hiding they were quite thankful for the coolness in the air, and spent the evening in the wet grass, shaking the water from their paws. As for me, I'm ready to spend the rest of today, which is starting much cooler, shaking the backlog of work from the shelves across the room. Until next time, which will arrive on Friday the 26th, take care, and don't tempt the powers that be. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Ridges_Everywhere { ; time=0:18:23.62--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-2.740404644979088/-0.0120562596393299/\ 8.460675e+010/1/-150/-0.00149391725933679942 params=2/0.9/2/-0.9/0/0 float=y maxiter=1800 inside=0 outside=tdis periodicity=10 colors=000RxwRttRqqRmnRijRdgRadRYaRT_RPVRMSRIPRDMR\ 9KR6HT9OVCVWF`YIg_Ln`OtdRzgTzjWzm_znVxpRkqOYsKLtF6\ vC0z0kw7jtDjqLinRikWi10V00VR_OL_HD`96`10g0`m00a03O\ 39IADAII4POAVSF`WKfaOkfTqjYwpaztfzxjzpmzgnw`qnSsgK\ v_CwR3zI0zA0z00z00z01z04z0gP4gO3iO3jO1kO1mO0mO0iM9\ dLI`KRWKYSIfOHnKHvICjI9`H4PH1FF03F00I6AKHRLRfM`vOj\ zPvxRzkSznTzqVwtWswYpz_mz`izafzcczc`zcizcqzczzW_`P\ 77MFALLDISHHYIFcLCjOApR9vS6zV4zY3z_0MD0RA3V97_6Ac4\ Fg1Kk0Op0Rt0Vx0_z0cz0fz0cz0az0_t0Yp0Vj0Tf0Ra0PW0MS\ 0LM0II0HC0D70C30A40A61A77A9DAAKACP9DV9F`9Hf9Ik9Kq9\ Lw9MzASzCWzD`zFdzHjzInzKszLwzMvxOtvPstRsqSqpTpmVpk\ WniYmf_md`kaaj`cjYdiWfgTggSc`R_VPVPPRKOMCOI6MD0M90\ L40LH7KSPIcfI3c09d3Df6If7MgARgCWiF`jIdjKikMmkOsmRw\ nTznVzpYzp_zqazscvtdpvfkwggwjcxkYzmTznPzpLzqIzqFzq\ DzqAzq9xq6xq4xqCnnKdkRVjYLgdAdj0cm3ap6aq7atAavDaxF\ azIazLazMapOccPdRRfSzzRzz } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

2 1

FOTD 22-07-02 (Seahorse Minibrot [7])
by Jim Muth 24 Jul '02

24 Jul '02

FOTD -- July 22, 2002 (Rating 7) Fractal visionaries and enthusiasts: For today's glorious fractal we return to perhaps the richest area in all of fractaldom -- Seahorse Valley of the Mandelbrot set. Yes, I realize that this area has been explored almost ad infinitum, but it holds so many promising places that I just can't let it alone. Today's image is one of a midget located deep in a seahorse-tail spiral on the west side of the valley. The nature of the location is made abundantly clear by the tightly-wound spirals around the midget. I have written the mathtolerance entry into the parameter file because the magnitude of the image is so great that the program has a tendency to flip into arbitrary math mode when calculating the image, with a big slow-down but no image improvement. Curiously, the outside=tdis setting is the cause of the 1-1/2 hour render time. When calculated with outside=iter, the image renders in 4 minutes. I have no idea why the <tdis> option should take over 20 times as long to render as the normal <iter> method. I named the image "Seahorse Minibrot" as more of a description than a title. Since I kind of like the amber coloring, I rated the image at an above average 7. The 90-minute render time of the parameter file is quite slow. Some may enjoy watching the image majestically paint itself onto the screen; most will decide to download the completed GIF image from Paul's site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Sunday here at Fractal Central was quite warm and muggy, which is typical for this time of year. The temperature of 90F 32C kept the fractal cats typically lazy until supper time, when they suddenly remembered they were hungry and began crying to be fed. One certain thing however is that the rest of this Monday will not be lazy, at least for me, burdened as I am with a pile of work to finish. So as I begin the task, take care, and know truth. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Seahorse_Minibrot { ; time=1:30:55.21--SF5 on a P200 reset=2002 type=mandel passes=1 mathtolerance=/1 center-mag=-0.75285852351178220/+0.043143142026493\ 12/1.333782e+013/1.0005 params=0/0 float=y inside=0 maxiter=36000 bailout=6 periodicity=10 outside=tdis colors=000m5zu8zr7zp5zm5zl4zj4zg2we2uc1ta1r`0pY0mW\ 0lT0jR0iQ0gN0dM0cJ0aI0`G0ZD0WC0VA0T80R50N70Q80RA0T\ A0VC2WD5YDA`FCaGFcIJdJMeLPgLRiJTgITgGTeGTeFTdDTdDT\ cCTcAVaAVaAV`8V`7VZ7VZ5VY4VY2WW2WW1WV0WV0WT0WT0WR0\ WR0YT2ZT5ZT8`TAaTDaVGcVJcVMdVPeVReWVgWYiW`iWcjWcoY\ dlWejWgiWigWjeVldVmcVmaVo`VpZTrYTtVTuTTwRRxQRxPRzN\ RzMRzLQzJQzIQzGQzFQzCLrAGjACc87W72P50700C10I40N70T\ A0ZD0cG0iJ0oN0uQ0zT0zW0xZ0p`0ja0cc1Wd2Qe5Jh7Ck87mA\ 0pA0tA0sC0sD0tD0qF0oG1nG2kI4hJ5gJ7eL8cMAcMAaNA`PC`\ PDZQFYRGYRIWTJVVLVVMTWNRYPRYQQZRP`TNZRP`RPaRQcRQdQ\ ReQReQTgQTiPVjPVlPWlPWmPYoNYpNZrNZrN`tM`uMawMaxMcx\ MczLdzLdzLezLezJgzJgzJizJizJizLgzMezMezNdxPduPcrQc\ oRalRaiT`eV`cVZ`WZYYYVYYRZWP`WM`VJaVGcTDcTAdR8eR5e\ Q2gQ0iP0iP0jN0iM0jN0lP0lQ0mQ0oR0oT2pT5pV8rWAtWDtYG\ uZJuZMw`PxaRxcVzcYzd`zeczeezgizilziozjrzluzpxzuzzl\ xzduzYtzQpzJozCla5zd5zi5z } END PARAMETER FILE=========================================

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Re: [Fractint] Whither the FOTD?
by Jim Muth 23 Jul '02

23 Jul '02

At 10:03 AM 7/22/02 +1200, Morgan Owens wrote: >So if you want to know the difference between >"whither" and "where" -- and don't want to have >to wait until the dictionary is released on >video -- hasten to the philofractal list where >Jim Muth has expounded on this vitally on-topic >distinction to the enlightenment of all. Why do I get the impression I'm being baited? >I'd've thought that announcements of posts on >the philofractal list would be subjects for the >philofractal list. On the philofractal list, an announcement of a post to the same philofractal list would not be needed. Morgan: I'm always ready to trade between-the-line epithets, but let's do it on the philofractal list (if you're still a member of that list). On this, the Fractint list, God is alive and well. His initials are TW and he casts out off-topic posters with an iron fist. Jim (mixed metaphor) Muth

4 3

xfractint license
by James S. Martin 22 Jul '02

22 Jul '02

Can someone tell me where I can find the license for fractint? I know that it's "freeware", but I wanted to exact terms. Thanks, James

4 3

lightning bolts
by JESSE F 22 Jul '02

22 Jul '02

hi all- I was in the kitchen today and my sister MADE me run into the family room because there was a tv show on about how lightning bruises the body if it strikes it and makes patterns on the skin like fractals. I think that is "nice" and "interesting" ;> ) provided the person hit does survive. -Jess 8 adjectives: Edgy tired alive vegan lie clear safe real "I wonder how you looked the day you were erased? To look down at your heart and watch it fade" -S-K, "Leave you behind" _________________________________________________________________ Join the worlds largest e-mail service with MSN Hotmail. http://www.hotmail.com

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Re: [Fractint] Whither the FOTD?
by Jim Muth 21 Jul '02

21 Jul '02

At 03:40 PM 7/21/02 +1200, Morgan Owens wrote: >At 03:07 21/07/2002, Jim Muth wrote: >>Whither the FOTD? See philofractal list for on-topic reply. >Oh, I thought this was going to be about some policy on future direction. >Don't you mean "Where the FOTD"? > >"Whence come I and whither go I? That is the great unfathomable question." Jim M.

2 1

FOTD 16-07-02 (Garden of Minibrot [5])
by Jim Muth 21 Jul '02

21 Jul '02

FOTD -- July 16, 2002 (Rating 5) Fractal visionaries and enthusiasts: I named today's 5-rated image with its well-set-off areas of color "Garden of Minibrot". The reason for the name now eludes me. The image is of another midget in the same unstable valley that held the FOTD of July 14. The midget at the center is clearly of the quadratic variety, but the number of elements surrounding the midget is somewhat confused. I am especially intrigued by the 12 reddish elements, which curve in a counter-clockwise direction and are in 4 sets of 1 large and 2 small elements. The curious feature is that the 8 smaller elements closer to the center curve in the opposite clockwise direction. The 14-minute render time is a bit long for a merely average image, but this 1/4 hour can be saved by downloading the finished GIF image file from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Monday here at Fractal Central was typical of this part of the world at this time of year, with hot sun and a high temperature of 90F 32C which kept the dynamic duo in the shade under the holly trees most of the day. For today, it's rather busy here in the old workshop, and time for me to get busy. Until next time on July 18, take care, and relax. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Garden_of_Minibrot { ; time=0:14:40.02--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.37194187831392370/+0.000145944584758\ 07/2.900839e+011/1/-144.99998415676535/2.147262286\ 30335303e-005 params=1/3/-0.3/5/0.29/0 float=y maxiter=1600 inside=0 logmap=320 periodicity=10 colors=000QtzLtzGrzCpz9pz5oz1mz0mz0kz0iz0iz0pz0xo0\ zb0zS2zODzLOtI`oGmiDzdAz`90_C0WG0UJ0TN0SQ0QT0OY0N`\ 0Ld0Jg0Ik0Gp0Ft0Dx0Cz0Az0Cx1CpCDkNDd_DYkFTzFNzFIzN\ NzTSt_Woe_gmdbtiYzoTzrUzxtpNT60Q90OA0ND0LF0IG0GJ0F\ L0DN0CQ09S08T06W05Y04_01b00d00g00i00k00o00p00r00v0\ 0x00z00z00z00z00z00z00z00z10z40z80zA0zF0zI0zN0zQ0z\ U0zY0zb0ze0zb0z`0vY0tW0pU0oS1kQ4iN6eL9dJA`GD_FGWCJ\ UANS9QQ6TN5WL4_I1bG0dD0gC0k90o80r50v40z10z00z00z00\ z00z00z00z05z0Dz0Nz0Oz0Oz0Qz0Qx0Qv0Sr0So0Tm0Ti0Te0\ Ud0U`0WY0WW1WT2YQ4YO5_L6_I8_GA`DC`ADb9Fb6Gb4Id2Jd0\ Le0Ne0Oe4J_CGTLDNd8CUAG0z42v55r58o69k6Cg6Fd8G`8JY8\ NT9OQ9SNAUJAWGA_DCbAC_4I`5G`5G`5Fb6Fb6Db6Dd8Cd8C2m\ z4kz5iz6gx8ev9dtAbrC`pC_mDYkFYiGWgIUeJTdLSbLQ_NOYO\ PWQQUSRTTSSUTQUUNWWLYYJ__I`aGbcFdeD0g`0i_0kY0mY0oW\ 0qW0rU0sU0tT0uS2vS4wQ6xQ8yO9zOCzNDzLGzLIzJLzJNzIOz\ ISzGTzFWzFYzD`zDbzz_zzUzz } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

2 1

FOTD 18-07-02 (Writhing Minibrot [6])
by Jim Muth 21 Jul '02

21 Jul '02

FOTD -- July 18, 2002 (Rating 6) Fractal visionaries and enthusiasts: Today's image is part of a fractal that takes the parent fractal of the most recent FOTD, makes a small change in the portions of Z, and adds 1/C instead of C. These changes create a grossly bloated fractal which has a totally new overall shape but retains the inner detail of the original. The scene of today's image is in a totally cut-off feature near a cubic-shaped bud of the parent fractal. I have no idea why a quadratic midget should be located near a cubic bud. I named the image "Writhing Minibrot" because of eight the twisting arms. An outzoom will reveal four arms which are even more twisted, but at this scale the central midget is invisible. Considering the vivid coloring, the rating of 6 is perhaps a bit conservative. But with its routine appearance, I really could not give the image a rating of 7. The render time of the parameter file is under 6 minutes. This is reasonably fast, but still slow enough to make a download of the completed GIF image file worth the slight effort. The download can be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Wednesday was very hot, with a temperature of 98F 37C that kept the dynamic fractal cats indoors. Today is just as hot, and also more humid. The cats will likely spend another day indoors. I'll spend most of the day indoors also, getting caught up in some unexpected work that came in. Until next time, which will be on July 20, take care, and what is more real, a quark or a lark. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Writhing_Minibrot { ; time=0:05:48.06--SF5 on a P200 ; Version 2002 Patchlevel 4 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.41757997728383400/+0.186116858405553\ 00/1.301984e+011/1/-87.5201974223679713/0.01523203\ 09024481793 params=1/3/-0.3/5/-2.5/0 float=y maxiter=1000 inside=0 logmap=100 periodicity=10 colors=0000Xm0`k2di8ggEigJmeRqdXubbvbgz`mzZszXxzXm\ xRdmLVdHLTCCH62820A00A00A00A00C00C00C00C00C00E00E0\ 0E00E00G00G00G00G00G00J00L00N60PE0RN0TV0Vd0Xk0Zu0`\ z0bz4bz8bzCbzGdzJdzLdzPdzTdzXez`ezdezeeziezmgzqgzu\ gzxgzzgzzbzzXzzRxzNxzHvzCvz6uz0uz0sz0sz0oz0kz0gz0d\ z0`x0Xv0Ts2Po2Lk4Hg6Ed6A`86Z84LH88RC0`G0gJ0iG0kC4m\ 8Co4Hq0Ps0Vu0bv0gv0im0id4kXCkNJkERm6Zm0em0mN0V00CE\ 0JTARgPZvdezsmzuezu`vuVsuPmuJiuEeu8bu2Xu0Tu0Pu0Lu0\ Gq0Cm08k62gE0eN0bV0Zd0Xk0Tu0Rz0Nv0Ls0Jo0Hi0Ee0Cb0A\ X08T04P02J00G00C00808J0JV0Vd0eo0qx0zz0zz0zz0xz2sz4\ mz8gzCbzEXzHPzLJzPEzR8zV2zZ0z`0zZ0zZ0zZ0zX0zX2xX6u\ V8qVAmVCiTEeTHbTJZRLVRNRRPNRRLLPJHNJELJALJ6JJ2KJ0U\ J0cJ0mJ0wJ0zJ0zJ0zN0zP0zT0zV0zX0z`0zb0ze2zg6zi8zmA\ zoEzsGzuHzvLzsNzqRzoTzmXziZzg`zedzdez`izZkzXmzVmzX\ mzXmzXmzXmzZmzZmzZmzZmz`mz`mz`mz`kzgizogzvgzzezzdz\ zdzzLzz2zq8zkCzg0zz0zv0zo } 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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Outside coloring = tdis
by David Dollevoet 21 Jul '02

21 Jul '02

Outside coloring = tdis. David Dollevoet djd(a)bytemeusa.com DD020719.par----------------------------------------------------- in=0_out=iter { ; (c) David Dollevoet 2002 ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=DD020719.FRM formulaname=DD_AA1 function=acos/cosh/ident/ident passes=2 center-mag=+0.00000000000000000/+0.00000000000000000/13817 params=2/1.02/0.93/0.95 float=y maxiter=56 inside=0 periodicity=0 sound=off colors=000TIERFDPCCK8BTHJbRTj`ashjiZjaQjSHjYOjbUjgajnflmhf<3>cZYUO\ YVNSSLQXQU_TYbZafebhgdjjgnnjlljiiigghdcfa`dZYcUTbRQ_NKXQNZTQ`VTbZT\ caYedaggcijeloioqlptorrjnnehiaceXZaRTYKOTFHTFPUFUXFaYFgZEodKndKmdK\ jdLicLgcLecNd<3>bOZbPYbPV<3>aRO<4>`TT`UU_UV_VX_XY<3>YZaYZbY_bX`c<5\ >YYcYXcZVc<3>_Tc_Sc_Sc_Rc`Qc_Rb_Rb<4>YT_YTZXUYXUXVVV<3>USSURRURR<8\ >SOOSNNRNNRNNRLLRLLQKKRKKSLKTLKUNK<3>ZPK_PK`QK<3>cSKdSKeTKfTIgUGhV\ EjXB<3>p_2<3>lYBjYDiXGhXIgVLeUP<2>fTIgSGgSC<2>iQ6jP3iP3<3>cK4bJ4aI\ 4`H4YG5YG5_G5<3>bK9bLAbOB<4>fUHgVIhXJiYKjZLl`O<2>l_Nl_Nl_L<3>lYKlY\ JlXJlXIlXIlVHlVHjUG<9>hOAhN9gL9<4>fI6fI5fH4fH4fG3eF2<4>dH7 } in=0_out=tdis { ; (c) David Dollevoet 2002 ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=DD020719.FRM formulaname=DD_AA1 function=acos/cosh/ident/ident passes=2 center-mag=+0.00000000000000000/+0.00000000000000000/13817 params=2/1.02/0.93/0.95 float=y maxiter=56 inside=0 outside=tdis periodicity=0 sound=off colors=000TIERFDPCCK8BTHJbRTj`ashjiZjaQjSHjYOjbUjgajnflmhf<3>cZYUO\ YVNSSLQXQU_TYbZafebhgdjjgnnjlljiiigghdcfa`dZYcUTbRQ_NKXQNZTQ`VTbZT\ caYedaggcijeloioqlptorrjnnehiaceXZaRTYKOTFHTFPUFUXFaYFgZEodKndKmdK\ jdLicLgcLecNd<3>bOZbPYbPV<3>aRO<4>`TT`UU_UV_VX_XY<3>YZaYZbY_bX`c<5\ >YYcYXcZVc<3>_Tc_Sc_Sc_Rc`Qc_Rb_Rb<4>YT_YTZXUYXUXVVV<3>USSURRURR<8\ >SOOSNNRNNRNNRLLRLLQKKRKKSLKTLKUNK<3>ZPK_PK`QK<3>cSKdSKeTKfTIgUGhV\ EjXB<3>p_2<3>lYBjYDiXGhXIgVLeUP<2>fTIgSGgSC<2>iQ6jP3iP3<3>cK4bJ4aI\ 4`H4YG5YG5_G5<3>bK9bLAbOB<4>fUHgVIhXJiYKjZLl`O<2>l_Nl_Nl_L<3>lYKlY\ JlXJlXIlXIlVHlVHjUG<9>hOAhN9gL9<4>fI6fI5fH4fH4fG3eF2<4>dH7 } in=fmod_out=tdis { ; (c) David Dollevoet 2002 ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=DD020719.FRM formulaname=DD_AA1 function=acos/cosh/ident/ident passes=2 center-mag=+0.00000000000000000/+0.00000000000000000/13817 params=2/1.02/0.93/0.95 float=y maxiter=56 inside=fmod outside=tdis periodicity=0 sound=off colors=000TIERFDPCCK8BTHJbRTj`ashjiZjaQjSHjYOjbUjgajnflmhf<3>cZYUO\ YVNSSLQXQU_TYbZafebhgdjjgnnjlljiiigghdcfa`dZYcUTbRQ_NKXQNZTQ`VTbZT\ caYedaggcijeloioqlptorrjnnehiaceXZaRTYKOTFHTFPUFUXFaYFgZEodKndKmdK\ jdLicLgcLecNd<3>bOZbPYbPV<3>aRO<4>`TT`UU_UV_VX_XY<3>YZaYZbY_bX`c<5\ >YYcYXcZVc<3>_Tc_Sc_Sc_Rc`Qc_Rb_Rb<4>YT_YTZXUYXUXVVV<3>USSURRURR<8\ >SOOSNNRNNRNNRLLRLLQKKRKKSLKTLKUNK<3>ZPK_PK`QK<3>cSKdSKeTKfTIgUGhV\ EjXB<3>p_2<3>lYBjYDiXGhXIgVLeUP<2>fTIgSGgSC<2>iQ6jP3iP3<3>cK4bJ4aI\ 4`H4YG5YG5_G5<3>bK9bLAbOB<4>fUHgVIhXJiYKjZLl`O<2>l_Nl_Nl_L<3>lYKlY\ JlXJlXIlXIlVHlVHjUG<9>hOAhN9gL9<4>fI6fI5fH4fH4fG3eF2<4>dH7 } DD020719.frm------------------------------------------------------ DD_AA1 {;(c) David Dollevoet 1998 IF (REAL(P1) || IMAG(P1)) Q1 = P1 ELSE Q1 = PIXEL ENDIF Q1R = REAL(Q1), R1R = 8^(ABS(Q1R)) IF (Q1R >= 0) S1R = 1 ELSE S1R = -1 ENDIF Q1I = IMAG(Q1) IF (REAL(P2) || IMAG(P2)) Q2 = P2 ELSE Q2 = PIXEL ENDIF Q2R = REAL(Q2), Q2I = IMAG(Q2) Z = PIXEL : Z = Q1I*FN1(FN2(Q2R*Z))+FN3(FN4(Q2I*Z)) ZM = |Z| Q2R = Q2R*S1R ZM <= R1R } end data----------------------------------------------------------

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Whither the FOTD?
by Jim Muth 21 Jul '02

21 Jul '02

Fractal fanatics: Due to a situation (power failure) beyond the fractalist's control, the FOTD for July 20 will appear in about 12 hours. Jim M.

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FOTD 20-07-02 (Fractal Saturday [5])
by Jim Muth 21 Jul '02

21 Jul '02

FOTD -- July 20, 2002 (Rating 5) Fractal visionaries and enthusiasts: Yes, I know that the FOTD is late, and I know that it's not the all-time best, but I have an alibi -- a power failure that struck in the middle of a non-FOTD rush job that was already giving me a hard time. Then, to add to the disruption, seeing how the power had failed just when I needed it most, I lost my fractal temper, which helped the situation not the slightest. Luckily, the storm that caused the interruption covered only the local area, and the lights were back on within two hours, but the damage to the work flow had already been done, and my mood remained foul for the rest of the day. But being angry while working at a computer makes one prone to errors. Hopefully, I made none, and the customer, who got his job only 1/2 hour late, will never know that his job gave such trouble. And yes, there is a better-late-than-never fractal for today. Being able to think of nothing better, I named it "Fractal Saturday" and rated it a nominal 5. The image mixes 0.7 parts of Z^(-1.5) with twice as much Z^0.8765 before adding 1/C. It might be the fastest-found FOTD image of all time. I found the scene in under 2 minutes and colored it in an equally short time. Actually, considering the haste with which the image was created, the rating of 5 is not so bad. The render time of under 5 minutes is also not so bad, but the download time of the GIF image file is even better. The download may be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Friday featured a muggy day with a high temperature of 91F 33C and a localized but intense thunder-storm in the afternoon, which struck the area with torrential rain and spectacular lightning, doused the fractal lights and sent the fractal cats scurrying for the most secure cover they could find behind the cartons in the basement storage area. Luckily for the dynamic duo, the flooding problem down there has been pretty much solved, and they came out a couple hours later, cautious but dry and unharmed. And barring another power failure, I'll return on schedule this Monday with the next FOTD, new and improved for your viewing pleasure. Until then, take care, and who knows what goodies lurk in the heart of the future. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Fractal_Saturday { ; time=0:04:16.01--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=b center-mag=-1.17085298919225900/+0.232302495487533\ 20/2.607014e+007/1/-42.5/8.15006835977460931e-008 params=0.7/-1.5/1.4/0.8765/0/-75 float=y maxiter=1150 inside=255 logmap=145 periodicity=10 colors=00009e0Gi0Ll0Nm0Nk0Li0Ig0Ge0Gb0E`5CZ99ZG9XL\ 7VR5RZ3Pb1Ni1Ln0Lu0IzNGzREzTCzU9zV7zW7zW9zXCzYEzWE\ ySGuMIn9IiELbGNZINVORNQTISULUVNWXNZZPa`PdbRgeRjgVm\ iVoiXpnZrp`trbuubuweuzgvziwzkyzkyznyzpzzrzzuzzuzzw\ zzyzzzzzzzzzzzzzzzwzzuzzpzznzzizzezzbzzZyzXuzRpzPn\ zLizGezE`z9Xz7Rz3Pz0Lz0Gz0Cz07z03z01z03z05z05z07z0\ 9z09z0Cz0Ez0Ez0Gz0Iy0Iu0Lr0Np0Nk0Pi0Rg0Rb0V`0XZ0XV\ 0ZR0`P0`R0XV0RX0NZ0I`0E`09b05e01g00i00i00k00n00p00\ r00r00k00e00Z00R00L00E007501900E00L00k00r00z00k10P\ 35P7CN9LNERNIZLLeLPkIRrIXzI`zGbzGgzEizEnzEpzCkz9iz\ 9gz7ez5bz5`z9eyEiwInuNprRupXyn`zkeziizgnzerzbwz`zz\ ZzzXzzXzzPzzLrzGgzCZz7Nz1Cz03z00z00z00z0Ny0zw3zz9z\ zGwzNpzXkzbgzi`zpXzwRzpXzkZzg`zbbzZezVgzNizIkzEnz9\ pz5rz1uz0wz0yz0zz0zz0zz0zz0zz0zz`zNkznwzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzwzzuzzpzznzzizzgzzbzz\ `zzZzzVzzRzzNzzLzzGwzE000 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] FOTD 14-07-02 (8-Legged Weirdo [6])
by Andrew Coppin 16 Jul '02

16 Jul '02

>From: JimMuth(a)aol.com >Reply-To: fractint(a)mailman.xmission.com >To: fractint(a)mailman.xmission.com >CC: philofractal(a)lists.fractalus.com >Subject: [Fractint] FOTD 14-07-02 (8-Legged Weirdo [6]) >Date: Sun, 14 Jul 2002 10:25:21 EDT > >FOTD -- July 14, 2002 (Rating 6) Hmm... nothing to do with the forthcomming move "Eight legged freaks"? ;-) Andrew. _________________________________________________________________ MSN Photos is the easiest way to share and print your photos: http://photos.msn.com/support/worldwide.aspx

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strange Newtons
by M J Benkers 15 Jul '02

15 Jul '02

Here are some new pictures from the wet, rainy Netherlands. Yes, I am still there, but I've got a new computer and it took me a long time before all programs were working well. I did some experimenting with Newton-formulas of somebody else and I found some nice fractals. Mary Begin parameter files: strangenewton_1 { ; 0.00.26.91 with AMD 1800+ and SF9 ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=crazynwt.frm formulaname=Nwtsqzz function=tan/sin center-mag=-1.77636e-015/9.99201e-016/0.5623188 params=2/2/1/0 float=y maxiter=1000 inside=0 colors=0000He<13>0Ze0_e0ae0be0ce0ee<26>HvvIwwJxx<2>LzzLzzMzy<56>vzPwzOxz\ NxzNyzMzzL<25>CCaAAa88b<2>22d00e00d<25>007006004003002000<57>00a00b00b00\ c00d<2>02e03e05e<7>0Fe } strangenewton_2 { ; 0.00.31.20 with AMD 1800+ and SF9 ; Version 2002 Patchlevel 3 ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=crazynwt.frm formulaname=Nwtsqzz function=sqr/sin center-mag=-1.77636e-015/9.99201e-016/0.5623188 params=1/1/1/0 float=y maxiter=1000 inside=0 colors=00048H<3>49I49J49J49J<2>5DL5EL5GM5IM<4>6QP7RP7TQ<2>7YR8_SA`S<8>_i\ JajIdkH<3>ppD<9>p_6pY5pW4<2>pR2pP1oP2<25>94X74Z53_42`21a00c<107>00200100\ 1<2>000000001<50>48H } strangenewton_3 { ; 0.00.18.74 with AMD 1800+ and SF9 ; Version 2002 Patchlevel 3 ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=crazynwt.frm formulaname=Komplexmatsch function=sin/sqr center-mag=0.722299/-1.21753/3.205128/1/34.9999999999999787/1.3107570584\ 4807544e-014 params=2/3/1/2 float=y maxiter=1000 inside=0 colors=00007B<17>0Wi0Xk0Zm<3>0du<6>XoRaqNfsI<3>zz0<20>EK8CI8AG9<3>07B<16\ >0Wh0Xj0Zl<3>0du<6>XoRaqNfsI<3>zz0<4>ZZ0TT0NN0<3>000<25>nnnppprrr<3>zzz<\ 9>OSVKPSGLO<3>07B<17>0Wi0Xk0Zm<3>0du<6>XoRaqNfsI<3>zz0<4>ZZ0TT0NN0<3>000\ <25>nnnppprrr<3>zzz<14>4BF } strangenewton_4 { ; 0.00.24.93 with AMD 1800+ and SF9 ; Version 2002 Patchlevel 3 ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=crazynwt.frm formulaname=Nwtsqzz function=sqr/cos center-mag=0/0/0.6666667 params=1/1/2/0 float=y colors=00048H<3>49J49J49J<2>5DL5EL5GM5IM<4>6QP7RP7TQ<2>7YR8_SA`S<8>_iJaj\ IdkH<3>ppD<9>p_6pY5pW4<2>pR2pP1oP2<25>94X74Z53_42`21a00c<107>002001001<2\ >000000001<51>48H } frm: Komplexmatsch { z=pixel+1/fn1(p2*pixel)+1/fn2(p2*pixel): z=((p1-1)*z^p1+1)/(p1*z^(p1-1)); 0.001<=|z^p1-1| } frm: Nwtsqzz { ; ;The factor exp(p1*...) rotates the pixels ;according to their distance from the origin if p1 is ;chosen complex. z = pixel*fn1(p2*exp(p1*fn2(|pixel|)*imag(pixel))) , Root = 1 : z = (4 * z^5 + Root) / (5 * z^4); .001 <= |z^5 - Root| } End parameter files

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FOTD 14-07-02 (8-Legged Weirdo [6])
by JimMuth＠aol.com 14 Jul '02

14 Jul '02

FOTD -- July 14, 2002 (Rating 6) Fractal visionaries and enthusiasts: The parent fractal of today's image is one to puzzle the fractal pundits. (If pundits can be puzzled, that is.) The puzzle lies not in today's image itself, which, with its eight arms ending in irregular holes, and well-defined areas, is pleasant enough, but in its location in relation to the entire parent fractal. The midget at the center of today's picture lies near an irregular hole, which lies just to the north of a quadratic midget, which in turn lies in the suburbs of a cubic midget, which lies in the basin of an order-6 midget, which lies in the center of a kind of unstable East Valley of the parent fractal. I'm not exaggerating all this variety. Set the logmap to 0, and do the outzooms to see for yourself. I call the valley unstable because it is very sensitive to changes in the real(p3) parameter. A string of midgets extends down the center line of this valley. Nothing unusual in a string of midgets, but no two midgets in this line are the same. Instead of the expected string of identical quadratic midgets, there are midgets of every shape and order, and some midgets that combine parts of midgets of different orders. Interesting exploration certainly waits in this valley, and I'll be wandering in it for the next several FOTD's. I might not find a lost civilization, but I'll find some interesting images for sure. I named today's image "8-Legged Weirdo". The picture itself, which rates a 6, is not that weird, but the area of the parent in which it lies is one of the most unusual I have ever ventured upon. The rating is conservative but honest. The render time of near 25 minutes on a classic P200 machine is on the slow side. A far more efficient way of seeing the scene is to download the completed GIF file from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Saturday featured lots of clouds and temperatures on the cool side for this, the hottest time of the year. But the high of 81F 27C was mild enough for the dynamic duo to spend several comfortable hours in the yard, remembering the days when they could actually catch those birds and squirrels they now only watch and chatter at. As I write this, it's Sunday morning and the clouds have turned to light rain. It's a perfect day for doing nothing and enjoying it. As always, I'll return in 2 days with the next in the unending series of FOTD images. Until then, take care, and keep your powder dry, (whatever that means.) Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ 8-Legged_Weirdo { ; time=0:24:40.96--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.4106409957710013/+0.0021028911297467\ /4.29809e+012/1/-150/-0.0559633657765741532 params=1/3/-0.3/5/0.29/0 float=y mathtolerance=/1 maxiter=2700 inside=0 logmap=421 periodicity=10 colors=00035y6Bw8GvBMuDRtGXrIaqLgpNloPjlRiiTgfUfcW\ d`YcYZaV``SbZPdYMeWJgVGiTDjSAlQ7nP4oO2eM8WKENJKPIN\ RHPTHSVGUXGWZFZ`F`aEccEeeDggDjiClkComBqnBspLtqVtrc\ tjXqbQnVJlWKkWLjXMiXMhYNgYOfZOeZPd_Qc_QbaNYcKUeHQg\ EMiCHk9Dm69o35p11l64iA6fF9cJB_NDXSGUWIR_KOdNKhPHlR\ EqUBuW8yYLscXnhiimudrtcotclscjscgscercbrb`qbYqbWqb\ TpbQpbOobLoaJoaGnaEnaBma9ma6ma4iY5eV6aS6YO7UL8RI8S\ OGTUNUZVVdaWjiWopYpnZpl_pj`qhaqfcqddqber`frZgrXhrV\ wyLjfKZOKN6K_SAll0jk1ik2hj3gj4ei5di6ch7bh8`g9_gAZf\ BYfCXfDZbC`ZCbVCdRBfNBhJBjFBlBAn7Ap3Ar0Aq29q49q68p\ 78p98pB7pD7oE7oG6oI6oK5nL5nN5nP4nR4mS4mU3mW3mX31SL\ DPUONa_KijIqgLndOkbQi_TfXVdVYaS__QbXNdVKgSIiQFlNDn\ LFmOHlRJkUKjXMi_OibQheRghTfkVenWeqYerZer`frafrcfrd\ fregrggrhgrigrfhqdhpbhp_hoYhoWhnTinRjmPkmNllKmkInk\ GojDpjBqi9ri6sh4th2ug0vg6whBxhGyiLziQziWzj`zjezkjz\ kozkmzi6zu5zv5zw4zw4zx3zy } 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] Piclab
by Multiple Bogeys 14 Jul '02

14 Jul '02

> I've always thought - and mentioned on this list! - that > what was needed was a back-end style Fractal > Processing Engine which contains all the functions > used to generate fractals, with a standard API for using > the back-end. Then the finicky OS-specific stuff like UI > widgets could be in a separate app that basically calls > the Fractal Processing Engine API as needed. Opens > up many fun possibilities - a wider variety of UIs for > generating fractals, a client/server architecture allowing > the FPE back-end to run on a different machine from > the UI, much greater platform independence. It would > be nice if Fractint's processing routines could be turned > into such a beast, but maybe Piclab would be a better > starting point. Or XFractint. Someone else has had this idea too. Check out protomatter.sourceforge.net. There's not been any change there for months though. It may be dead, or on some kind of hiatus. The image samples on the site are neat though.Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com

2 1

color cycling in Xfractint
by James S. Martin 13 Jul '02

13 Jul '02

Hi folks. It's been about 8 years since I last played with Fractint-- back then I was using the DOS version. I recently downloaded the latest source and compiled it on my Linux box. For the life of me I cannot get color cycling to work. From what I've read I press 'C' and then '+' or '-' after an image is loaded. I've tried this and it does not work. I'm using XFree86 4.2 and KDE 3.02. I've combed through all the documentation and I think Google is sick of me right now. Can some help me out with this? James

5 5

FOTD 12-07-02 (Midget-01 [5])
by Jim Muth 12 Jul '02

12 Jul '02

FOTD -- July 12, 2002 (Rating 5) Fractal visionaries and enthusiasts: The high point of Thursday came at 2pm when a 3-alarm fire broke out in the local animal hospital. Luckily the staff got all the animals out of the building in time, but the building is a total loss. When I told the news to the dynamic duo, they looked up and said, 'good, now we'll never have to go to that terrible place again.' Unlike the cats' trips to that particular hospital, my trips to the Mandelbrot set will never come to an end. Simply too much stuff exists to be seen there. In today's image for example, we travel to a midget just beyond the negative stem of a midget in the eastern suburbs of the prominent midget on the negative stem of the M-set. If you can decipher that last sentence, you know where today's scene is located. The rendering is boringly conventional, with equal-iteration- bands on the outside and the color 000 on the inside. The only change from the default is the bailout, which has been raised from 4 to 6. I named the image "Midget-01" more as a catalog entry than a description. After a few minutes of study, I rated the image at a perfectly normal 5. I put too little effort into creating the image and coloring it to rate the result any higher. A careful study of the image will reveal features characteristic of both the Eastern and Western suburbs of Mandelbrot midgets. Combined with the resetting of the number of elements surrounding the central midget, this is a sure sign that the midget in today's image is part of the family of a larger midget. I entered the mathtolerance=/0 parameter into the parameter file by hand to force the program to use arbitrary precision math. Though the image renders using both conventional and arbitrary math, the arbitrary math, which takes 70 times as long, results in a slightly better image. Those willing to spend 8 minutes watching the image appear can run the attached parameter file. Those with more important ways to spend their time may download the completed GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Thursday was absolutely perfect, with a temperature of 80F 27C and a crystal blue sky streaked with angel-hair cirrus. The dynamic duo made the most of the perfection by spending the entire afternoon in the yard. They seemed not the least concerned about their doctor's office burning down. As for myself, today will seem a lot more perfect when the work is behind me. But to bring about that condition I must begin, and the time to begin is now. Until next time on the 14th, take care, and the unexpected strikes when least expected. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Midget-01 { ; time=0:07:59.45--SF5 on a P200 reset=2002 type=mandel mathtolerance=/0 center-mag=-1.74259033650061656/0.0108269125319204\ 82/3.416697e+012/1/-35.0070018490356247/-0.0174293\ 321394581244 params=0/0 float=y maxiter=975 bailout=6 inside=0 logmap=180 periodicity=10 colors=000KbmKakK`kKagK`fK_fKZdKYbKXbKW`JV`ET`9PW8\ MK7Ab9F`AK_COZDTYEXXGaVHfUJjTKoSLqRKgSKXSJMSJBSFJN\ CQJ8XE5cA2j63f84b95ZB6VC7RD8NF9JG9FHIDJQBLY9Ne7Pm6\ Qn7To7Vo7Zp7cp7hq7kr7ms7ot7qu7sv7uw7wx7xy7yz7zpBtl\ EqhHmcKj_OfWRcRU_NXXJ_UHbZGdcHeeHffHggHghHhiHijIjl\ IjmIknIloImpImqKlnLklMjjNjgOiePhcQgaSgZTfXUeVVdTWd\ QXcOYbMZbKYaLYaLX`MX`MX_MW_NWZNWZNVYOVYOVXOUXPUWPU\ WPTSUTPYTLaTIeSEjSBnS7rS4vS1zV4rX7k_AcaDXdGPfJIhLB\ gKCfJDfIEeHFeGGdFHdEIcEJcDKbCLbBMaANa9O`8P`8QZCRXF\ SVITULTSOUQRVPUVNXWL`XKcXIfYGiZFlZDo_Br`Au`Bq_CmZD\ jYDfYEcXF_WGXVGTVHQUIMTJJSJFSKCRL8QL5QN9RPDRQHRSLS\ TOSVSSWWSY_TZcT`fTajTcnUdrUfvUgyUhtRhpPhkNigLibJiZ\ HjUFjQDjLBkH9kC7k85ZVKMqZOoXPmVQkTRjRShPTfNUeLVcJW\ aHX`FYZDZXB_W9aYDc_GeaJgcMhePjgSliVnkYpm`qocsqfusi\ wtlxuoTvXVwVXxTYyR_zP`zNbzLczJezIgzGhzEjzCkzAmz8nz\ 6hzzkzzgzwczt`zrXzoUzmTzk } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 10-07-02 (Midget Squid [6])
by Franktal Gallery 12 Jul '02

12 Jul '02

All this tentacle talking reminded me of a wonderfully disturbing picture, by Paul DeCelle... http://www.fractalus.com/paul/cthulhu.html Cthulhu fthagn ! Miguel >From: sqrt_-1(a)juno.com >Reply-To: fractint(a)mailman.xmission.com >To: fractint(a)mailman.xmission.com >Subject: Re: [Fractint] FOTD 10-07-02 (Midget Squid [6]) >Date: Thu, 11 Jul 2002 19:00:08 -0500 > >I found this a few years ago and the name "Midget Squid" reminded me of >it. > >JK > > >mutant_octopus { ; it has eight legs, right? 90 min at 1024x768 > reset=1930 type=mandel passes=b > center-mag=-1.759895432332375466/0.01229829457725998347/5.665433e+015 > params=0/0 float=y maxiter=5000 > >colors=000_ao<21>DGdBEcBEc<29>BBLAAKCDK<14>kuC<15>AAK<15>z00<14>zvvzzzxv\ > >w<12>c0K<2>g4Ji5Ij6Hl7Gm9G<2>rCDsEDuFCvHCxIBzKA<2>zREzUFzXGz_HzaJ<8>zzU<\ > 15>9C`ADaBEc<46>xxyzzzyyz<22>`bo > } > > >On Wed, 10 Jul 2002 10:59:00 -0400 Jim Muth <jamth(a)mindspring.com> >writes: > > > > FOTD -- July 10, 2002 (Rating 6) > > > > Fractal visionaries and enthusiasts: > > > > In the depths of the world's oceans lurks the giant squid, so > > far unseen while alive and known only from dead specimens washed > > up on beaches or dredged up in fishing nets. In the depths of > > the world's fractals lurks the midget squid, neither alive nor > > dead and known only by a whimsical name given in a moment of > > fancy. > > > > For some strange reason, while viewing today's image, I was > > reminded of a squid. (I thought I saw suckers.) Since the size > > of the features in the image is in the sub-atomic range, I named > > the picture "Midget Squid". _________________________________________________________________ MSN Photos is the easiest way to share and print your photos: http://photos.msn.com/support/worldwide.aspx

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Re: [Fractint] FOTD 10-07-02 (Midget Squid [6])
by sqrt_-1＠juno.com 11 Jul '02

11 Jul '02

I found this a few years ago and the name "Midget Squid" reminded me of it. JK mutant_octopus { ; it has eight legs, right? 90 min at 1024x768 reset=1930 type=mandel passes=b center-mag=-1.759895432332375466/0.01229829457725998347/5.665433e+015 params=0/0 float=y maxiter=5000 colors=000_ao<21>DGdBEcBEc<29>BBLAAKCDK<14>kuC<15>AAK<15>z00<14>zvvzzzxv\ w<12>c0K<2>g4Ji5Ij6Hl7Gm9G<2>rCDsEDuFCvHCxIBzKA<2>zREzUFzXGz_HzaJ<8>zzU<\ 15>9C`ADaBEc<46>xxyzzzyyz<22>`bo } On Wed, 10 Jul 2002 10:59:00 -0400 Jim Muth <jamth(a)mindspring.com> writes: > > FOTD -- July 10, 2002 (Rating 6) > > Fractal visionaries and enthusiasts: > > In the depths of the world's oceans lurks the giant squid, so > far unseen while alive and known only from dead specimens washed > up on beaches or dredged up in fishing nets. In the depths of > the world's fractals lurks the midget squid, neither alive nor > dead and known only by a whimsical name given in a moment of > fancy. > > For some strange reason, while viewing today's image, I was > reminded of a squid. (I thought I saw suckers.) Since the size > of the features in the image is in the sub-atomic range, I named > the picture "Midget Squid". > > It's a pretty ordinary formula that generates the image -- > 4(Z^(-0.1))+0.4(Z^2)+C -- a formula that generates a moth-eaten > parent fractal with more curious nooks and crannies to explore > than a fractalist can shake his iterations at. In today's case, > I chose the vague 'East Valley' appearing area of the parent to > investigate. I got quite far down before the signs of the tiny > midget finally appeared. > > Because of its less-than-expert coloring, the image rates a 5 or > a 6. Feeling generous, I rated it a 6. A better way of rating > the FOTD images might be to have the viewers decide. I've been > thinking about such a system for some time. Perhaps I'll decide > about the ratings when the FOTD-CD is ready. > > The parameter file's render time of 10 minutes is a bit slow for > today's busy world. Time can be saved by downloading the > finished GIF image from Paul's web site at: > > <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> > > or from Scott's site at: > > <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> > > The fractal weather Tuesday was once again hotter than a > far-cracker. But in the early evening the temperature of 99F > 37C was knocked down to 72F 22C by a whopper of a thunder-storm, > which sent the intrepid duo of house-cats scurrying for cover > and kept them hidden until 10pm. > > Today promises to be less hot, but before I can enjoy the milder > conditions, I must finish some work. And before I can finish, I > must start. So until the next FOTD on July 12, take care and be > ready for anything. > > > Jim Muth > jamth(a)mindspring.com > jimmuth(a)aol.com > > > START 20.0 PAR-FORMULA FILE================================ > > Midget_Squid { ; time=0:10:24.07--SF5 on a p200 > reset=2002 type=formula formulafile=allinone.frm > formulaname=MandelbrotMix4 function=ident passes=1 > center-mag=-3.18686290593923700/-0.012918240803433\ > 52/9.031838e+011/1/-110.25/0.31625297457531909 > params=4/-0.1/0.4/2/0/0 float=y maxiter=1200 > inside=0 logmap=209 periodicity=10 > colors=0000Ki0Mh0Og0Qf0Se0Ud0Wc0Yb0_a0a`4c_6eY8gWA\ > iUBjSDlQFnTGoWIqZKsaLudNwgPxjQvmRtgRpbTkXXfSWaMWYH\ > YUB`P6`E1YE3YE5_E7bE9dEBfEDhEFkEHnEJqELtENvDRvFQtH\ > QrIQpKQnMQlNQjPQgRQeSQcUQaWQ_XQYZQW_QZ`Sa`Uc`WfaYh\ > a_kaanbcpbesbgubivcdvd`veWvfSvfNwgJwhEwiAwj5wj1c_A\ > e`Jg`Ri`Tk`Um`Ti`SdaS_aRVbRQbQLcPGcPBdO6dO8fP9gQAh\ > QCiRDjREkSFlTHnTIoUJpUKqVMrWNsWOtXPuXUt_Ytaascesei\ > rhmrjqqluqnyqpypkyogyobynZymVymQylMylItjLohOkgQfeT\ > acVYbYT`_OZbKYdFWgBViJYhQ_gYafddelfdshdoh`khXghUch\ > Q_hMWhJShFOhBKh8Gh4Ch1Ib7OYDUTJ_OOeJUkE_q9dnDakH_i\ > LYfPVdTTaXR_`OXdMVgKXcIY`H_YG`UFbREcOCeLBfHAhE9iB8\ > j87kB9lEAmHBmKCnNEoQFoTGpWHqZJqaKrdLsgMsjNpiMniOmi\ > RliUkhXjc_iZbhUegPhfKkeFndAqc5tb6qc7nc8kc9hc8hc8ic\ > 8jc8kc7lc7md7oe7qf6sg6uh6wi6yj6zkGzlPzmQznQzoRzpRz\ > qRzrSzsSztTzuTzvTzwVzxWzyXzzXzzYzzZzzZzz_zz`zz`zzY\ > zzVzzTzzQzzOzzLzzIzzGzzqz } > > 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================================== > > > _______________________________________________ > Fractint mailing list > Fractint(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint > ________________________________________________________________ GET INTERNET ACCESS FROM JUNO! Juno offers FREE or PREMIUM Internet access for less! Join Juno today! For your FREE software, visit: http://dl.www.juno.com/get/web/.

1 0

Piclab
by Tim Wegner 10 Jul '02

10 Jul '02

I just got the following email from Gary Osborn. REAL old timer fractint users will remember "Stone Souper" Lee Crocker and the Piclab program. BTW, Lee maintains a page at www.piclab.com. <<quote>> If you still have any interest in the piclab image processing program then I have recently converted it to a 32-bit Windows program. It is finally free of the DOS memory limitations. It can be downloaded from www.s-4.com/download. This image shows some of the new capabilites of the program. <<unquote>> Tim

7 11

FOTD 10-07-02 (Midget Squid [6])
by Jim Muth 10 Jul '02

10 Jul '02

FOTD -- July 10, 2002 (Rating 6) Fractal visionaries and enthusiasts: In the depths of the world's oceans lurks the giant squid, so far unseen while alive and known only from dead specimens washed up on beaches or dredged up in fishing nets. In the depths of the world's fractals lurks the midget squid, neither alive nor dead and known only by a whimsical name given in a moment of fancy. For some strange reason, while viewing today's image, I was reminded of a squid. (I thought I saw suckers.) Since the size of the features in the image is in the sub-atomic range, I named the picture "Midget Squid". It's a pretty ordinary formula that generates the image -- 4(Z^(-0.1))+0.4(Z^2)+C -- a formula that generates a moth-eaten parent fractal with more curious nooks and crannies to explore than a fractalist can shake his iterations at. In today's case, I chose the vague 'East Valley' appearing area of the parent to investigate. I got quite far down before the signs of the tiny midget finally appeared. Because of its less-than-expert coloring, the image rates a 5 or a 6. Feeling generous, I rated it a 6. A better way of rating the FOTD images might be to have the viewers decide. I've been thinking about such a system for some time. Perhaps I'll decide about the ratings when the FOTD-CD is ready. The parameter file's render time of 10 minutes is a bit slow for today's busy world. Time can be saved by downloading the finished GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Tuesday was once again hotter than a far-cracker. But in the early evening the temperature of 99F 37C was knocked down to 72F 22C by a whopper of a thunder-storm, which sent the intrepid duo of house-cats scurrying for cover and kept them hidden until 10pm. Today promises to be less hot, but before I can enjoy the milder conditions, I must finish some work. And before I can finish, I must start. So until the next FOTD on July 12, take care and be ready for anything. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Midget_Squid { ; time=0:10:24.07--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-3.18686290593923700/-0.012918240803433\ 52/9.031838e+011/1/-110.25/0.31625297457531909 params=4/-0.1/0.4/2/0/0 float=y maxiter=1200 inside=0 logmap=209 periodicity=10 colors=0000Ki0Mh0Og0Qf0Se0Ud0Wc0Yb0_a0a`4c_6eY8gWA\ iUBjSDlQFnTGoWIqZKsaLudNwgPxjQvmRtgRpbTkXXfSWaMWYH\ YUB`P6`E1YE3YE5_E7bE9dEBfEDhEFkEHnEJqELtENvDRvFQtH\ QrIQpKQnMQlNQjPQgRQeSQcUQaWQ_XQYZQW_QZ`Sa`Uc`WfaYh\ a_kaanbcpbesbgubivcdvd`veWvfSvfNwgJwhEwiAwj5wj1c_A\ e`Jg`Ri`Tk`Um`Ti`SdaS_aRVbRQbQLcPGcPBdO6dO8fP9gQAh\ QCiRDjREkSFlTHnTIoUJpUKqVMrWNsWOtXPuXUt_Ytaascesei\ rhmrjqqluqnyqpypkyogyobynZymVymQylMylItjLohOkgQfeT\ acVYbYT`_OZbKYdFWgBViJYhQ_gYafddelfdshdoh`khXghUch\ Q_hMWhJShFOhBKh8Gh4Ch1Ib7OYDUTJ_OOeJUkE_q9dnDakH_i\ LYfPVdTTaXR_`OXdMVgKXcIY`H_YG`UFbREcOCeLBfHAhE9iB8\ j87kB9lEAmHBmKCnNEoQFoTGpWHqZJqaKrdLsgMsjNpiMniOmi\ RliUkhXjc_iZbhUegPhfKkeFndAqc5tb6qc7nc8kc9hc8hc8ic\ 8jc8kc7lc7md7oe7qf6sg6uh6wi6yj6zkGzlPzmQznQzoRzpRz\ qRzrSzsSztTzuTzvTzwVzxWzyXzzXzzYzzZzzZzz_zz`zz`zzY\ zzVzzTzzQzzOzzLzzIzzGzzqz } 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 08-07-02 (A Blue Creation [7])
by Jim Muth 08 Jul '02

08 Jul '02

FOTD -- July 08, 2002 (Rating 7) Fractal visionaries and enthusiasts: Fractals are infinite -- which is why they are called fractals. They are infinite in many ways. But what is infinity. At one time I thought that infinity was the largest possible number. Somewhat later, I realized that if infinity were the largest number, that number could be represented by the letter X and increased by any desired amount by adding another number to it as in X+Y=Z. Of course, the new number represented by Z could be given the same treatment, and the process continued forever, demonstrating that no largest number exists. Infinity is not a number, it is a condition -- the condition of being without limit. This condition is quite easy to see in a case such as a toy train track arranged in a circle. The track has no limit, and a toy train running along it will travel a trip without a limit. As a basic concept, infinity is easy to understand. Paradoxes arise however when we begin asking meaningless questions about infinity. The toy train going in a circle is a simple concept, but if we ask how many circuits of the track will the train eventually make if nothing ever stops it and nothing wears out, or how many days will the train continue running before it comes to the end of the line, we find ourselves faced with questions without answers. In our everyday lives we ask such questions, often without realizing it. Questions about the beginning and end of time and space are puzzling for the same reason that questions involving the end of the toy-train line are puzzling -- we are trying to introduce into our intuitive world-view something that does not exist. I admit that it is fun to wonder about what happened 'before' the 'big-bang', (if the bang itself actually happened), but being able to perceive time intuitively only as an infinite straight line with no imaginable beginning or end, I know that I will never find an answer that appears intuitively correct. And speaking of infinity, today's fractal contains infinite detail, an infinitesimal part of which appears in today's image. I named the scene "A Blue Creation", though I have not decided whether I created it when I entered the parameters, or merely discovered it. Regardless of its origin, the image rates a 7, which makes it almost worth the 6 minutes required to render it from the parameter file. As always, the completed image is available on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Sunday here at Fractal Central was smoky. Smoke from forest fires in Canada blew in on north winds and gave us a day with a dull grey sky and visibility of less than 1km. The smell of burning timber was quite noticeable, which may be why the dynamic duo remained outdoors only a few minutes. The temperature of 81F 27C was quite pleasant but hard to enjoy with the smoke totally obscuring the sun. If I'm lucky, I'll get done the things that need to be done, and have enough time left over to enjoy part of the afternoon. But before I hope to finish, I must begin. Until next time on July 10, take care, and before we can know the truth we must know the question. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Blue_Creation { ; time=0:06:15.52--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-1.164418403483855/-0.00416714065635447\ /4.784102e+008/1/-7.5/-1.34769670230433514e-005 params=1.75/0.8/0.175/-8/0/0 float=y maxiter=750 inside=0 logmap=111 periodicity=10 colors=0000005E46D38B0990z0zr0nl0hc0`W3ZQ6YJ9YBDY5\ J_4K`4Lb4Oa3Pb3Qc3Rd2Se2Tf2Ug0Vh0Wj0Xl0Ym0Xq0Vt3St\ 5Op9KkBIfEHcKHbKIYKJUQKRTLPWMLZNJaOGdMEfMBiQFjTIkV\ KnZMo`PpcTsfVtiYul_xoayqezthzxjzzlzzozypzvqztszptz\ nuzkvyhxyexxcyx_zvYzuVzuRztPztMzhflYzVTxPPvJKuDGs6\ Bq08p0Bk0Fh3Jd6M_AQWEUTIYPL`KQdGUhDYk8`o4ds0hv0kq3\ jn8ijEheJfaPeZUeUZdQdcMiaIo`Et_Ay_FscKlePhhUajZYlc\ RphMslGuqBxv5zz0zx2xu3tt3oq4ko4fn5ck5Zi6Vh6Qe8Mc8I\ a9E_99YA5WA2`DAdEJiFRlI_qJhuKpyLxsIynEzhBzc8zZ5zYA\ vYFpYKjYPdYTZTVaPWeLYhG_kD`o9aqFWtLQuQKxWEy`8zf2zk\ 0zl3zn8xoDuoIqpMoqRlqWis`ftedtjavk_xkZykYzkWzkVznV\ ypVysVxuVxvVvyVuzVuzVtzVtzVazeLzo4zy3xv2qu0ks0eq0_\ o0Un0Ok0JjfJihGkhFlhEnhDohAqh9sh8th6u`DsVJqPPoJVnD\ `l6fj0li0sh6piIniTkjcijnfjkjaioUjqkqxuyzzxzzxzxxzu\ vzsvzpvznuzjuzhuzetzctz`tzZtzWkzUdzTYzQQzPIzOAzL3z\ K0zJ0zG0zF0zE0zB2zA3z93z8 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

2 1

Fairly Gratuitous
by Morgan L. Owens 06 Jul '02

06 Jul '02

Okay, I'll confess. I did the par for the sake of using the title. What interest it has is based on watching it render (this is why I recommend a resolution of 1600x1200: at other resolutions the aliasing effects are different and not the ones I tuned the viewing box for). Watching the rendering, one might see (at least, if one is as sick and twisted as I am) the aliasing as something the title might be alluding to. Another allusion is the fact that the formula derives from the classic Liar Paradox (in the form "Statement 1: Statement 2 is true. Statement 2: Statement 1 is false") via Fuzzy Logic and Scientific American. Chuck Ebbert's Liar1 attack on this problem appears in fractint.frm. I had also written the same formula prior to its inclusion in fractint.frm, but to give the user something to do I parameterised the bailout - in effect, allowing a certain amount of inconsistency to remain in the final result. More lies. It was almost inevitable that p1 would be replaced by pixel to produce what's called below "ChaoticDualist1M". But as I suggested, the title came first and then the par to suit. It had been sitting around on my harddrive until today, when I bethought to dig it up, tweak it, and post it. In short (hurray!), I'm using this whole thing as an excuse to reuse the title of a story by Greg Egan that appeared ten years ago this month in Interzone magazine. Otherwise I probably wouldn't have bothered. Morgan L. Owens "Hey, I marked Galileo's tenth anniversary here, and the twentieth of the Mandelbrot Set's discovery..." UnstableOrbits { ; Unstable Orbits in the Space of Lies ; Best viewed at 1600x1200 ; Greg Egan, Interzone #61, July 1992 ; Version 2001 Patchlevel 8 reset=2001 type=formula formulafile=logic.frm formulaname=chaoticdualist1m passes=d center-mag=0.67703/0.67703/0.589404/1/44.999 float=y maxiter=16 inside=atan outside=255 periodicity=0 colors=000JG2<24>OG2PG2PG2PG2PG2<2>QH4RI5RJ6SK7TK8<46>vusvvtwvu<3>zzz030\ <9>010010000<6>000000000<52>1E01E02F0<87>JG2 } frm:ChaoticDualist1M{ bailout=pixel z=pixel: x=real(z) y=imag(z) z=1-abs(x-y)+flip(1-abs(x+y-1)) |z|<=|bailout|}

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FOTD 06-07-02 (Interesting Midget [6])
by Jim Muth 06 Jul '02

06 Jul '02

FOTD -- July 06, 2002 (Rating 6) Fractal visionaries and enthusiasts: Today's image is named "Interesting Midget". 'Interesting' or 'nice' is what I say about something when I want to say something good but can't find any particular aspect to say something good about. I use the words frequently in my non-fractal life when I must decline customers' suggestions that I know will never work. The midget in today's image, with its vaguely familiar decorations, is 'nice' in a broad, generic sort of way -- In other words, it is interesting. Finding interesting midgets, or interesting fractals of any kind, can sometimes be a real challenge. Though the parent fractals may appear promising, all too often they hold no midgets, or if the midgets are there, they merely exhibit a duplication of features found in various parts of the Mandelbrot set. When I first saw the oversized parent fractal of today's scene, it did not even look promising, but something told me that a FOTD was hiding somewhere down in its depths. And indeed, my intuition turned out to be true. The midget lay very deep indeed, but it was there, waiting to be discovered and revealed to the world, or at least a small part thereof. The route down to the midget was long and quite eventful, and can be traveled in reverse by setting the logmap to zero and outzooming about 10 times. The formula itself, which adds 1/10 part of Z^(-11.1) to Z^(-1.11) then adds (1/C), is unexceptional, but in the world of fractals, unexceptional beginnings sometimes lead to exceptional ends. Undecided whether to rate today's image a 6 or a 7, I finally decided on a 6. It is a bit above average, though if I continue to produce fractals of this same quality, the average will rise, and I'll need to start rating them a 5. The render time of around 8 minutes on a run-down P200 machine is marginal, but the wait can be avoided by letting Paul and Scott render the image and then picking it up from their web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Friday here at Fractal Central was sunny and still very warm, but the temperature of 92F 33C and drier air was far better than the humid 106F 41C that was registered in the center of the city Thursday. The cats actually spent an entire hour outdoors in the shade of the dogwood tree, watching the starlings fly by. As for me, I'm planning another restful day. There's not too much work to be done, and I might actually get a chance to rest. But regardless, I'll return in two days on Monday, July 8, with another glorious (I hope) fractal to delight and amaze. Until then, take care, and don't let the fractals obstruct your view. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Interesting_Midget { ; time=0:07:51.48--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+49.36527881043839000/+30.4157556183393\ 0000/2.374188e+009/1/50/-9.25530275780669931e-005 params=1/-1.11/0.1/-11.1/0.5/0 float=y maxiter=800 inside=0 logmap=165 periodicity=10 colors=000EV0GY1JY6Nb9OdERgIViNXiQ_iTbiTdiTbiTaiT_\ iTYiTXiTTgTQfTNdTJbTGYTDXQlTLdNNXIJQEGI9BB48214000\ 000000000001204B08I0BO0EV0Ib1Li2Op4Rx6Vz8Yz9az9dzD\ azG_zJYzQXzQVzWRzXQz`OzbNzdLziIxlEqpDks9dw8Yz4Rz1T\ z0iz0zz0zz0zz0zz1zzDizOTtYJniOgtTbzV_zXVzYRz_NzaIz\ bEzd9zf6zg1zg0zd2za6z_BzXEwTJsRNpORkNVgJ_dGb_EgXBi\ T9iO6iL2iI1iD0q90z60zz0qz0iz0Tz0Dw40p90gE0aJ0TO0NT\ 0EY08b01g0Bk0Ln1Tq6bwBkzEtzJzzOzzRzw_zifzXnsJtk6za\ 0zT0zL0s00n00k00f00b01Y06V09Q1EN1II2NE2R94V64_16b0\ 6g08k08p09s09q0Bq0Dq0Eq0Gq0Iq0Jq0Jq0Lq1Nq2Oq6Qq8Rq\ 9TqBTn9Vk8Xg6Xd6Ya4_Y2_V2aR1aO0bL0dI0dE0fB0g80g40i\ 10i00k00l00l00n00n00p00p00p00q01q04q08q0Bs0Ds0Gs0J\ t0Nt0Qt0Rt0Vw0Yw0aw0bw1as1aq1_p1_n1_l2Yk2_i2ag2bf2\ dd2fb4g_4iY4kX4lV4nT6pR6qQ6sO6tN6wL6xJ8zL8zL9zL9zL\ BzLBzLDzLDzNEzNEzNGzNGzNIzNIzNIzNTzGdzBnz6kzbJzT0z\ L0zJOzVJzJEz89z04z08z0Bz0 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 04-07-02 (Mandelbrot Network [7])
by Jim Muth 04 Jul '02

04 Jul '02

FOTD -- July 04, 2002 (Rating 7) Fractal visionaries and enthusiasts: Sensible people see a fractal, say ho-hum, and forget about the thing. Others, not quite as sensible, discover fractals and are surprised at their variety, then experiment with them for maybe a month or two, and eventually grow bored and move on to more sensible and productive endeavors. Those like myself, who have gone beyond the need to act with common sense, become obsessed with the endless intricacies and spend years, perhaps a life- time, exploring the limitless varieties of the things numbers do. And like those fractal fans, some fractals make no sense at all. (Maybe all fractals make no sense, but that's another story.) Today's image is an example of a senseless, illogical and thoroughly irrational fractal. For some reason known only to who or whatever is in charge of the things numbers do, the midget in today's image lies exactly on the shoreline of its parent, with its east (bottom) half surrounded by the expected outside material, but its west (top) half existing invisibly in the potential inside material that forms the upper half of the image. Since invisible things are hard to see, I made the invisible visible by coloring the inside with the <fmod> option, with the proximity set to 0.085. The result is one of the more unusual midgets in the FOTD series. The real(p3) parameter is the one that works the mischief. It is critical, and must be set just right to get the half-and-half effect. I named the image "Mandelbrot Network" because of the delicate network-like elements in the top half of the image. Because of the unusual nature of the image, I raised the rating one point from a 6 to a 7. I suppose it's worth the rating. The render time of 2 to 3 minutes is quite reasonable for an image with so much inside area colored with the <fmod> option. And as always, those who would rather not render may find the finished image posted to Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and to Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> For the benefit of those who concern themselves with the weather in far corners of the earth, the fractal weather Wednesday here at Fractal Central, which is located not far from 39,21N 76,32W, was hotter than a firecracker, with blazing sun and a tempera- ture of 104F 40C. In response, the fractal cats spent the day under the air conditioning vent, stretched to near twice their normal length. Today promises to be just as hot if not hotter, but it's the Independence Day holiday here in the USA, the day when fireworks displays are everywhere, (except where they have been banned because of fear of terrorism), and it's supposed to be hot on the Fourth of July, as the day is usually called. I might wander over to the local fireworks display this evening; or I might not. I haven't decided. In either case, I'll have another glorious FOTD in two days on July 6. Until then, take care, and I'll bet there's snow falling in the New Zealand Alps. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Mandelbrot_Network { ; time=0:02:50.60-SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.523994586278288/0/121.9547/1/90/-1.2\ 3373533611470521e-014 params=1/0.35/-1/0.3/32.175/0 float=y maxiter=500 inside=fmod proximity=0.085 logmap=yes periodicity=10 colors=0008PdAPcCPaEOaGO_INZKNXMMWOMURLSTKRVJPXIOZ\ HM`GKbGJdFHfEGiEEkDDmCBoC9qB8sA6uA5v93x81y92y93x93\ xA4wA4wA5vB6vB6uB7uC7tC8tC9sD9sDArDArEBqECqECpFDpF\ DoFEoGFnGFnGGmHGmHHmHIlIIlIJkIJkJKjJLjJLiKMiKMhKNh\ LOgLOgLPfMPfMQeMReNRdNSdNScOTcOUbOUbPVaPVaPWbOVaPW\ aPWaQWaQXaQXaRXaRYaSY`SY`SY`TZ`TZ`UZ`U_`U_`V_`V`_W\ `_W`_W`_Xa_Xa_Ya_Yb_Yb_ZbZZcZ_cZ_cZ_cZ`dZ`dZadZaeZ\ aeYbeYbfYcfYcfYcfYdgYdgYegYehXehXfhXfiXgiXgiXgiXhj\ XhjXijWikWikWjkWjlWklWklWklWlmWlmVmmVmnVmnVnnVnoVo\ oVooVooVppUppUqpUqqUqqUrqUrrUsrUsrTuqUsrVrrWprXosY\ nsZls_kt`itahtbguceudduecvfavg`vhZwiYwjXwkVxlUxmTx\ kUviUuhUtfUreUqcUpbUo`Um_VlYVkXVjVVhUVgSVfQVdPVcNV\ bMWaKW_JWZHWYGWXEWVDWUBWTAWSAWRAWRAWQAWQBWPBWPBXPB\ XOBXOBXNBXNBXMCXMCYMCYLCYLCYKCYKCYJCYJCYJBXIBXIBXI\ BXIBXHBXHBXHAWHAWHAWGAWGAWGAWGAWGBVHCVIBUJAUKAUKAU\ KAUKAUKAUKAUKAUKAUKAUKAUK } 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] Fractal Haircut
by Morgan L. Owens 04 Jul '02

04 Jul '02

At 08:42 01/07/2002, David Boddington wrote: >Dear Fractalists: > >Did anyone else on the list take note of Ronaldo's fractal haircut >during the latter stages of WC Korea\Japan 2002? Better yet, >can anyone provide a par formula? Dunno about Ronaldo (he _has_ hair?), but what about Ahn Jung-Hwan's?! Now _that's_ what I call filamentary structure! Morgan L. Owens "Doesn't really do it justice." Ahn_Jung-Hwan { ; ...or at least his hairstyle ; ...kinda (someone improve the colouring?). ; Version 2001 Patchlevel 8 reset=2001 type=formula formulafile=chby9.frm formulaname=c07-09 function=cos center-mag=-0.146825/0.146825/0.6426667/1/-45 params=0.01/0.002 float=y maxiter=1023 inside=255 logmap=yes colors=777zzz<35>zzzyzzzyzzyyyyyyyyyyz<9>yyyxyyyxyyxxxxxxxxxxy<5>xxxwxxx\ wxxwwwwwwwwwwx<5>wwwvwwwvwwvvvvvvvvvvwvvvvvvuvvvuvvuuuuuuuuuuvuuuuuutuuu\ tuuttttttttttuttttttstttsttsssssssssstssssssrsssrssrrrrrqrrrqsrqqqqqqqqq\ qrqqqqqqpqqqpqqpppppopppoqpooooonooonponnnnnnnnnnonnnnnnmnnnmnnmmmmmlmmm\ lnmlllllklllkmlkkkkkjkkkjlkjjjjjijjjikjiiiiihiiihjihhhhhghhhgihgggggfggg\ fhgfffffefffegfeeeeeceeecfecccccbcccbecbbbbbabbbacbaaaaa_aaa_ba_____Z___\ Za_ZZZZZXZZZX_ZXXXXXVXXXVZXVVVVVUVVVUXVUUUUUSUUUSVUSSSSSQSSSQUSQQQQQPQQQ\ PSQPPPPPNPPPNQPNNNNNLNNNLPNLLLLLKLLLKNLKKKKKIKKKILKIIIIIGIIIGKIGGGGGEGGG\ EIGEEEEECEEECGECCCCCACCCAECAAAAA7AAA7CA77777777777 } frm:C07-09 {; V.1.1 - earlier versions may be discarded ; Copyright (c)1998,1999 Morgan L. Owens ; = zC06-C05 t=p1, bailout=4, z=pixel: x=real(z), y=imag(z) xx=x*x, yy=y*y Tx=fn1(x*(xx*(xx*(xx-7)+12)-5)) Ty=fn1(y*(yy*(yy*(yy-7)+12)-5)) x=x-t*Ty, y=y+t*Tx z=x+flip(y) |z|<=bailout }

5 5

Another color map for Ahn_Jung-Hwan fractal
by Harold Lane 03 Jul '02

03 Jul '02

>>Did anyone else on the list take note of Ronaldo's fractal haircut >>during the latter stages of WC Korea\Japan 2002? Better yet, >>can anyone provide a par formula? >Dunno about Ronaldo (he _has_ hair?), but what about Ahn Jung-Hwan's?! Now >_that's_ what I call filamentary structure! > >Morgan L. Owens >"Doesn't really do it justice." > >Ahn_Jung-Hwan { ; ...or at least his hairstyle > ; ...kinda (someone improve the colouring?). > ; Version 2001 Patchlevel 8 >reset=2001 type=formula formulafile=chby9.frm formulaname=c07-09 >function=cos center-mag=-0.146825/0.146825/0.6426667/1/-45 >params=0.01/0.002 float=y maxiter=1023 inside=255 logmap=yes >colors=777zzz<35>zzzyzzzyzzyyyyyyyyyyz<9>yyyxyyyxyyxxxxxxxxxxy<5>xxxwxxx\ >wxxwwwwwwwwwwx<5>wwwvwwwvwwvvvvvvvvvvwvvvvvvuvvvuvvuuuuuuuuuuvuuuuuutuuu\ >tuuttttttttttuttttttstttsttsssssssssstssssssrsssrssrrrrrqrrrqsrqqqqqqqqq\ >qrqqqqqqpqqqpqqpppppopppoqpooooonooonponnnnnnnnnnonnnnnnmnnnmnnmmmmmlmmm\ >lnmlllllklllkmlkkkkkjkkkjlkjjjjjijjjikjiiiiihiiihjihhhhhghhhgihgggggfggg\ >fhgfffffefffegfeeeeeceeecfecccccbcccbecbbbbbabbbacbaaaaa_aaa_ba_____Z___\ >Za_ZZZZZXZZZX_ZXXXXXVXXXVZXVVVVVUVVVUXVUUUUUSUUUSVUSSSSSQSSSQUSQQQQQPQQQ\ >PSQPPPPPNPPPNQPNNNNNLNNNLPNLLLLLKLLLKNLKKKKKIKKKILKIIIIIGIIIGKIGGGGGEGGG\ >EIGEEEEECEEECGECCCCCACCCAECAAAAA7AAA7CA77777777777 >} > >frm:C07-09 {; V.1.1 - earlier versions may be discarded > ; Copyright (c)1998,1999 Morgan L. Owens > ; = zC06-C05 > t=p1, bailout=4, z=pixel: > x=real(z), y=imag(z) > xx=x*x, yy=y*y > Tx=fn1(x*(xx*(xx*(xx-7)+12)-5)) > Ty=fn1(y*(yy*(yy*(yy-7)+12)-5)) > x=x-t*Ty, y=y+t*Tx > z=x+flip(y) > |z|<=bailout >} ################################################# Owen, in response to: "someone improve the colouring?" here's a color map I created applied to (a slightly zoomed out version of) your fractal: - Hal Lane ################################################# Ahn_Jung-Hwan2 { ; ...or at least his hairstyle kinda ; Fractal parm file by Morgan L. Owens ; Color map by Hal Lane 7-2-02 ; 7:05 at 1024 x 768 on a PII 400 ; Owen's par file: Version 2001 Patchlevel 8 ; This par file: Version 2002 Patchlevel 3 reset=2001 type=formula formulafile=pastengo.par formulaname=c07-09 function=cos center-mag=-0.00337391/0.00337391/0.4804985/1/-44.9999999999\ 999929/3.88578058618804789e-016 params=0.01/0.002 float=y maxiter=1023 inside=255 logmap=yes sound=off colors=000000yv0<7>qP0pL0oH0<3>k00<43>400<3>000000000<58>00u\ 00v00w<2>00z00z00y<57>005004003002001<60>w00 } frm:C07-09 {; V.1.1 - earlier versions may be discarded ; Copyright (c)1998,1999 Morgan L. Owens ; = zC06-C05 t=p1, bailout=4, z=pixel: x=real(z), y=imag(z) xx=x*x, yy=y*y Tx=fn1(x*(xx*(xx*(xx-7)+12)-5)) Ty=fn1(y*(yy*(yy*(yy-7)+12)-5)) x=x-t*Ty, y=y+t*Tx z=x+flip(y) |z|<=bailout }

2 1

Problems with '3D's after equals signs
by Harold Lane 03 Jul '02

03 Jul '02

Why have all the equals signs in my posts to fractint(a)mailman.xmission.com had the characters '3D' inserted after them? How can I keep this from happening? I note that other posters to fractint(a)mailman.xmission.com do not have this problem. I have not had other people that I correspond with say that they have had trouble with this problem although an equals sign is not often used in correspondence. I use Robin Bussell's excellent freeware "Fractint paste and go utility" to remove the '3D's after equals signs with the single push of a button when I find them in a par file: http://web.ukonline.co.uk/robin.b2/pastengo.htm Robin's small (15k) utility (V1.3) uses the Microsoft visual basic runtime DLL which he also makes available if you do not already have it on your system. Paste N Go makes using parameter and formula files with Fractint extremely easy. I avoided using parameter and formula files with Fractint for a long time. Now that I have discovered Paste N Go I use them quite often. I use Compuserve 4.0.2 under Win98 original version for my email. If anyone knows how to avoid creating '3D's after equals signs during posts I would really like to know. I do not enjoy creating problems for other people. - Hal Lane

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RE: [Fractint] FOTD 27-06-02 (Birth [6])
by nick.grasso＠hrads.com 02 Jul '02

02 Jul '02

Mark A. Freeze wrote: >>>I have just subscribed to this group. In the future, can I expect more fractal-based discussions AND this childish back-and-forth bantering? I hope so! I love it! Fractals, arrogance, ignorance, conspiracy!!! All in one place! How lucky I am to have found you!<<< Welcome Mark. You may also want to subscribe to the Philofractal list (Fractals and Philosophy). That list has freewheeling philosophical discussions vaguely related to fractals, and perhaps some childish back-and-forth bantering also <g>. I don't have the subscription info, but I think it is run by Jim Muth who is also on this list. Nick

6 7

FOTD 02-07-02 (One Froggy Morning [7])
by Jim Muth 02 Jul '02

02 Jul '02

FOTD -- July 02, 2002 (Rating 7) Fractal visionaries and enthusiasts: Fractals of the Mandel-Julia variety are filled with holes, especially when the iterated expression contains more than one power of Z. These holes come in many varieties. There are the obvious Mandelbrot midgets and Julia sets, and then there are the other types of holes that defy description. Today's image features one of these 'other' holes. The area in question was pointed out to me by Lee Skinner in an image he sent privately several days ago. The orange-colored holes near the center are of a type I have seen in images created with the branch-cuts formula when the exponent of Z is in the area of 1.15, but in today's image, several things appear to be happening at the same time. It almost appears that the two different powers of Z are doing things independently of each other. A math expert might be able to tell what is going on in today's image, but not being a math expert, I have no idea. While studying the image, I had the distinct impression of a frog staring back at me. I promptly named the image, "One Froggy Morning". The rating of 7 is justified because the image is a bit -- well -- cute. The render time of over one hour on a P200 machine is not cute however. I advise letting Paul and Scott do the heavy work and downloading the completed image from their one of the web sites. Paul's site is at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's is at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Monday at Fractal Central was typical summer fare for these parts of the world -- HHH -- hazy, hot and humid. The temperature of 92F 33C, combined with the high humidity and foul air, made the outdoors unpleasant for most of the day. The dynamic duo of cats must have agreed, for they stayed on the porch only a few minutes before coming in and asking for their tuna treat. As for me, it's another Tuesday, even hotter than yesterday, and I've got a bit of work to finish before returning to the FOTD CD, which should be ready for distribution by the end of summer. But the end of summer is still over 2-1/2 months away, and before then we'll have many more fractals added to the ever- growing list. The next fractal will appear on July 4. Until then, take care, and digress but don't egress. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ One_Froggy_Morning { ; time=1:09:42.15--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip center-mag=6.57209/0.000937142/22.6787/1/-80/-1.23\ 37353361147052e-014 params=-0.2/-1.25/-0.2/-0.8/0/0 float=y maxiter=160000 inside=0 logmap=19 periodicity=20 colors=000j85Q85h96g96fA6eA7eB7dB7c\ C8bC8aD8`D9_E9ZE9YEAXFAWFAVGBVGBUHBTHCSICRICQJDPJD\ OKDNKEMLELLEKMFKNFKNFLOFLOFLPFLPFMQFMQFMRFMRFMSFNS\ FNTFNTFNUFOUFOVFOVFOWFOWFPXFPXFPYFPYFQZFQZFQ_FR_FR\ `FR`FRaFRaGSaGSbHTbITbJUbJUbKVbLVcLWcMWcNXcNXcOYcP\ YdQZdQZdRZeS_eT_eU`eU`eV_eV_eX`fZ`f_`gaagcageahfah\ hbhjbilbimcjocjqckrcktdlvdlxemzgnzhozjpzlqzmrzoszp\ tzruztvzvwzwxzyyzxxywwxuwwtvvsuurutqtrosqnrpmrolqn\ jqmipkgojfniemhcluckfnmtakhchWahlZZZb`_eb`idamgcni\ goklpmpqpupotonrnlqmkoljnjhligkgfjfeiddhccgaaf``eZ\ _dYZcWXaWW_VUYUTWTRUSPSSOQRMOQLMPJKOIINGGLEEKCCLDC\ NEDOEDQFDRGESHEUHEVIFXJFYKG_KG`LGaMHcNHdNHfOIgPIiQ\ JjRJlSKnTLoULqVMsWNuXOwZPw`QwbRwdRxfSxhTxjUxlUxnVx\ pWyrXytYzvZzx_zz`zw_zuYzrXzoVzmUzjSzgRzePzbOz_MzYL\ zVJzSIzQGzNFzKDzHCzFAzC9yA7y75y54y32z00y00x11yA1zK\ 1zN1zQ2zT2zU2zU3zU3zU3zU4zU4zU4zU4zU0zU0 } 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] Fractal Haircut
by Franktal Gallery 02 Jul '02

02 Jul '02

For a nice fractal hair turbulence example : http://www.geocities.com/franktal2002/fb/Nn06_b.jpg Miguel >>Did anyone else on the list take note of Ronaldo's fractal haircut >>during the latter stages of WC Korea\Japan 2002? Better yet, >>can anyone provide a par formula? > >Dunno about Ronaldo (he _has_ hair?), but what about Ahn Jung-Hwan's?! Now >_that's_ what I call filamentary structure! > _________________________________________________________________ MSN Photos is the easiest way to share and print your photos: http://photos.msn.com/support/worldwide.aspx

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FOTD 29 June
by John Lewis 30 Jun '02

30 Jun '02

I must say Jim's algae are much better looking than the stuff that grows in my pond! John -- John Lewis, jlewis(a)clara.net on 06/30/2002

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Scienide
by Andrew Coppin 30 Jun '02

30 Jun '02

>From: Jim Muth <jamth(a)mindspring.com> >Reply-To: fractint(a)mailman.xmission.com >To: fractint(a)mailman.xmission.com >CC: philofractal(a)lists.fractalus.com >Subject: [Fractint] FOTD 30-06-02 (Algae [7]) >Date: Sun, 30 Jun 2002 10:45:15 -0400 > >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 >} Question: what does this little critter actually do??? As far as I can tell, it iterates z = k(az^b + bz^f)+c (a strange choice of variable names, but hey...) I notice from the way the formula works that both the coefs and exponents have to be purely real. Then there's just the small matter of z0... I'm not sure, but isn't (-abgh)^j the same as the (f-b)th root of (-ab)/fd? And if so... why?!? I find it hard to belive that it just seemed like a nice expression to initialise the orbit to... Another question: when E is not a positive real integer, Z^E is multivalued. How about if E is an imaginary positive integer? Is it multivalued or single valued? Whimsical observation: Z^0.5 is double-valued; Z^0.25 has 4 values, z^0.1 has 10 values, z^0.01 has 100 values... by induction, z^0 has infinity values ;-) [of course, since the solutions to z^0.5, etc get progressively closer together, at z^0 all the infinity of solutions are THE SAME ONE: "1"] Andrew. "More scienide..." _________________________________________________________________ Send and receive Hotmail on your mobile device: http://mobile.msn.com

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FOTD 30-06-02 (Algae [7])
by Jim Muth 30 Jun '02

30 Jun '02

FOTD -- June 30, 2002 (Rating 7) Fractal visionaries and enthusiasts: Today we rise one step out of the rating-of-six rut that we've been mired in for several weeks, all the way up to a rating of 7. The rating seems fairly accurate, considering the unusual textures created by the reference standard outside coloring method of equal iteration bands. Normally, the powers of Z between 0 and +1 do not make fractals, but by using certain tricks, fractals can be coaxed from these powers. One of my favorite methods of getting fractals where none exist is to take the difference between two non-fractal- producing expressions and multiply it by a factor sufficient to create an image. In today's case, that factor is 13. The iterated formula subtracts 13 parts of Z^0.7 from 13 parts of Z^0.75 then adds C. The resulting parent fractal is quite sensitive to its bailout radius. In fact, changing the bailout has such a great effect on today's image that I suspect the entire image might be an artifact rather than a true fractal. But artifact or not, the image is worth being included in that ever-growing list of FOTD's. Studying the image, I was reminded of something that I could not quite remember. Then it came to me. The texture of the fractal elements mimics the texture of algae growing on rocks in a swift- flowing stream not too far from Fractal Central. The name "Algae" soon followed. If the bailout radius of today's image is raised, the picture goes totally black. The image evaporates as all the points become trapped. But then the image can be restored in a new form by setting the logmap to 0 and the inside fill to something non-flat, such as bof61. The 9-minute render time is somewhat slow, but fast relief for rendering pain is available in the form of a download from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Saturday here at Fractal Central was not perfect, but compared to how it can be in this part of the world at this time of year, it was good enough. The temperature of 88F 31C, combined with a hot sun, was warm enough for the kiddies to enjoy a splash in their back yard pools, and the humidity was not so high that the more strenuous activities engaged in by adults became unbearable. The cats spent most of the day just being cats and sleeping. As for me, I've got another curious fractal already waiting for the next appearance of the FOTD, which will be on July 2. (Starting in July, I am increasing the frequency of the FOTD to one every even-numbered day.) Until then, I've got the FOTD-CD to work on and a few fun things to do. Until July 2nd, take care, and do the things that need to be done, while ignoring the things that don't need to be done. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Algae { ; time=0:09:33.15--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.74222863652301170/+0.608902701512313\ 80/4.102563e+009/1/-125/-1.60218892474028873e-006 params=1/0.75/-1/0.7/12/1600 float=y maxiter=1500 inside=0 logmap=199 periodicity=20 colors=000f0T_0Mo0za3zQJzF_z3oz0zz0yx0ss4mo7gjCagG\ XcJS_OMVSGSVAO_4Jc0Ff0C`39XC7SJ4OS3I`0Dg09p04u06g0\ 6T66FCCL9GP6LV3PX1Tf0Yi0am0fs0jx0oz0pz0pz0ry0ry0rx\ 0sx0sv0sz0uu0uT0vs0Fg0zr0xr0xp0xp0loC`SPPo`Dom1oz0\ zz7izPyzfxvxzpzzlzzjzzjzyjyxjvxirviouijsifricrg_pg\ XogSmgPmgLfiI_jDSjALl6Fd37z00o00p00p30sCcuL3xV7ycD\ zlIzuMzvOxxOpyOjzOczOXzOQzOJzODxSApX7i_4ac1Vf0Tg3S\ i6Qi9PjAOlDMlGLmJJmLVdPfXTrOYzF`zGYyIXxITvJSuLPsLO\ rMLpMJoOGmPFlPCjQAiS7gS6fT3dT1fX3g_3ia4id4jf4li6ml\ 6mo7or7ps7rv9ry9szAuzAuzAuz7sz6sz4sz3vz0xz0zv0zp0z\ j0zf0z`0zX0z`0ucAlfLdjXXmfPppIsz0Ax0Iu0Os4Vr7`pAfo\ FmmIslLyjOziPziSzgTzgXzgYzf`zfazddzdfzdizcjzcmzaoz\ apzarz_syYuvXvsTvpSxmQyjPziMzfLzcJzdIzgFzjDzmCzpAp\ sF`vIJvM3vP6vT7vX9v_AvaCvfDviFvlGvoIvrSvmavilvdvva\ svdpvfmvgjviivjfxlcym`zoYzpXzrTzsQzuOzvMzxPzvSzuVz\ sYzs_zr_zp_zo_zo_zm_zl_zl } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] FOTD 27-06-02 (Birth [6])
by Jim Muth 29 Jun '02

29 Jun '02

At 08:00 AM 6/29/02 EDT, Bob Carr wrote: >Are discussions about religious, political and >moral issues really needed on this fractal group >get together? It's getting to be disgusting! I agree. I also accept responsibility for this round of off-topic banter. Being in a rush, I tried to save a minute or two by sending the same letter to the two lists via a C.Copy. I should have taken the time to edit the political stuff from the version that went to the Fractint list. Such blatantly off-topic material will not be posted to this list again. The philofractal list, which thrives on frivolous debate is a different story. Jim M.

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Re: [Fractint] FOTD 27-06-02 (Birth [6])
by Genealogy1＠aol.com 29 Jun '02

29 Jun '02

Are discussions about religious, political and moral issues really needed on this fractal group get together? It's getting to be disgusting! --Bob Carr--(Ocala, FL)

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FOTD 27-06-02 (Birth [6])
by Jim Muth 27 Jun '02

27 Jun '02

FOTD -- June 27, 2002 (Rating 6) Fractal visionaries and enthusiasts: I enjoy human foolishness and today we have a lot of it. The pledge of allegiance to the flag of the U.S.A. has been declared unconstitutional because it mentions God. I suppose the Declaration of Independence and Constitution are also unconstitutional because they also mention God. And our money is also unconstitutional because 'In God We Trust' is written on it. I wonder why Atheists are so intense in their disbelief. I happen to believe in some-something that in some way fits the description of a God. But I do not become offended when Atheists tell me that I am mistaken, or deluded, or clinging to a crying-towel etc. I simply enjoy the debate, satisfied that I am right and they are wrong, while having fun seeing their futile arguments. Why then do Atheists so often become offended when believers tell them and futilely try to convince them that they are mistaken in their disbelief? Actually, as I see it, Atheism is not so much a disbelief in a god as it is a continued belief in and a defense of the philosophy of positivism, a world-view which, IMO, lost credibility about 100 years ago, and except among Atheists has been declining ever since. As to what world-view will prevail to replace it, I have no idea. But one thing is certain -- a new world-view will need to extend beyond the traditional five senses. Most of the universe is invisible to our senses even aided by the best instruments. And we do have a fractal for today. For a change, there is no quadratic midget at the center. In fact, today's image consists of the entire fractal created by the formula -0.2(Z^(-1.25)-0.2(Z^(-0.8)+(1/C). While studying the image, I had the impression of a butterfly emerging from its cocoon. I named the image "Birth". I rated it at a run-of-the-mill 6. The 11-minute render time can be avoided by downloading the completed GIF file from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Wednesday here at Fractal Central was hot. In fact, it was the hottest day of the young summer. The temperature of 99F 37C and high humidity kept the cats confined to the shade of the porch and the fractalist confined to the coolness of the air-conditioning. Late in the afternoon a shower threatened, but died out before reaching Fractal Central. Today promises to be a repeat of yesterday, and the cats are already in their lazy mode. As for me, I've got work to do. As long as the air cooler keeps working, I'll be fine. Until next time on the 30th, take care, and see you then. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Birth { ; time=0:11:53.49--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-53.5822/78.0626/0.003628592/1/-112.5/-\ 3.77822773067748585e-014 params=-0.2/-1.25/-0.2/-0\ .8/0/0 float=y maxiter=12000 inside=0 logmap=yes periodicity=20 colors=000zzzzzxzwxzfvzatzZtzXrzVpz\ TnzRnzPlzNlzLjzJjzHfyFgxDdwBfxBbu9dt9`s7ap7`p7`n5Z\ m5Zj5Zj3Zh3Zh1Zd1Xe1Xb0Xb0XZ0X_0VX0VX0VU0VU0VR0VR0\ TR0TN0TM0TJ0TH0TF0RD0RD0RB0R90R70P70P50P30P10P10P0\ 0N00N00N00N00N00L00L00L00L00L00L00J00J00J00J00J00J\ 00H00H00F00F00F00D00D00D00B00B00B00900900900700700\ 50050050030030030010010010000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00300500900B01F05H09L0BN0FR0HT0LX0NZ0Rb0Vd0Xh0`j0b\ n0fp0ht0lv0pz0rz0vz0xz0zz0zz5tz9jzD`vHTrHVrJVrJXrJ\ XpLXpLZpLZpN`nN`nP`nP_nPYlRWlRUhQScRQZSOUTMPULKVJF\ dB1l50n70p90p90rB0rD1tD3tF5vH9vHBxJDxLHzLJzNLzPNzP\ RzRTzTVzTZzV`zXbzXdzZhz`jz`lzbpzdrzdtzfvzhzzhzzjzz\ lzzlzznzzpzzpzzrzztzzrzztzztzztzztzztzzvzzvzzvzzvz\ zvzzvzzxzzxzzxzzxzzxzzxzzzzzzzzzzzzxzzxzzvzztzztzz\ rzzpzzpzznzzlzzlzzjzzjzzhzzfzzfzzdzzbzzb } 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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Off-topic?
by John Wilson 27 Jun '02

27 Jun '02

Do our fractal lists not have any "off-topic" rule? Who cares about U.S. oaths, other than a few Americans? John W.

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Re: [Fractint] JuhYhgtFFe2
by Mark Christenson 26 Jun '02

26 Jun '02

At 05:00 PM 6/25/02 +1200, MLO wrote: >... >Morgan L. Owens >"And JuhYhgtFFe2 to you to! In fact, FuhhDCekGhgh43p as well! And the horse >you rode in on!" Reminds me of an absolutely hilarious bit Phil HNarFFtmanZ did on Letterman years ago. Egg Latin - including several completely filthy examples, the least offensive of which was "eggassheggole." Ahola, Bud

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Re: [Fractint] JuhYhgtFFe2
by Andrew Coppin 25 Jun '02

25 Jun '02

Ah, Mr. Lee, concise as ever! Andrew. "I read a lot of math litriture, but don't know much about it!" >From: "Paul N. Lee" <Paul.N.Lee(a)Worldnet.att.net> >Reply-To: fractint(a)mailman.xmission.com >To: fractint(a)mailman.xmission.com >Subject: Re: [Fractint] JuhYhgtFFe2 >Date: Mon, 24 Jun 2002 04:39:03 -0500 > >corollary (kôr´e-lèr-ê, kòr´-) noun > plural corollaries > Abbr. corol. > 1. A proposition that follows with little or no proof > required from one already proven. > 2. A deduction or an inference. > 3. A natural consequence or effect; a result. > >lemma (lèm´e) noun > plural lemmas or lemmata (lèm´e-te) > 1. A subsidiary proposition assumed to be valid and used to > demonstrate a principal proposition. > 2. A theme, an argument, or a subject indicated in a title. > 3. A word or phrase treated in a glossary or similar listing. _________________________________________________________________ Send and receive Hotmail on your mobile device: http://mobile.msn.com

4 6

FOTD 21-06-02 (A Nebular Minibrot [6])
by Jim Muth 25 Jun '02

25 Jun '02

FOTD -- June 21, 2002 (Rating 6) Fractal visionaries and enthusiasts: As I write these words, it is 9:24am EDT, the moment of the summer solstice in the northern hemisphere. The sun is now as far north as it ever gets. Actually, the sun is not located any farther north that it always is, for there is no north and south in space. What has happened is that the earth has reached the point in its orbit where the north end of its axis is tilted directly toward the sun, which makes today the longest day of the year. Today is not however the day with the latest sunset. Because the sun is now falling farther behind clock time each day, the day of latest sunset arrives in about one week. In the southern hemisphere, where everyone hangs from the earth's surface by their feet and Christmas comes in the summer, all this is reversed! Today's fractal is not upside down, but it *has* been rotated to the 'normal' position, with the negative stem actually pointing left, the way all proper stems should point. The image is the latest in the apparently unending series of Minibrots, and as such, features an object sometimes known as an atom, but better known as a Mandelbrot Midget. The formula that created not only today's scene but an entire fractal universe, mixes portions of Z^(-1.16) and Z^(-12.5) then adds 1/C instead of just plain C. I named the image "A Nebular Minibrot". The name is justified because the image does have a galactic feeling to it, complete with stars and greenish glowing clouds of gas. I rated the image at a 6, which is above average but not outstanding. The rendering time, for those who choose to run the parameter file, is a nominal 5-1/2 minutes on my lazy P200 machine. And as always, the completed image will soon be available on the two FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Thursday here at Fractal Central was pleasing to man and cats alike, though the cats had more time to enjoy the perfection. Brilliant sun, crystal blue skies, puffy white clouds, gentle winds, and a temperature of 83F 28C made everyone happy. As is usually the case however, I have a bit of work to accomplish before I can enjoy today, which promises to be a repeat of Thursday. Until next FOTD, which will arrive on the 24th, take care, and I'm not as dumb as I appear and not as smart as I pretend. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Nebular_Minibrot { ; time=0:05:27.90--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.9255785497758036/-1.12533132705048/8\ .889599e+009/1/10/0.000691584037123986473 params=1/-1.16/0.8/-12.5/0/0 float=y maxiter=1200 inside=0 logmap=112 periodicity=10 colors=000E758939C49E5AG5AJ6AL6BN7BQ7CS8CU8CX9DZ9D\ `AEcAEeBEgBJcCO`CTYCYVCbSCgPClMCqJCpNCoRCnUCmYClaC\ ldCkhCjlCioChsCgwCrqCXpWNgoQUUSG8PHBNIELIGJJJHJMFK\ ODKRBLT9LW7MZ5M`3Nc1Ne3Rb5U_7YX9`UBcRDgOFjLHmIJqFL\ tCMwAKvBIvBGvBEvCCvCAvC8vC6vD4vDzzD1vD5uB8uACu9Ft8\ Jt7Mt5Qs4Ts3Xs2_s1clMgefkZziYvhYsfYpeYldYibYfaYb`Y\ _ZYXYYTWYQVYNUYJSYGRYDQYAPXEOXHNXLMXOMXSLXVKWZJWaJ\ WeIhzHWlGWoGWrHZmI`iJbeKeaKgYLiUMlQNnMOpIOrERoFTmG\ VkHXiIZgJ`eKbcLe`LgZMiXNkVOmTPoRQqPRsNRhWTZdVPlWSk\ XVkYXkY_kZbk_dk_gk`jjaljaojbrjctjcwjdyjdtgcoeckccf\ aca_cYYcTVbPTbKRbFPbBNb6Lb2JbQ`_lqXnkUpfRr`OtWLvQI\ wLFqMLlNRgNWbOaYPgTPlOQrJQwMbcPnKSz0Uv4Vs8WoCXlGYi\ KZeO_bS`ZWaW_bTbZVaWW`SX`PY_LZZI_ZE`YBaX8bXFcTMePT\ gL_iIfkEmmAto7sq9rsBquDpwEoyGnzImzJlzLkzNjzOizQhzS\ hzTizRjzQkzOlzNlzMmzKnzJozIpzGpzFqzErzCszBszArzRrz\ frzvnzujztazHazHWzEQzBKz8 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 24-06-02 (Green Scene [6])
by Jim Muth 24 Jun '02

24 Jun '02

FOTD -- June 24, 2002 (Rating 6) Fractal visionaries and enthusiasts: When I checked my e-mail box a few minutes ago, I found among the 22 junk letters four letters that told me I had 'opted in' to something or other, two letters that were a 'reply to my inquiry', and two letters that had bounced back because I had sent them to a bad address. Curiously enough, I have no memory of 'opting in' to anything or 'making an inquiry' about anything or sending any letters to any invalid addresses. All of these letters had a line saying something like 'if this letter has reached you in error'. The puzzle of the day is why such a line needs to be included in letters that I supposedly have asked to receive. Does the sender have reason to suspect that he actually *is* sending the letter in error? If so, then the letter with the misleading subject is not an error but a deliberate effort to sell something to me. Most of these letters have no chance to succeed, particularly with me, since I have no desire to get a bogus diploma or consolidate my debts or increase my size, (I'm already a bit overweight). In addition, many of the letters are in <html> format and I have my e-mail reader set to display <html> coding as text, which makes the over-designed letters virtually impossible to read and destined for immediate consignment to the trash bin. Now that I've got that off my chest, I see that we have a fractal to at least acknowledge. The image is that of another Mandelbrot midget. This one is just different enough to make it worth the position of honor as FOTD for June 24. The parent fractal was created when I iterated the unusually simple even for me formula (Z^3)+0.357(Z^4)+C. I named the image "Green Scene". The name is purely descriptive, and based on the strong green coloring which appears in the image. The rating of 6 has become normal since the FOTD slipped to its temporary every-three-days schedule. The render time of 10 minutes can be cut by 3/4 by downloading the GIF image from Paul's web site: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather Sunday here at Fractal Central featured a bit too much of a good thing. The sun was a bit too hot, the air a bit too still, the humidity a bit too high, the ground a bit too dry, and the temperature of 91F 33C a bit too warm for cat comfort. The cats in question, after a few minutes outdoors, chose to spend the day in the indoor air conditioning. Which is where I'll spend most of today while I tend to the things that need to be done. Until next time, on the 27th, take care, and always try to separate truth from fiction. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Green_Scene { ; time=0:10:28.40--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.50637533704881520/+0.000758454262473\ 48/8.225209e+010/1/80.0208434512356774/-0.02262412\ 96535609898 params=1/3/0.357/4/0/0 float=y maxiter=1600 inside=0 logmap=218 periodicity=10 colors=000AFKGJREWfCgvWAsYDq_FoaImbKkdMifPhhRfiTdk\ WbmY`o`_pbYrdWtgUviSwkRjRSiLTfBUdCScCQbCPaDN_DMZDK\ YEIXEHVEFUGETICSKBQMAPOAOQAMS9LU9KW9IY8H_8Ga8Gc7Ge\ 7Gg7Gi7Gk6Gl6Gn6Gp6Gr5Gt5Gu5Gt5BrYDpXEnXGlWHjWJhWK\ gVMeVNcVOaUQ_URZTTXTUVTWTSXRSYQSZRQ_RP`SNaSMdTLgTJ\ jUImUGoVFqVEoTEmRElQEjOEhNEgLEeJEcIEbGE_FEYDEWBETA\ EQ8EQ7EUBDXEC`ICbLBdPBfSAgWAhZ9jb9ke8lh8mi7nj6oj6o\ k5pk5ql4rl4rm3sm3tn2un2uo1vo1wp0wp0cgJKZa1Rt8NoEKk\ KHgQEbWBZa8V`7W`7X_7Y_7Z_7_Z7_Z7`Z7aY7bY7cX7cX7dX7\ eW7fW7gW7gR8hM9iIAjDBk8Cl4CmAHmGMmLRmRWmW_madmfiml\ nmqrmmjZibKeW5``BWdHRhNMlTHpYGoWGoUFnTFnREmQEmODlM\ DlLCkJCkIBjGBjFAhG9gG8fG8dH7cH6bH5aH5_I4ZI3YI3XI4Y\ K5ZM6_O7`P7`R8aT9bVAcWBdYBd_CeaDfbEgdFhfFhgHffJgfL\ ifNkePmeRoeTqeVsdXudZwd`xdbycdzcfzchzcUzSFzHIzILzJ\ NzKQzLSzMVzNXzN_zOazPdzQfzRizSkzSnzRqzQtzPwzOyzOoz\ QfzRYzTOzUFzW6zXGzRGzRGzR } 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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JuhYhgtFFe2
by Andrew Coppin 24 Jun '02

24 Jun '02

Question: It's nothing to do with fractals, but what does the word "corollary" actaully mean? And while we're on the subject, what's a "lemma"? >From: "Morgan L. Owens" <packrat(a)nznet.gen.nz> >Reply-To: fractint(a)mailman.xmission.com >To: fractint(a)mailman.xmission.com, <fractint(a)mailman.xmission.com> >Subject: Re: [Fractint] FOTD 18-06-02 (Squaring the Circle [6]) >Date: Mon, 24 Jun 2002 13:09:47 +1200 > >At 06:21 24/06/2002, Multiple Bogeys wrote: >> > "Any sufficiently advanced technology is indistinguistable from magic?" >> >> > (If anyone knows whom wrote that, I'd be interested to know...) >> >>Arthur C. Clarke...I thought everyone knew that :) > >Corollary: Any technology distinguishable from magic is insufficiently >advanced. > >Morgan L. Owens >"Your mail seems awfully slow these days..." > > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint _________________________________________________________________ Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp.

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Re: [Fractint] FOTD 21-06-02 (A Nebular Minibrot [6])
by Jim Muth 24 Jun '02

24 Jun '02

I wrote: >>...What has happened is that the earth has reached the >>point in its orbit where the north end of its axis is >>tilted directly toward the sun,... Morgan clarified: >So the Sun's directly over the North pole? Don't you >mean that the Earth's Northern axis is intersecting a >line drawn through the sun perpendicular to the plane of >the Earth's orbit about the sun (since the Sun's own >rotational axis is irrelevant, even if it's the same)? Yes, this is what I meant. I simplified the wording. But on the planet Uranus, the sun does appear almost directly over the north pole once every Uranian year. Jim M.

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Re: [Fractint] FOTD 18-06-02 (Squaring the Circle [6])
by Multiple Bogeys 24 Jun '02

24 Jun '02

> "Any sufficiently advanced technology is indistinguistable from magic?" > (If anyone knows whom wrote that, I'd be interested to know...) Arthur C. Clarke...I thought everyone knew that :)Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com

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Re: [Fractint] FOTD 18-06-02 (Squaring the Circle [6])
by Jim Muth 19 Jun '02

19 Jun '02

A reply to Morgan's reply is posted to the philofractal list under the subject 'Theory of Everything'. Jim M.

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FOTD 18-06-02 (Squaring the Circle [6])
by Jim Muth 19 Jun '02

19 Jun '02

FOTD -- June 18, 2002 (Rating 6) Fractal visionaries and enthusiasts: I recently got hooked by one of those science book club offers. This club gives a joining gift of five popular science books at a bargain price in return for the obligation to purchase at least one not-so-popular science book at full price within a year. The books I received are mostly about the effort to apply Quantum Mechanics to the universe at large and find a Theory of Everything. (Via something like those trendy super-strings, I assume.) (I also noticed a recent letter from Osher Doctorow on the Fractint list about the topic.) Finding a T.O.E. is fine, but is the T.O.E. the books tell of really about *everything*? So far, I have had time only to skim the books, but in none of the indexes do I find an entry for mind or consciousness. It is as though the mind that is doing the searching does not exist, or if it does, is not included in the set of everything. Maybe self-awareness is simply too spooky for any respectable scientist to take a serious interest in. Maybe it is so mysterious that serious scientists would never tackle the problem for fear of being labelled soft on mysticism. I also find myself concerned that the theory of everything, when and if it comes and whether or not it includes the mind, will be in the form of mathematics so abstruse that only the initiated will be able to comprehend it. I do not want to settle for a watered-down version in a popularized (simplified) book, which will demand faith in the words I read. I want a theory that I can think about, understand, and connect to the 'real' world. I want to be able to say, 'yes, that explains everything', and observe the proof. (I realize that this will not happen.) A theory, the proof of which can be comprehended only by the high priests of science, would be of no satisfaction at all. In fact, IMO, it would border on mysticism. But then, considering how little of the world of science the common man can actually observe, science has been bordering on mysticism for the past 100 years. I'll have many more thoughts on this topic as I work my way through the five books. And by the way, there is a fractal for today -- another midget. This one is found in a prominent valley of the fractal that results when Z^(-1.54) is added to Z^(-15.4). I named today's picture "Squaring the Circle", and impossibility we learn in high school, and rated it a not-too-bad 6. The render time of 6 minutes is not bad either. For convenience, the completed GIF image is available for download on the W.W.Web at Paul's site: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at Scott's site: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Monday's weather here at Fractal Central was near perfect, making for contented cats and a pleased fractalist. The temperature of 82F 28C was made even more comfortable by the dry atmosphere, and best of all, at least 2 more similar days are forecast. The cats will be ecstatic. With a day's work before me, I'm not quite ecstatic, but ecstasy is within my grasp if only I play my cards right. While deciding which card to lead, I'll get a little real work finished. Until next time, which will arrive in about 72 hours, take care, and when the theory of everything appears, be sure it really explains everything, including why we need a theory of everything. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ SquaringTheCircle { ; time=0:06:28.87--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+2.13533630348576/-0.000841184669495/28\ 39969/1/72.5/-2.86436934102130003e-008 params=1/-1\ .54/1/-15.4/0/525 float=y maxiter=1300 inside=0 logmap=110 colors=000HSEHVGHZIHbKHeMHiOHlQHpSHsUHw\ WHzXLvZPr`SobWkdZgfbdhe`jiYllUnjQhsNrwJtzGvrMsjRpb\ WnV`kNeiFjf8od7j`7fY7bV7YR7UO7QL7LHzzz7DBwmHonJmbK\ jSMhGNf5ObBP_GQWLRTQSPVTM_UIdVFiWBnX8sY5xZAsZEnZIi\ ZMdZQ_ZUVZYQZaLZeGZqGYpHXpHWpHWpHVpHUpHUpHTpHToHSo\ HRomRoHQoHPoHPoHOoHOlJRiKTfLWcMY`N`YPbVQeSRgPSiMTl\ JVnGWqDXsAYv7Zx4_z7Wv9TrCQnENjHKfJHcME_OBWR8ST5OV2\ LU8OTDQTITSNVSSXRX_RaaQfcQkfPphPujSogUidWcbYY__SXa\ MVcGSeAPg5Ni4Rj3Uk2Ym2`n1do0gp0jl6hhBgdGe`LdXQbTVa\ P__LdZHiXDnW9sU5xTEtWMqZVmabjdkfgscjudaweUyfMzgEqb\ IhYM_TQROUJKXLL_NMaPNdROfTPhUQkWRmYSo_TraUtbUvcXuc\ Zuc`tdbtdesdgseirekrenqfpqfrpftpfvpgkcgaRgSEdUJaVO\ _WSXXXVYaSZeQ_jN`oLasS_nZZie_dl`_saVpbWmcWjdWgeWdf\ WagWahWciWejWgkWilWkmWmnWooWqpWsqWurewsozukzwhzxez\ ybzzZzzWzzTzzQzzMzzJzzGzzDzz9zz6zz3zz0zz5zzAzzFzzK\ zzPzzUzzYzzXzzWzzVzzUzzTzzSzzRzzAzzC } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] FOTD 18-06-02 (Squaring the Circle [6])
by Andrew Coppin 19 Jun '02

19 Jun '02

>From: Jim Muth <jamth(a)mindspring.com> >Reply-To: fractint(a)mailman.xmission.com >To: fractint(a)mailman.xmission.com >CC: philofractal(a)lists.fractalus.com >Subject: [Fractint] FOTD 18-06-02 (Squaring the Circle [6]) >Date: Tue, 18 Jun 2002 11:54:15 -0400 > >FOTD -- June 18, 2002 (Rating 6) > >Fractal visionaries and enthusiasts: > >I want a theory that I can think about, understand, and connect >to the 'real' world. I want to be able to say, 'yes, that >explains everything', and observe the proof. (I realize that >this will not happen.) A theory, the proof of which can be >comprehended only by the high priests of science, would be of no >satisfaction at all. In fact, IMO, it would border on >mysticism. But then, considering how little of the world of >science the common man can actually observe, science has been >bordering on mysticism for the past 100 years. "Any sufficiently advanced technology is indistinguistable from magic?" (If anyone knows whom wrote that, I'd be interested to know...) Thanks. Andrew. _________________________________________________________________ MSN Photos is the easiest way to share and print your photos: http://photos.msn.com/support/worldwide.aspx

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Re: [Fractint] FOTD 18-06-02 (Squaring the Circle [6])
by Franktal Gallery 18 Jun '02

18 Jun '02

Usually attributed to SF author Arthur C. Clarke. >From: "Andrew Coppin" <orphi69(a)hotmail.com> > >"Any sufficiently advanced technology is indistinguistable from magic?" > >(If anyone knows whom wrote that, I'd be interested to know...) _________________________________________________________________ MSN Photos is the easiest way to share and print your photos: http://photos.msn.com/support/worldwide.aspx

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A Fractal-Related Theory of Everything (TOE)
by Osher Doctorow 17 Jun '02

17 Jun '02

From: Osher Doctorow osher(a)ix.netcom.com, Mon. June 17, 2002 1:54PM Current physics fads explain the universe and its parts (toward a *Theory of Everything* or TOE) by discrete entities (quanta) and *fields* on the microscopic level and by bending of space on the macroscopic level, with the general opinion (for what it is worth) being that the quantum ultimately will explain everything. String/brane/duality/loop theories add string tension (sort of like how stiff a violin string is) to eliminate paradoxes, of which the standard quantum field theories are full, and to try to relate the microscopic and macroscopic in *quantum gravity*, which so far has not been achieved. Is there something wrong with this picture? I would say yes, but one must look at it quite a bit to come to that conclusion. One way to determine this is to ask what mathematical tools the physicists are using. It turns out that they are almost entirely using algebraic topology and algebraic geometry. Since Creative Genius tends to be most profound when it is across verbal and quantitative fields (like Leonardo Da Vinci), and since Creative Genius tends to be heavily interdisciplinary, the almost exclusive use of two mathematical techniques (which, by the way, provide extremely few intuitive explanatory concepts and are super-abstract) arouses some warning signals. There's actually a good candidate for an alternative TOE right amidst fractal- and chaos-related disciplines provided that we also use many interdisciplinary methods. It turns out that the most characteristic feature of the universe is its expansion (or theoretically expansion-contraction), which is growth, which is quite similar to the growth feature of life. But we know from botany that life solves the *packing with growth* problem of mathematics by putting seeds and buds and so on at an angle equal to the Golden Ratio (also known as the Golden Mean - not the ethical concept). The Golden Ratio in turn is related to the Harmonic and Geometric and Arithmetic Means, especially the Harmonic Mean. Is there an equation which we can PROVE MATHEMATICALLY that might give us some handle on a TOE? Yes. Here it is: 1) (x - y)/(xy) = (1/y) - (1/x) for real x, y, with y < = x. Recall that the harmonic mean h of x and y is given by: 2) h = 2/[(1/x) + (1/y)] I have introduced the *real conjugate* of u + v for u < = v, namely u - v (any real u, v), and I denote it by an asterisk: 3) (u + v)* = u - v for u < = v Now, the universe is divided into three types of events/process (events for short): Rare (R), Fairly Frequent (F), and Very Frequent (V). R corresponds to Lukaciewicz (L) fuzzy multivalued logical implication (x-->y)L = 1 + y - x, V to Godel fuzzy multivalued logical implication (x-->y)G = y, where L and G here are supposed to be subscripts on (x-->y). L, in turn, corresponds to Logic-Based-Probability-Statistics (LBP), G to Independent Probability-Statistics (IPS), and F to Bayesian Conditional Probability-Statistics (BCP). The correspondence continues across proximity-geometry-topology. So if we can rewrite (1) in terms of L and G and either the harmonic mean or the Golden Ratio, we will have related quite a few interdisciplinary fields. Here is the rewritten equivalent version: 4) [1 - (x-->y)L]/[(x-->y)G (y-->x)G] = -2HAR*(x, y) where HAR(x, y) = 1/h. Noting that the left side of (4) is the ratio of *extreme* events in the sense that L and G are rare vs very frequent events, while the third type of fuzzy multivalued logic Product-Goguen (PG) is *mean* or *intermediate* (fairly frequent events), we recall that Euclid defined the Golden Ratio as the solution of the extreme-mean ratio of line segment lengths: divide a line segment or string into two parts, one longer and one shorter, and the original segment is then the longest, the shorter cut segment is the shortest, and the other segment is the *mean* segment. The fraction or ratio of the shorter cut length divided by the longer cut length is now set equal to the ratio of the longer cut length to the uncut length. This yields an equation whose solution is the Golden Ratio. The similarity of extreme and mean lemgths and extreme and mean frequency events is remarkable. Osher Doctorow

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FOTD 15-06-02 (Fractal in Holland [7])
by Jim Muth 17 Jun '02

17 Jun '02

FOTD -- June 15, 2002 (Rating 7) Fractal visionaries and enthusiasts: I'm trying to remember the point at which fractals became art. When I discovered them almost 20 years ago, fractals were mathematical abstractions made visible, if not tangible, through the miracle of the modern computer. They were not considered art. But by 1996 they had become art. Now, we're involved in futile debates about whether fractals based on spirals make good or bad fractal art. I am still undecided whether fractals should be considered art at all. I am also undecided whether the present-day images should be considered fractals or computer art. Whatever they are, the images certainly are great things to chat about. But a work of art is a recording of human emotion, rendered in such a way that those of similar psychological make-up, by experiencing the work of art, can feel some measure of the emotions the artist felt while creating the art. When I sit at my machine to create (or find) fractals, it is a means of relaxing after days too often filled with frustration. I sometimes put little if any emotion into the images, preferring instead to sit and watch half interested as the numbers do what they will. (I expend a bit more creative energy when something unexpected appears.) But if a work has so little emotion put into it at the time of its creation, how can it be considered art? In contrast, I find the greatest emotional satisfaction while experiencing the supposedly insentient things of nature, such as the universe, with its stars and galaxies, and the atmosphere with its alternating sun and storms. These things are not created to be art; they simply just happen. Where then does the emotion and artistic satisfaction that I feel when experiencing nature, originate? It originates within myself. Art exists in the eye of the beholder. And perhaps the images that I put so little into can create something in others just as nature creates enjoyment in me. I have many more thoughts tumbling around, but after rambling for nearly 1/2 hour, I see that we have a fractal image to discuss. I named today's picture "Fractal in Holland" when I noticed the windmill-blade shape of the elements around the ubiquitous midget (not a spiral) at the center. I rated it at a 7 because it's kind of a nice picture. The formula behind the image is Z^(-0.75)+4Z^(-7.5)+(1/C). The (1/C) turns the originally inside-out parent fractal inside out again, making it into a normal fractal with a bay at its center. Such doubly inside-out fractals are very rich hunting grounds. The 15-minute render time of the parameter file makes a download of the completed GIF image the best choice. The download may be found at Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather here at Fractal Central was rainy both Thursday and Friday, with a cool temperature in the 60's. After being stuck indoors for two days, the fractal cats became restless and testy, but this morning is dry if not sunny, and the cats should soon be venturing into the yard for fun and games. As for me, I'm going to venture into the continuing preparation of the FOTD-CD, which will include pictures of the fractal cats. Until next time, which will arrive on June 18, take care, and be artistic. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_in_Holland { ; time=0:15:24.06--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.39512827318548100/-0.082052873710134\ 88/1825094/1/87.4999997863123724/2.302319189462220\ 81e-007 params=1/-0.75/4/-7.5/0/525 float=y maxiter=3600 inside=0 logmap=142 periodicity=10 colors=000tI8tJ9oJ9lK9gKAdLAaMAbN9cO9eP9fR9hS9iT9k\ V9lW9nX9oZ9q_9r`9tb9uc9vd9se8pf8nf7kg7ih6fh6di5aj5\ _j5`i9ahCbhFcgIdfLdfOeeRfdUgdXhc_ibbibegZceWacT_aQ\ ZSScJThAUm1Vr5Uo8TmCSkFRhJQfMPdQPaTO_XNY_MVcLTfKRi\ KPfMNdOLbPJ`RHZSFXUEVWCTXARZ8P_6Na4Lb3Md4Me5Mg5Mh6\ Ni6Nk7Nl7Nn8Oo8Op9Or9OsAOtAPpCPlEQhGQdIRaJRYLSUNSQ\ PTMRTJSUFUUBWV7YV3_V0`R8cOFfKMiHTlD_oAfr7mtCioGekK\ agOYbTUZXQV`MQdIMhFIdIJ`LJXOKUQKQTLMWLIZMF`MBcN7fN\ 3iO0kO1iQ2gR3fT4dU5bW5aX6_Z7Z_8X`9Vb9UcASeBQfCPhDN\ iDMjHPeKSaNVYQYUT`PWcLZfHahDajIakMalQamUanYaoaaqea\ riasmatqauuavybuubtrbsnbrkbrhbqdbpaboYboVbnSbmOblL\ blIedQgcYjeelgmnitjkpgnldqhateYwaVzYSzVPzRMzNIzJFz\ GCzC9z86z5Dz9KzCRzGYzJUzMRzOOzRLzTNzUOzVPzVRzWSzXT\ zXVzYWzYXzZZz__z_`z`az`_zXYzUWzQUzNSzKQzGOzDNzAPzG\ RzLTzQVzVWz`Yze_zjazobzt_ztYztWztUztSztPztNztLztJz\ tHztEztCztAzt8zt6zt4zt7zo } 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] Fractalus Universe calendar choices for 2004
by Franktal Gallery 16 Jun '02

16 Jun '02

I wish I did ...;-) >From: Guy Marson <guy.marson(a)mnhn.lu> >wouwww.. did you made this paint? > >http://www.geocities.com/franktal2002/fb/Nn01_b.jpg > >Cheers, > >Guy _________________________________________________________________ MSN Photos is the easiest way to share and print your photos: http://photos.msn.com/support/worldwide.aspx

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Re: [fractal-art] Controversial Issue...
by Franktal Gallery 16 Jun '02

16 Jun '02

>>>From: "gumbycat" <gumbykat(a)tampabay.rr.com> >>>I don't know what program Miguel Fliguer uses, but his were sent to >>>Avalanche. It's good to hear that! ;-) The images were made with the venerable Vivid raytracer (and a lot of patience). >>>So far, the only discussion I saw was this one. I'm subscribed to the UF >>>List, and the Fractal Arts List, only. After you posted your message, I >>>gave abpf, FractalWorld, and Renderosity a quick look. I didn't see any >>>discussion, so either it wasn't there, >>>I missed it, or it was deleted before I got there. I posted my comments about the spiral-oriented calendar a few days ago on the good ol' Fractint mailing list. I believe the final selections were a reflection of the publisher's taste, and even if all entries would have been sent directly to Avalanche, we'd end with a different, but still spiral-dominated, calendar. Thanks everybody for the stimulating discussion ! Miguel http://www.geocities.com/franktal2002 _________________________________________________________________ MSN Photos is the easiest way to share and print your photos: http://photos.msn.com/support/worldwide.aspx

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Re: [Fractint] Fractalus Universe calendar choices for 2004
by Franktal Gallery 14 Jun '02

14 Jun '02

Overall, these are very nice selections. However, all eleven pictures have the spiral shape as a distinctive feature. I would've liked to see more variety... Anyway, just my opinion. Best regards, Miguel http://www.geocities.com/franktal2002 >From: "gumbycat" <gumbycat(a)allisonart.com> >Reply-To: fractint(a)mailman.xmission.com >To: <Fractint(a)mailman.xmission.com> >Subject: [Fractint] Fractalus Universe calendar choices for 2004 >Date: Sun, 9 Jun 2002 14:53:19 -0400 > >Hi, > >Avalanche is done choosing images for the 2004 "Fractal Universe" calendar. >Congratulations to those artists that had one or more images chosen! Those >artists are: > >Linda Bucklin >Keith Mackay >Edward Perry >Jen Gierek >Johan Groth >Damien Jones >Anna Laurie >Doug Owens >Etienne Saint-Amant > >Avalanche also chose one of Tina's images and two of Linda's. The final >selection can be seen on the gallery page at: >http://www.fractalforum.com/fc2004/index.html > >Our thanks to all of you who participated in the submission and selection >process. > _________________________________________________________________ Join the worlds largest e-mail service with MSN Hotmail. http://www.hotmail.com

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FOTD 12-06-02 (Fractal Olives [5])
by Jim Muth 12 Jun '02

12 Jun '02

FOTD -- June 12, 2002 (Rating 5) Fractal visionaries and enthusiasts: Yesterday I checked the winning fractal images that will appear in the 2004 fractal calendar. They're all good images, well worth the honor they have been given, but I couldn't shake the impression that beneath the glitter they all look alike. Then I checked my recent fractal offerings and noticed that beneath the various adornments, they also all look alike. The largest percentage of the calendar fractals are embellished spirals; most of my FOTD fractals are Mandelbrot midgets, not quite as embellished, but still starting to look monotonously alike. Is this similarity the beginning of the path to a fractal dead end? Or have I merely decided to specialize in one inexhaustible aspect of the world of fractals? Perhaps I should add some variety to my fractal explorations -- take a few new paths in the months to come. I'll make that decision when the FOTD CD is safely wrapped up. Today's image however is one of another quadratic midget, this one located in a spurious valley of the fractal created by mixing various portions of Z^(-0.876) and Z^(-8.76), then adding (1/C). I named the image "Fractal Olives" because of the olive- green color of the eight small spirals surrounding the midget, and not because I like olives. In fact, I can't stand the disgusting fruit or berry or whatever it is. I rated the image at a perfectly average 5. After all, it's just another midget, with little or nothing to remember it by. The 15-minute render time is rather slow for such a mediocre image. The better way of viewing the image is to download it from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather Tuesday here at Fractal Central was quite hot and humid, with unhealthy air that made things even worse. The temperature of 93F 34C kept the cats confined to the shade of the porch. The health warnings broadcast by the media got me to wondering about the silence from the environmentalists. Why do the environmentalists, who speak so loudly about possible future environmental hazards, remain so silent about already existing hazards such as the dangerously polluted air in our big cities? But that's another story for another time. Right now, it's another hot and polluted day, and there's graphic work to be done. So until next time, take care, and try not to wonder about too many puzzling things. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Olives { ; time=0:15:56.15--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.899069712774904/+1.705978163181609/\ 1.805295e+007/1/102.5/2.05521459022833808e-006 params=3/-0.876/1/-8.76/-0.683/0 float=y maxiter=1600 inside=0 logmap=267 periodicity=10 colors=000dO0eQ2dQ6fR8eR9fTBeTFgVGgUIhXMgYOhZPh`Rh\ aVhaXjcZjeajecngeqhgujhyjjzjlzjnzjpzjuzjyzjzzjzzjz\ zjyzjwzjszjpzjnzjjzjgzjezjazj`zjXzjTzjRzjOzjMzjPzj\ RzjTzjVzjXzjZuj`qjanjchjeejgajhZjjTjnPlpMnqGpsDqu9\ uw4wy0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz2zz6zz8zzBzz\ FzzIzzMzzPzyTzyVzwZzwazwezuhzulzspzsqzsszuszuuzwuz\ wwwywsywpyylzwgzyczw`zwXywTywPwwMwwKuwIuuMsuOuwRww\ TyyXzyZzw`zwczuezuhzsjzqjzqlzplzpnznnzlnzlpzjpzjqz\ hqzgqzgszeszeuzcuzauzawz`wz`yzZyzZyzZyzXzeZzgZzg`z\ h`zhazjazjazjczlczlezneznhzqeznazlZsjVlhRegOaeMacP\ g`TjZXjX0jVXjTTjTPjRMjRIjPFjPBgO8aO4XM0RM0MK0GK0BI\ 06I00M02I08F0FD2K99P6GX4Oa0Tg0`n0gs0lt0ju0hs0gq0ep\ 0el0cj0ah0`g0Ze2Za4X`6VZ6TX8RV9RRBPPBOODMMFKGDMKFM\ MFMOGMPGMTIOVIOXKOZKOaMOcMPeOPgOPhPPlPRnRTpRVqTXuT\ ZwV`yVazXczXezZgzZhz`jzZlz`nzapzcqzcszeuzgwzhyzhzz\ jzzjzzjzzjzzjzzjzzjzzjzzj } 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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Xfractint 20.2.04
by Scott D. Boyd 10 Jun '02

10 Jun '02

Hi all, I have *finally* updated my binary package of Xfractint that is available on my Web site. It's now updated to the latest developers version - 20.2.04, and my Xfractint page has gone through a major re-design. For more details, and to download Xfractint 20.2.04, please go to: http://sdboyd.dyndns.org/~sdboyd/xfractint/xfractint.html Have fun! Scott Boyd

4 4

Kleinian Pars
by JoWeber 09 Jun '02

09 Jun '02

Hi all, somme pars with kleinian-formulas. Enjoy --Jo Weber-- http://www.joweber.de jo_kl_02 { ; June 02, 2002 0:00:53.77 ; Pentium 900 Mhz by Jochen Weber ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=formulas.frm formulaname=mod5klein_group passes=1 center-mag=0.794169/-1.15521/2.593386/1/115.000000039194887/-1.455482248\ 89102684e-007 params=1/1.25/1.5/2.25/0.25/0.5/1/0 float=y maxiter=15000 inside=bof60 outside=atan periodicity=0 colors=000fH0<3>sM0wO0zP0<8>PA0L80H70<3>000<3>B94EB5HD6JF7MH8<2>RMBSNBTN\ CUOCVOCVPC<3>SNBRMBPKAOJ9<3>EB5C94973<2>000<4>0KU0NZ0Qc0Uh0Wl0Zp0`s0bu0c\ x0dy0ez<3>0cx0bu0`s0Zp0Wl0Uh<3>0FN0BH07B046000<3>B94EB5HD6JF7MH8<2>RMBSN\ BTNCUOCVOCVPC<3>SNBRMBPKAOJ9<3>EB5B84863642321611<3>U55Z66c77h88l99pAAsB\ BuBBxBByCCzCC<3>xBBuBBsBBpAA<3>Z66U55O44<3>000<3>9J4BN5DR6<3>KdAMgBNiBNj\ BOlCOlCPmCOlCOlCNjBNiB<2>Ja9HZ8FV7<3>6D3492241000<3>99OBBUDDZFFcHHhJJlKK\ pMMsNNuNNxOOyOOzPPzOOyOOyNNxNNuMMsKKp<3>DDZBBU99O<3>000<3>OJ4UN5ZR6cV7hZ\ 8la9pdAsgBuiBxjBylCzlCzmCzlCylCxjBuiBsgBpdA<3>ZR6UN5OJ4<3>000620C40<7>bF\ 0 } jo_kl_06 { ; June 02, 2002 0:00:32.30 ; Pentium 900 Mhz by Jochen Weber ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=formulas.frm formulaname=mod5klein_group passes=1 center-mag=0.540167/1.42224/2.655525/1/-135.000000055134819/4.3111121429\ 6842071e-008 params=1.25/2/1.5/2.25/0.25/0.5/1/0 float=y maxiter=15000 inside=bof60 outside=atan periodicity=0 colors=000<3>000000UUU___oie<6>eSQdQOcNM<3>YDDWBAV88T55<9>kA9mB9oBA<2>uD\ BwECwGC<10>yf4yi3yk2ym1<3>zz0<4>ye1ya1yY1<3>xH2<9>N61J51F41<3>000<4>000<\ 2>000<3>D08H0AJ09<3>T05V04Y03<2>d00<20>K5GJ6HI6H<2>F7JD8KA9J<2>0BG<28>1R\ c1Sc1Sd1Te1Ue<6>7Xf8Xf9Ye<41>nsbotbptb<2>svbtwbuwd<2>zzm<3>ojjlfiibhfZgc\ Uf<3>OIQKFMGCH<3>000000zaF000 } jo_kl_10 { ; June 02, 2002 0:01:37.99 ; Pentium 900 Mhz by Jochen Weber ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=formulas.frm formulaname=mod5klein_group passes=1 center-mag=-0.52781230222012580/+1.43454734330997400/971.0747/1/37.50000\ 00000024016/-5.55922669009945025e-012 params=25/1/3.5/2/5/5/5/0 float=y maxiter=1000 proximity=2 outside=fmod periodicity=0 cyclerange=0/255 colors=000SPV<13>E__D``Ca`<2>9da8da9b_<18>CFGCEFCCD<2>C8AD79D79<55>lZ8m_\ 8n`7<18>pc6pd6pd6<4>oc6oc6oc6nb6nb6nb6<79>NCAMBAMBA<3>K9BGAB<23>po3rq2ss\ 2<3>zz0TOV } jo_kl_13 { ; June 02, 2002 0:00:50.37 ; Pentium 900 Mhz by Jochen Weber ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=formulas.frm formulaname=mod5klein_group passes=1 center-mag=-1.95883/2.28763/20.11368/0.8969/49.0566696128656687/2.050903\ 62691718253 params=5/2.5/3.5/2/5/5/5/0 float=y maxiter=1000 inside=0 proximity=2.1 outside=fmod periodicity=0 cyclerange=0/255 colors=000FF0<55>vv0vv0ww0<2>zz0zz0yy0<55>KK0JJ0II0<3>FF000F<57>00v00v00\ w<2>00z00z00y<55>00K00J00I<3>00FFF0 } jo_kl_15 { ; June 02, 2002 0:01:45.36 ; Pentium 900 Mhz by Jochen Weber ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=formulas.frm formulaname=mod5klein_group passes=1 center-mag=-83.7064/-101.095/0.08510823/1/-90/-1.23373533611470521e-014 params=2.9/0.58/1.5/1/0/1.51/0.85/0 float=y maxiter=1023 proximity=3.45 outside=fmod periodicity=0 colors=000qsw<15>WgnUfnTfm<3>NbkMajKajJ`iH_h<2>LaiNbjPcjRdkSel<8>gnqiorj\ pr<3>rtutuvuvvwww<8>WZgTWeQUc<3>DIWAFUCHV<17>eglgimhjn<3>pqrrststuuvv<5>\ kloijnghmffldek<2>``hZ_gXYfVWdUUc<6>IIWGGVEFU<3>77Q55P44O22N00L<5>99RBBS\ DDTFFUGGV<6>SSaUUbWWcYYdZZe``g<6>llonnpppq<2>uutwwvwwt<17>ysUysSysR<2>ys\ MzrKypK<8>saHr_HqYH<2>oTGnRFlQE<7>QB6OA5L84<3>A00<4>F00<3>K00<3>TC0<8>lc\ `ngepji<3>zwz<5>rtx } jo_kl_17 { ; June 02, 2002 0:00:12.03 ; Pentium 900 Mhz by Jochen Weber ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=formulas.frm formulaname=inv4klein_group passes=1 center-mag=0.253411/-0.0274059/0.381288 params=2/4/0/0.54 float=y maxiter=1000 inside=0 proximity=6 outside=fmod periodicity=0 cyclerange=0/255 colors=000d_h<93>WL5WL5WL4<2>VK3VK3VL4<88>swhtwhtxi<3>uyjuyjtxj<55>bhg } frm:Mod5Klein_Group {;Modification of "4Klein_Group" by Morgan L. Owens ;Circle 1 and 2 touch, 3 and 4 each touch 1 and 2. ;Parameters of circle 5 are not restricted. Circle has "inverted" function. ;periodicity=no ;------------------------------------ ;p1r: radius 1 ;p1i: radius 2 ;p2r: radius 3 ;p2i: radius 4 ;p3r: Center of circle 5 x-coordinate ;p3i: Center of circle 5 y-coordinate ;p4r: radius 5 ;------------------------------------ r1 = real(p1) r2 = imag(p1) r3 = real(p2) r4 = imag(p2) r5 = real(p4) ;c1 = -r1 ;c2 = r2 c3 = ((r1-r2)*r3+flip(sqrt((r1+r2+r3)*r1*r2*r3)*2))/(r1+r2) c4 = ((r1-r2)*r4-flip(sqrt((r1+r2+r4)*r1*r2*r4)*2))/(r1+r2) rr1 = sqr(r1) rr2 = sqr(r2) rr3 = sqr(r3) rr4 = sqr(r4) rr5 = sqr(r5) z = pixel: inside = 0 IF (|z+r1| < rr1) z = r1*conj(r1/(z+r1)) - r1 inside = 1 ELSEIF (|z-r2| < rr2) z = r2*conj(r2/(z-r2)) + r2 inside = 1 ELSEIF (|z-c3| < rr3) z = r3*conj(r3/(z-c3)) + c3 inside = 1 ELSEIF (|z-c4| < rr4) z = r4*conj(r4/(z-c4)) + c4 inside = 1 ELSEIF (|z-p3| > rr5) z = r5*conj(r5/(z-p3)) + p3 inside = 1 ENDIF inside } frm:Inv4Klein_Group {;Modification of "3Klein_Group" by Morgan L. Owens ;Circle 4 has "inverted" function. ;periodicity=no ;( Circles all touching: r123 = sqrt(3)/2 ; r4 = sqrt(3)/2 + 1 ; c4 = 0 ) ;------------------------------------ ;p1r: radii 1 to 3 ;p1i: radius 4 ;p2r: Center of circle 4 x-coordinate ;p2i: Center of circle 4 y-coordinate ;------------------------------------ ; ang = 2*pi/3 c1 = 1 c2 = exp((0,1)*ang) c3 = exp((0,2)*ang) r123 = real(p1) r4 = imag(p1) rr123 = sqr(r123) rr4 = sqr(r4) z = pixel: inside = 0 IF (|z-c1| < rr123) z = r123*conj(r123/(z-c1)) + c1 inside = 1 ELSEIF (|z-c2| < rr123) z = r123*conj(r123/(z-c2)) + c2 inside = 1 ELSEIF (|z-c3| < rr123) z = r123*conj(r123/(z-c3)) + c3 inside = 1 ELSEIF (|z-p2| > rr4) z = r4*conj(r4/(z-p2)) + p2 inside = 1 ENDIF inside }

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Xfractint 20.2.04
by Scott D. Boyd 09 Jun '02

09 Jun '02

Hi all! My binary package ox Xfractint has been updated once again. This time, I re-compiled with nasm assembler support, which allows Xfractint to generate the mandel and julia types much quicker. I've both updated the full package files, and put the updated executable file on my Website. http://sdboyd.dyndns.org/~sdboyd/xfractint/xfractint.html Scott Boyd

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Fractalus Universe calendar choices for 2004
by gumbycat 09 Jun '02

09 Jun '02

Hi, Avalanche is done choosing images for the 2004 "Fractal Universe" calendar. Congratulations to those artists that had one or more images chosen! Those artists are: Linda Bucklin Keith Mackay Edward Perry Jen Gierek Johan Groth Damien Jones Anna Laurie Doug Owens Etienne Saint-Amant Avalanche also chose one of Tina's images and two of Linda's. The final selection can be seen on the gallery page at: http://www.fractalforum.com/fc2004/index.html Our thanks to all of you who participated in the submission and selection process. Tina and Linda

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FOTD 09-06-02 (Ice-World [4])
by Jim Muth 09 Jun '02

09 Jun '02

FOTD -- June 09, 2002 (Rating 4) Fractal visionaries and enthusiasts: As I have stated several times in the past, I do not do fractal transformations or layers. The reason is not that I feel something is wrong with doing these things, but that I enjoy discovering the basic fractal shapes rather than doing artistic things with my discoveries. My fractals are indeed discoveries rather than works of art. On rare occasions however, my artistic impulse has gotten the better of me, and I have dabbled in fractal transformations. Today's simple 3-D transformation of a type=plasma image is a result of some Fractint dabbling I did about 9 years ago. The image, which I found while gathering old images for the upcoming FOTD CD, is basically 9 years old. I did nothing but a slight adjustment of the colors to produce today's FOTD image. As is the case with so many of my old images, many of which were created by programs other than Fractint, today's image has no saved parameters that can be used to reconstruct the image, making it necessary to download the image itself from either Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> I named the image "Ice-World". The reason is obvious. It takes no imagination to see a jagged icy scene on perhaps the water ice planet Europa, a moon of Jupiter. Since the image is a transformation, and I'm not supposed to do transformations, I could rate it no higher than a 4, the highest rating that is still below average. The fractal weather Saturday here at Fractal Central was close to perfect. The blue skies, sharp shafts of sunlight through the trees, light winds, low humidity, and a temperature of 77F 25C could hardly be exceeded. The fractal cats, who enjoy perfection, were nearly perfectly happy in the yard all day, even forgetting for a while that they were hungry. When the sun sank low in the west, and the chill of evening set in, they finally thought of food, and cried to be fed. Since it looks like another near perfect day coming up today, I'm going to try to join the cats and be as close to perfectly happy as possible. To keep my mind occupied, I'll start reading Hawking's newest book, "The Universe in a Nutshell", which I picked up last week. Of course, I'll probably never reach the ideal of absolute perfection in happiness, but I'll enjoy myself trying to come as close as possible. Until next time and next FOTD, which will appear on June 12, take care, and don't lose your cool when you see the ice. Finally, do not despair. The FOTD will return to its daily schedule in only a few months. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com NO PARAMETER FILE AVAILABLE

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Re: [Fractint] Kleinian Group formulas - Pars (and) More pars
by Sylvie Gallet 08 Jun '02

08 Jun '02

Hi Gerald, >> That's the first time I've seen images by you *and* knowing beforehand >> the formulas they are based on (therefore probably having formed a kind >> of preconception what kind of pictures I could expect). I haven't posted any image in a while... >> Needless to say your images were a 100 percent surprise. :-) Thanks for the formulas. Here's a couple more pars: m5KLN04 { ; . t= 0:04:08.38 ; Copyright Sylvie Gallet, May 28, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=klein.frm formulaname=Mod5Klein_Group passes=1 center-mag=-0.714769/1.47741/11.17785/1/-27.500000000000032/\ 3.85524945301085609e-014 params=25/1/3.5/2/5/5/5/0 float=y maxiter=1000 inside=0 proximity=2 outside=fmod periodicity=0 cyclerange=0/255 sound=off colors=Wab<27>hlohloimp<3>jnqjnqjnq<6>imoimoimo<3>hlnhkngkn<\ 108>QTTQTTQTTQTSPTSPTS<79>CGCBGCBGB<3>AFAAA0<2>K00 } m5KLN05 { ; . t= 0:02:55.71 ; Copyright Sylvie Gallet, May 28, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=klein.frm formulaname=Mod5Klein_Group passes=1 center-mag=-0.91962/2.94147/1.470554/1.1205/137.802234114105\ 147/-0.571944980072052411 params=5/2.5/3.5/2/5/5/5/0 float=y maxiter=1000 inside=0 proximity=2.1 outside=fmod periodicity=0 cyclerange=0/255 sound=off colors=hloWab<26>hlohloimp<3>jnqjnqjnq<135>TXWTXWTXW<70>CHCC\ HCBGC<3>AFAFA0<2>K00 } Cheers, - Sylvie ----------------------------------------------- E-mail: Sylvie_Gallet(a)CompuServe.com Web site: http://www.fractalus.com/sylvie/homepage.htm -----------------------------------------------

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Re: [Fractint] FOTD 30-05-02 (Mandelbrot Atom [6])
by Multiple Bogeys 07 Jun '02

07 Jun '02

>The weather here at Fractal Central was near perfect Wednesday. >Only a bit too much humidity kept it from being absolutely >perfect. The brilliant sun and temperature of 82F 28C was ideal >for any activity including sleeping, which the fractal cats did >most of the day and which is not exactly an activity. But they >did it anyway, and they did it well. More like an inactivity. :)Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com

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Re: [Fractint] Fwd: Ikenaga Fractals???
by Multiple Bogeys 07 Jun '02

07 Jun '02

>The reason you iterate z = 0 with the quadratic is that it's a >critical point of f(z) = z^2 + 1. By analogy, for the cubic you >should iterate the critical points (plural) and (I hope I don't >screw this up!) see if *at least one* escapes. (If I'm wrong, >then you see if *both* escape; unfortunately, I know nothing >about dynamics. As I said, I don't work in the area!) The >derivative for the cubic is 3z^2 + (c - 1). So you need to set >this equal to 0 and solve for z (which gives two complex square >roots, which gives two critical points). You iterate these >guys, not z = 0. Thus, you'll be iterating different points, >depending on the current value of c. In these kinds of situations I have my computer study the fate of both points, and plot distinct color gradients depending on what pattern occurs. The results can be quite spectacular. With Ultra Fractal there's a nifty trick. Make a formula, and make the critical point selection a parameter. Generate a two-layer image with each layer having the same settings save critical point selection. Give them distinct outside gradients. Then you can get, say, black where both points are trapped, dark gradients where one escapes and a different shade depending on which, and where both escape, a colorful gradient that has filaments of two different colors present. Inside Mandelbrot-like regions can be found dendrites studded with filled-in Julia set like forms, as well as more mini Mandelbrots, in black; the Julia like forms have both critical points sucked into the same attractor, and the smaller Mandelbrot figures have them going to separate attractors. Of course, it gets hairier with quartics. Then there are three critical points... >Feel free to copy this to others if it helps to correct this. >Oh ... do any of those fractal-generating programs actually do >the cubic, but the *correct* way? If not, you could do a favor >for the people who write these things by letting them know. Well I have both Fractint formulas, Ultra Fractal formulas, and C code that produce generic cubic images. They use the two-parameter cubic family z^3 - 3a^2z + c, however, with critical points +/-a. >(Maybe go ask a dynamical systems person first whether you want >*at least one* or whether you want *both* critical points to >escape in order to color the point c. Don't take my word for it >--- as you can see, I'm not a good source for this!) This depends on what kind of picture you want to generate. The usual rigorous Mandelbrot analogue is the set where all critical points are trapped. For all polynomials, this set is connected, though you may be looking at a space with a large number of parameters. For each critical point you can get interesting fate maps. To really have a map of the full dynamic behavior of the function, though, you need to do the Ultra Fractal layering thing. (In particular, the high-iteration stuff of different critical points should get distinct colors, which means layering with different gradients.)Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com

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FOTD 06-06-02 (Stems [6])
by Jim Muth 06 Jun '02

06 Jun '02

FOTD -- June 06, 2002 (Rating 6) Fractal visionaries and enthusiasts: Take four lines with a length of -1 meter and arrange them as the sides of a square. The result is a square with an area of one square meter and four sides that measure one meter less than nothing. This is not only getting something from nothing; it is getting something from less than nothing. Then take six of these square meters with sides less than zero and arrange them as the sides of a cube. The result is a cube with a volume of one cubic meter less than nothing. I shall not attempt to describe this incredible beast, but I shall note that if eight of these weird cubes were arranged as the cells of a 4-D hypercube, that unimaginable object would have a hypervolume of 1 quartic meter more than nothing. This situation is mathematically correct, though I have yet to see a line with a length of -1 meter. It simply shows that much mathematics extends far beyond the everyday world in which we live. I have also never seen a real-life fractal, though I have seen hundreds of thousands of pictures of fractals. Today's image simply adds one more fractal picture to the ever-growing list. The image is a scene in the fractal created by the formula (Z^3)+0.4(Z^5)+C. I named it "Stems" because of the sprawling stem-like features surrounding the midget at the center. Like so many other recent FOTD images, today's image rates a nominal 6. The render time of 2 minutes makes running the parameter file not too great a task. And as always, the GIF file of the completed image is available on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Wednesday was very warm and muggy, with a temperature of 92F 33C and humidity to match. In the late afternoon a very noisy thunder-storm developed, which sent the dynamic duo of fractal cats scurrying for cover. They stayed out of sight until hunger brought them into the open around nightfall. As for myself, as is normally the case, I've got too much work to do and too little time in which to do it. The remedy for such a situation is to get busy and resume productive activity. So until Sunday June 9, take care, and be of good humor. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Stems { ; time=0:02:48.18--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=ident passes=1 center-mag=+0.54332395099606500/+0.517188441425538\ 80/1.244136e+010/1/-67.5000495545287009/7.69023680\ 009528476e-005 params=1/3/0.4/5/0/0/0/0 float=y maxiter=300 inside=0 logmap=49 periodicity=10 colors=000HfuHcqH`lHYhHVcHS_HPVHNTHLRHIQKFPNHNQKNT\ NOWQQZTR`XSg`RmeQtkPzpOykQygRxcTx_UxWWwSXwPZvL_vIa\ vFbuCdu9et6gt3ht0ip8fmGdiOafW_cbYbaZa`Z`_Z___ZZ_ZY\ _YX`XX`WW`VVaUUaUUaYYY`aVcdRfhOjlKmoHpsDsvAmwFgxJa\ xOWySRyWDlT0_R6ZMCZHHYDNY8SY4TZBT_HT_NT`UU`_UaeUal\ UbrUbxVcrWclXcgYcaZcX_cR`cMacGacBiiDqoFyuGwpFulFsh\ FqdFo`FnXFlTFjPFhLFfHFeDF`KKWRPSXUNcZJibGk`DmZBoY8\ qW6rV9pXCoYEn_Hl`JkbMjcPheRgfUfhWdiZckablc`nf_ohZp\ jVqlRrnOrpKsqHsrFprEnsDlsCjtAht9fu8cu7av5_v4Yw3Ww2\ Uw1SuNHth7ti9tjBtkCtlEtmFtnHtoItoKtpMtqNtrPtsQttSt\ uTtvVtxWhzaYzfNzkCzpRzbezPtzBrzDqzEpzFozGnzHlzIkzJ\ jzKizLhzMgzPfzRfzTezVezXdzZdz`czcczebzgbziazkazm`z\ o`zqYzjVzdSzYPzSMzMJzFGz9Dz3Fz8GzCIzHJzLLzQMzUOzZP\ zbRzgSzkTzoVzkWzgYzcZz`VzaRzbNzcJzdFzeBzf7zg3zgGz`\ TzVezPdzQdzRdzSazQ_zOXzNVzLSzKQzIOzHLzFJzDGzCEzABz\ 99z77z6FzHNzSVzaWzROzhHzz } 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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Kleinian Group formulas - Pars (and) More pars
by Sylvie Gallet 04 Jun '02

04 Jun '02

I4KLN07 { ; . t= 0:02:52.14 ; Copyright Sylvie Gallet, Jun 03, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=klein.frm formulaname=inv4klein_group passes=1 center-mag=47.4891/-37.7833/0.4930351/1/-80.0000000000000995\ /1.40332190312619787e-013 params=1.1/2.2/0/0.54 float=y maxiter=1000 inside=0 proximity=6 outside=fmod periodicity=0 cyclerange=0/255 sound=off colors=PCZPD_<3>PLhPMkPOmPQpPSs<5>WhvXjwYmw<2>`vybyzeyz<3>sx\ zwwzxxzzzz<6>sswrrvqqv<7>kkpkkojjojjo<12>``d__cZZb<13>QQTPPS\ OOR<11>IILIILHHK<23>BBDAACAACAABAAB<8>889889778<108>11111111\ 1<3>000U0F<2>R5QP7UP8VPAX } I4KLN08 { ; . t= 0:01:22.29 ; Copyright Sylvie Gallet, Jun 03, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=klein.frm formulaname=inv4klein_group passes=1 center-mag=1.31098/-0.214135/4.645177 params=2/4/0/0.54 float=y maxiter=1000 inside=0 proximity=6 outside=fmod periodicity=0 cyclerange=0/255 sound=off colors=K0A<2>L3GL5JL6LL8NL9P<5>NJaOLcOMf<2>PRlPTnQVn<4>WgsYi\ tZlu<2>bsxcvydvy<4>lvxnvxovw<3>vvv<62>FFIEEHEEGDDGCCF<28>222\ 222111<98>000000000<3>000<8>zzz } I4KLN09 { ; 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. t= 0:05:24.67 ; Copyright Sylvie Gallet, Jun 04, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=klein.frm formulaname=inv4klein_group passes=1 center-mag=-0.639835/-2.16756/2.519123/1/-70/1.3107570584480\ 7544e-014 params=3.12/4.05/0/0.51 float=y maxiter=1000 inside=0 proximity=6 outside=fmod periodicity=0 cyclerange=1/253 sound=off colors=000<105>000000000<3>000wc0<7>WI0SF0PC0<3>A00<9>400400\ 300<3>000UUw<24>E6KE5JD4H<3>A0AE5IC3EA0A<6>60A50A50A<3>20A80\ 0<54>100100100<3>000nnnzzz } I4KLN16 { ; . t= 0:09:26.12 ; Copyright Sylvie Gallet, Jun 04, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=klein.frm formulaname=inv4klein_group passes=1 center-mag=-8.31486/-10.129/0.09108612/1/-140/1.310757058448\ 07544e-014 params=3.1/3.1/0/0.8 float=y maxiter=1000 inside=0 proximity=4.6 outside=fmod periodicity=0 cyclerange=0/255 sound=off colors=000<182>000000000000000<10>0A00B00C00D00E0<2>2G03H05I\ 0<3>AM0BN0CO0DP0<10>_fDahFciGekHgmIjoK<3>ptSruUruV<8>txitxju\ xl<3>vzs000<2>000 } 4akln01 { ; . t= 0:01:27.94 ; Copyright Sylvie Gallet, Jun 05, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=klein.frm formulaname=4apolloklein1 passes=1 center-mag=0.0159799/0.027678/1.572327/1/29.9999999999999964\ /-1.23373533611470521e-014 params=-0.5/0.8660253999999999/0.8660253999999999/-0.5/-0.86\ 60253999999999/0.8660253999999999/1/0/0.8660253999999999/0 float=y maxiter=1000 inside=0 proximity=1.5 outside=fmod periodicity=0 cyclerange=0/255 sound=off colors=111<3>000A00<4>J40L50N50<3>V90XA0ZB0<2>bE1cG1dH1fJ1gK\ 1<6>oV1pW1rY1<2>ua1wc0vb0<18>bF0aE0_D0ZC0YA0<26>720620520<3>\ 000A00<39>720720720<2>630630741<2>963963963963963<104>111 } ----------------------------------------------- E-mail: Sylvie_Gallet(a)CompuServe.com Web site: http://www.fractalus.com/sylvie/homepage.htm -----------------------------------------------

1 0

FOTD 03-06-02 (Cubic Mandelbrot [6])
by Jim Muth 03 Jun '02

03 Jun '02

FOTD -- June 03, 2002 (Rating 6) Fractal visionaries and enthusiasts: Things are moving on schedule here at fractal headquarters, which means that the CD is entering the late mid-stage, the ongoing fractals are continuing to appear, the cats are sleeping, but I have yet to receive the 24-million dollars I was promised by that man who sent me the e-mail. :-) Today we take a trip to the cubic Mandelbrot set to see a cubic midget. The cubic set is basically an extension of the classic quadratic set M-set, with corresponding features in corresponding areas. The main difference is that there are 2 lobes in the buds, and instead of the 2,4,8... arrangement of elements around the midgets, the arrangement is 3,9,27... It also becomes meaningless in the cubic set to orient midgets in the 'normal' manner, as I do with quadratic midgets, since cubic midgets have 4-way symmetry. I have given today's midget a diagonal orientation, which is both dynamic and somewhat artistic. As is the case with most of the FOTD's, the coloring is done with the standard equal- iteration-band method, with the inside set to black. Feeling that the image has at least a modicum of worth, I rated it at a 6. The name "Cubic Mandelbrot" is a description of the image, with no pretense at cleverness. The 11-minute render time makes running the parameter file a drag. The wiser choice is to let Paul and Scott do the dragging, and download the completed image from their web sites. Paul's site can be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's is at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Sunday here at Fractal Central was near perfect, with total sunshine and reasonably happy cats. The slightly too-warm temperature of 88F 31C was offset by low humidity and a fresh breeze. The cats would rather have had no wind, because wind conceals the presence of intruders. But they took the breezes in stride and explored the yard peacefully. Being faced with a day of work, I must now end this latest chapter in the unending series of FOTD's, but I'll return on schedule on the next day evenly divisible by 3 -- June 6. Until then, take care, and search for the meaning in fractals. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Cubic_Mandelbrot { ; time=0:11:06.68--SF5 on a P200 reset=2002 type=formula formulafile=slices.frm formulaname=MandelbrotCube passes=1 center-mag=-0.00037280362079087/+1.091145090358868\ 00/1.05861e+010/1/-19.9998811849355604/-0.00012469\ 0785224791656 params=0/0/0/0 float=y maxiter=6000 inside=0 logmap=836 periodicity=10 colors=000Skz_mzhozspzqqzqrzqtzqtzqtzqszqrzqqzppzp\ ozpnzpmzplzpkzpjzpizphzngznhznhznhznizniznjznlznkz\ mlzmkzmkzmkzmizmizmhzmhzmhzhgzegzbgu_enXehUe`PcWMc\ OJcIGbCEb5Bb06`08b08b08b08b08b18b29b59c69c89cB9cC9\ cEBcFBcIBeJBeLBeOBePCeRCeUCeWCgXCgZCg`EgbEgcEggEgh\ EhiEhmFhnFhpFhqFhuFhvFiwGizGizGizGizGizGizGizZX0XW\ 0XW0WW0WW0WW0UW0UW0UW1SW4SW5RW6RW8RW9PWBPWCPWEOWGO\ WIMWJMWLMWMLWOLWPJUPLWRMWSMXUOXWOXXPZZPZ_RZ_S_`S_b\ U`cU`eW`gWbhXbi__hXbiWekUhmSimRmnOppMsqLuqJwsIzuFz\ vEzvCzwBzy9zyBzvCzsCzpEzmEyiFvgGscGp`InZIkWJhSLePL\ bMM`JMZGOWEPRBPO8RJ5RF2SB0S90W80X80Z90_90`91bB1c92\ e92gB4hB4iB5kC5mB6nB6pC8qC8sC8uC9vC9wBByBBzBCzBEzB\ GzBJz9Mz9Pz9Sz9Wz9Zz9`z9czGgzMizSmzZpzeszkvzqwzwyz\ uzzszzqzznzzmzykzwhzugzsezqczpczmczkcziczhczeczccz\ bcz`czZczXczWczPczUczXcz_czcczgczgczgczgczgczgczgc\ zgczgczgczgczgczgczgczgcz } frm:MandelbrotCube {; Jim Muth real(c),imag(c) z=p1, c=pixel+p2: z=z*(sqr(z))+c, |z| <= 16 } END 20.0 PAR-FORMULA FILE==================================

1 0

Is the list working?
by Jim Muth 31 May '02

31 May '02

test

3 2

FOTD 30-05-02 (Mandelbrot Atom [6])
by Jim Muth 30 May '02

30 May '02

FOTD -- May 30, 2002 (Rating 6) Fractal visionaries and enthusiasts: Today's 6-rated fractal, (I couldn't rate it any higher), is a scene in the classic Mandelbrot set, created with the classic Mandel formula. The midget at the center of the image is a third-order one located on a minor filament of a larger midget, which in turn is located on a filament extending from the second bud of the largest midget of all -- the one at -1.75 of the M-set. To find today's scene, I chose an area where the filaments are ready to collapse from broad areas of chaos to strings of zero width. Like everything else in the M-set, the exact point where this happens is elusive and always a few in-zooms beyond the image on the screen, but today's fractal gives a fairly good idea of the nature of the area where the collapse happens. I named the picture "Mandelbrot Atom". Midgets are sometimes referred to as 'atoms' and a name such as "Mandelbrot Midget" would have been a bit too trite a name for a FOTD. ;-) On my aging machine, the parameter file, which requires arbitrary precision math, takes one hour to complete. Those with time or a computer to spare will enjoy watching the scene slowly appear on the screen. Most of us will give Paul and Scott a chance to render and post the image, then download the completed image from their web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather here at Fractal Central was near perfect Wednesday. Only a bit too much humidity kept it from being absolutely perfect. The brilliant sun and temperature of 82F 28C was ideal for any activity including sleeping, which the fractal cats did most of the day and which is not exactly an activity. But they did it anyway, and they did it well. As for me, I find myself faced with work, which is the normal situation but which still needs to be done. So until next FOTD on June 3, (the 4-day break is a one-time thing), take care, and the time is growing near. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandelbrot_Atom { ; time=1:02:50.48--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-1.77798264679014900/+0.001373710930217\ 95/4.689928e+014/0.9712/-155.53268793254648/0.1495\ 21230492996648 params=0/0 float=y maxiter=3200 inside=0 logmap=-849 symmetry=none periodicity=10 colors=000O0PP0RR0US2WU6_V9aWCdYFg_Ij`LlaOocRrdUue\ Wxg_zehzeqzdyzdzzgzzjwzlqzokzrezs`zwVyyPyzKyzEyz7y\ z2yw1xy5wuAurFssQqqUooUmmUkkUiiUggUkeYqecujjzmozrw\ zzzzmyzexzWwzSszMrzIqxCnu7lr2ko7llAljFlhIleLlcPlaS\ l_VnW_nVanSdnPhnOknLnnKtl0zk0yd6j_LVS_FMl0Hy1Eu4Aq\ 67n94jA2gE0cH0_I0WL0SM0PE0K47E0F7gccHmq0mz0mz6myEm\ xLmuSms_mqednljlsojzuhqxkgylYzoPzqOsnOklOckOV`MMTM\ ERM4QM0UV0`c0gk1js2ko7jkCjgHjcLj`PjWUjSYjOajLejHjj\ Cnj7rj4uj6ol7kn9goAcqC_sEVuFPwHLxIHzKCzL7zM2z00Y7E\ cLRgYckjoouzsqzunywkxxhwxeuycsz`szYrzVqzSozPnzMlzK\ kzHkzPWuYIhe2Wn0Kg0F`4CUC9ML4FS17_00e07c0E`4LY9RVC\ WSHcRLhOPnLSuIWzF`zEcw7gn2jk1lh0ne0qd0ra0u_0wW0yV0\ zS0zP0zM0zL0zgh6dj4ck2ak1_l1Yn0Wn0Uo0Sq0Rq0Or0Mt0L\ u0Iv0Hx0Fy0Hz2IzHKzUKzeSza`z_hzWrzczzjzzqzzozzoyzo\ wzorznnznjzngznczl_zlVzlSzlOzkKzkFzkCzkEzhFzeHzdIz\ aKz_LzYMzVOzUqzoozlozjnzh } END PARAMETER FILE=========================================

1 0

OT?? Real-time fractl/visual generator to music
by Rich 30 May '02

30 May '02

Hi, sorry for the slightly off-topic post. I'm looking for a (preferably) freeware fractal/other wierd visual generating software that can produce shapes/forms/bizarre computer fractal-y type stuff in real time to an audio in source to my PC. This is to generate real-time visuals for a show I'm doing in a couple of weeks., I have tried Cthugha, but the output in far below the resolution I need (at least 640x480 output). Does anyone know of such software? I don't have that meaty a computer, so please bear that in mind Thanks! Rich arkive(a)btopenworld.com www.geocities.com/arkive2097 http://artists.mp3s.com/artists/393/arkive.html

6 6

Two beginnings and no end.
by Morgan L. Owens 29 May '02

29 May '02

It's been a little bit tricky deciding how I was to approach this. "Begin at the beginning," they say, "and go on till you come to the end. Then stop." Which is all very well in most cases, but in this one - well, it had two beginnings and the end is nowhere in sight. I shall start with a salving of my conscience. Not too long ago I argued somewhat manically that, just as the classical Mandelbrot set serves as an index to the classical Julia sets, so too it could serve as an index into an uncountable infinity of other sets. And just as the two-dimensional Julias could be thought of as being stacked up in two dimensions to form a four-dimensional Julibrot (with the Mandelbrot set itself forming the binding), so too could these other sets be stacked up in however many dimensions might be deemed necessary - in which the binding itself can be pictured as being made up of stack of sets which has the original Mandelbrot set as binding. I gave some examples of _extensions_ to the Mandelbrot set, the quaternions and hypercomplex numbers, some other four-dimensional numbers I'd made up on the spot, and some further extensions to the quaternions (specifically, octonions, decanions, and pentadecanions). But to be honest, none of these were actually presented as being extensions of the Julibrot set in any way - the four-dimensional quaternion Julia sets are not the four-dimensional Julibrot. Of course, the quaternion Julias themselves have a quaternion Mandelbrot, and the two combine to produce an eight-dimensional quaternion Julibrot - in the heart of which the classical Mandelbrot is still to be found. But really there was more handwaving going on than I was really comfortable with. So I decided to actually construct a beast that (a) gave the classical Mandelbrot set an explicit role as an index into the associated Julias, and (b) strongly suggested how other different beasts could be constructed in the same way - makng it obvious that at least a countable infinity of others could be constructed. Where the classical Julibrot has four dimensions - two to index the Julia sets' parameters (these being the two the Mandelbrot set lives in) and two to carry the Julias themselves - the "Quarterblend" (to use the name I just made up for it) Julibrot has ten. The Julia sets are still two-dimensional, but it takes four complex parameters to specify them - so the corresponding Mandelbrot set lives in eight dimensions. The thing is, the eight-dimensional Mandelbrot can itself be looked upon as a Julibrot - with two-dimensional Julias being indexed by a six-dimensional Mandelbrot. This reduction can continue, so that six dimensions split into two and four, with the four- dimensional index set resulting being none other than our familiar classical Julibrot, with two-dimensional Julias being indexed by a two-dimensional Mandelbrot. In a sense this sort of thing can happen anyway when you have a load of independent parameters: with n independent parameters, if you fix all but m you specify an m-dimensional Julia, the set of which is indexed by an (n-m)-dimensional Mandelbrot; and hence an n-dimensional Julibrot. But I wanted to show one where the classical Mandelbrot set could be easily found. As I said, the Quarterblend Julibrot is ten-dimensional. Since the Julia sets I'm drawing are two-dimensional, that means I have to fix eight dimensions. The obvious way to do that is to have four complex parameters. Without any further ado, here's the formula for Quarterblend Julias. quarterblend_pJJJJ{ z=pixel if(imag(pixel)>0) if(real(pixel)<0) c=p1 else c=p2 endif else if(real(pixel)>0) c=p3 else c=p4 endif endif : z=sqr(z)+c |z|<=4} It's simple enough that it's operation should be apparent even without playing with the thing. Now we want to index this. In the same way that Julia sets get indexed by the Mandelbrot: Julia { z = pixel, c = p1: z = sqr(z) + c, |z| <= 4 } Mandelbrot { z = pixel, c = pixel: z = sqr(z) + c, |z| <= 4 } The only difference (apart from the name) is that where in the Julia the parameter is specified and fixed by the user, in the Mandelbrot it's become "pixel": each distinct point in the Mandelbrot corresponds to a distinct Julia set. The formula for the Mandelbrot set isn't entirely truthful: to save one iteration per pixel, the first iteration has actually be done by hand. It should really read: Mandelbrot { z = 0, c = pixel: z = sqr(z) + c, |z| <= 4 } Where 0 is a critical point of the quadratic map z^2+c. Note that after one iteration through the formula, z becomes equal to pixel and the situation matches the earlier version of the Mandelbrot formula. I mention this bit about truth because I'd like you to compare the initialisers of the Julia and "real" Mandelbrot formulae: z = pixel, c = p1: z = 0, c = pixel: Each pixel P of the Mandelbrot set is initialised to z=0, c=P. And the point 0 of the Julia set with parameter c=P is initialised to z=0, c=P. In other words, these two points (one in the Mandelbrot, one in the Julia) have the same initial conditions, and follow identical dynamical rules. Each point of the Mandelbrot set is the zero point of a Julia set, and vice versa. This is what is meant by the Mandelbrot set "indexing" the Julia set, and is the basis of the Julibrot; with two-dimensional Julia sets lying at right angles to the two-dimensional Mandelbrot set, all intersecting it at single points; the whole shebang yielding the four-dimensional Julibrot. So now we can index the quarterblend_pJJJJ formula. There are a variety of ways to do this, some more extreme than others. You might want to build an index in the p1 plane (the plane in which p1 takes all possible values). This would give quarterblend_pMJJJ{ z=pixel if(imag(pixel)>0) if(real(pixel)<0) c=pixel else c=p2 endif else if(real(pixel)>0) c=p3 else c=p4 endif endif : z=sqr(z)+c |z|<=4} or instead index p1 and p3 simultaneously: quarterblend_pMJMJ{ z=pixel if(imag(pixel)>0) if(real(pixel)<0) c=pixel else c=p2 endif else if(real(pixel)>0) c=pixel else c=p4 endif endif : z=sqr(z)+c |z|<=4} Both of these could be called "Mandelbrot" sets, in which a quantity is allowed to vary that could instead be fixed at a particular value to produce corresponding Julia sets. But equally, they could still perhaps be called "Julia" sets, because they do still contain arbitrary parameters. Let's index all of those parameters now: quarterblend_pMMMM{ z=pixel if(imag(pixel)>0) if(real(pixel)<0) c=pixel else c=pixel endif else if(real(pixel)>0) c=pixel else c=pixel endif endif : z=sqr(z)+c |z|<=4} And do some obvious simplifications of the if-else-endif logic: quarterblend_pMMMM{ z=pixel c=pixel : z=sqr(z)+c |z|<=4} Now that looks familiar. The Quarterblend Julibrot is a ten-dimensional structure. An eight-dimensional stack of two-dimensional Julias. The stack is itself a six-dimensional stack of two-dimensional Julias. That stack in turn is a four-dimensional stack of two-dimensional Julias. And _that_ stack is our familiar Julibrot - a two- dimensional stack of two-dimensional Julias. All of the Julias in that last step intersecting with a single plane at their critical points to produce a two-dimensional Mandelbrot - index page for the two-dimensional stack. So yes, it does look patchy, being cut into regions like that, but all the bits all still hang together in one single consistent ten-dimensional shape. And there you have it. Just one of what is (what should be) clearly an (at least countable) infinity of different formulae that all have the classical Mandelbrot set serving to index its Julia sets; just altering the placement of the regime boundaries (real(pixel)<0, etc.), or adding more would be sufficient. Actually, with a little thought it's clear that the different formulae are uncountable in number; the boundaries between the different regions could placed in uncountably many different ways (just nudging one ever so slightly would be enough). Now I can start on the other beginning. I was mulling the difference between the Mandelbrot set and Julia sets, and one of the distinctions I saw concerned memory. Now, I don't say that this is any sort of defining characteristic between them, but it is a difference between them, that can be applied elsewhere. Consider the idea of a dynamical system. We have a space, S, for the sake of argument, and a so-called "vector field", that attaches, to every point of S, a wee arrow which is taken to mean "go this way next". We insert a particle into S at a particular point and then watch what happens, as it moves from point to point, following the arrows. For escape-time fractals such as those rendered by Fractint's formula type, we do this for virtually every point visible in the space, colouring that point according to what happens to a particle starting from that point "in the end" (where "in the end" is defined in terms of bailout condition and maximum iterations). Other Fractint types offer other views of dynamical systems. But this can't really be the entire story. The Mandelbrot set itself looks like its breaking the rule. Mandelbrot { z = 0, c = pixel: z = sqr(z) + c, |z| <= 4 } Let's say you've come across a freeze-frame of a Mandelbrot set in progress. There is a particle sitting at a particular point. The question is: where is it going to go next? Where is the little arrow pointing? The answers are: You can't tell. The arrow isn't defined. It's not? No, because that particle could have started out from a number of different points. Where it goes next depends on c, which is defined to be the point from where the particle originally started from. If you don't know that, you don't know c, and you can't work out sqr(z)+c. This is what I meant by "memory" - the particle remembers where it came from, and this memory affects where it will go, in a fashion not catered for by a simple dynamical system. Julia sets are simple dynamical systems in this case. If we were in the situation of trying to predict where a particle will go next, we will be able to. It still obeys z=sqr(z)+c, but this time we know what c is - it's the Julia set parameter. The particle itself has no need to remember it, because it's already built into the little arrows we're again free to place at every point. In a sense, every single point of the Mandelbrot set represents a different dynamical system - one for each value of c. But this is just another way of saying that the Mandelbrot set indexes the Julia sets - by sampling all of the different dynamical systems and providing a summary. Now the two plot lines I've been developing here can merge. The Kleinian Circle formulas don't have such a memory: The only per-pixel initialisation is the last "z=pixel" for specifying where the particle was to start. After that, the rest was predetermined - you could set up the vector field and all its wee arrows in advance, and every particle arriving at a particular point would all behave the same way, all following the same wee arrow telling them where to go next. (This was why my "precalc" hack could work.) In contrast, my Quarterblend fractal (even the JJJJ julias) does have a memory. Each particle remembers which region (upper/lower left/right) it started out in. Without knowing that about a particle, you wouldn't be able to predict where it was going next. Something had to be done. At least, it suggested something that could be done. So I lobotomised the particles that were supposed to be following the Quarterblend dynamics. No longer could they remember which region they started from; instead they were to just use whatever rule applied in whatever region they happend to be in at the time. The example Quarterblend slices I gave above became: quarterblend_iJJJJ{ z=pixel: if(imag(z)>0) if(real(z)<0) c=p1 else c=p2 endif else if(real(z)>0) c=p3 else c=p4 endif endif z=sqr(z)+c |z|<=4} quarterblend_iMJJJ{ z=pixel: if(imag(z)>0) if(real(z)<0) c=pixel else c=p2 endif else if(real(z)>0) c=p3 else c=p4 endif endif z=sqr(z)+c |z|<=4} quarterblend_iMJMJ{ z=pixel: if(imag(z)>0) if(real(z)<0) c=pixel else c=p2 endif else if(real(z)>0) c=pixel else c=p4 endif endif z=sqr(z)+c |z|<=4} and quarterblend_iMMMM{ z=pixel: c=pixel z=sqr(z)+c |z|<=4} Again, that last one looks familiar. (And now you know what that extra 'p' was for!) All the talk about the quarterblend_p???? fractal applies to this one as well, so the extensions suggested there can all be carried in bulk to this one as well. This one has the advantage that its ten-dimensional space can be filled up with the wee arrows of a vector field in advance and looked at as a pure dynamical system, without giving mere particles anything so pretentious as a memory. Plus the pictures look a bit better. Morgan L. Owens "Pass the dried frog pills."

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Re: [Fractint] At it again...
by Franktal Gallery 28 May '02

28 May '02

Andrew, you might like to check out my ray-traced fractals made from infinite reflections inside a stack of mirrored spheres. I think these pictures show something impossible to reproduce in the real world, because of the perturbation introduced by a real camera. This seems related to the uncertainty principle, I guess.... The virtual camera overcomes this obstacle. Best regards, Miguel Fliguer . Buenos Aires, Argentina Franktal Gallery - http://www.geocities.com/franktal2002 >From: "Andrew Coppin" <orphi69(a)hotmail.com> ><snip> >I've come up with the "hall of mirrors" analogy. Have you ever been to a >department store where they have mirrors on the columns supporting the >roof? >If you stand between two columns (assuming both have mirrors), you can see >an infinite number of reflections of yourself! But, of course, the mirrors >are always slightly greenish (never any other colou... mmm....) and never >completely flat. > >The Julia sets are the same. It seems that the infinite progression of >spirals/forks/dust are mirror images of one single such feature. _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com

8 25

A very basic experiment
by John W. 28 May '02

28 May '02

This is an experiment to see if I could reproduce in Fractint a fractal which I originally found in UltraFractal. It's just a midget, in the basic Mandelbrot set, which reminded me of Arthur C. Clarke's description of of the startup of the engines of the spacecraft / worldlet. John W. Rama { ; Originally in UltraFractal ; Version 2002 Patchlevel 4 reset=2002 type=formula formulafile=fractint.frm formulaname=mandelbrot center-mag=-1.77335946455868600/+0.00624724158563847/1.619802e+010/1/90/\ 3.88578058618804789e-016 float=y maxiter=1249 colors=00000I<13>004003002000000000<25>00d00f00h00i00k00m<26>0ew0fx0hx0i\ y0ky0mz<25>nwzpwzrxz<3>zzz<42>7zz6zz4zz3zz2zz0zz<42>07z06z04z03z02z00z<4\ 3>00J }

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Re: [Fractint] outside=tdis
by JimMuth＠aol.com 28 May '02

28 May '02

Ricardo M. Forno wrote: >I downloaded developers' version 20.0.9, which I understand >is the last, but outside=tdis doesn't work in it. Morgan Owens' >formulas posted recently use this feature. What am I doing >wrong? You are not using the latest version. The latest version is version 20.02.4. It is available on the Fractint web site. Jim M.

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Fwd: Ikenaga Fractals???
by Jim Muth 28 May '02

28 May '02

From: Bruce Ikenaga <bikenaga(a)bellatlantic.net> Subject: Ikenaga fractals??? Hi- Well, in a fit of hubris, I did a Google search on my name and turned up the page: http://home.att.net/~Paul.N.Lee/FotD/FotD_01-01-21.html which has a link to my home page, so I assume you're referring to me. I recalled getting a puzzling email from someone two or three years ago asking me about the "Ikenaga set", and I told the guy I had no idea what in the world he was talking about. But when I saw the formula on another page http://www.geocities.com/CapeCanaveral/Launchpad/5113/fr25.htm it jogged my memory. This is the stupid thing that appeared in A. K. Dewdney's Scientific American column, isn't it? Oh geez. In the first place, I never did (what mathematicians would call) research on this. Back around 1984, I heard about the Mandelbrot set --- a friend actually did some of the programming for John Hubbard, who with Adrien Douady did a lot of the *real* work on it about that time. So I was cranking out pictures of the M-set, first on the DEC Pro-350 in the math department at CWRU, and later on my Tandy 2000 (my first computer!). I printed out nifty color pictures on my old CGP-220 color inkjet (one of the first commercially available). Mathematicians generalize at the drop of a hat, so one day I asked Mike Hurley, the resident dynamical systems guy, what would be the cubic "equivalent" of the M-set. Mike told me that up to topological conjugacy (if I recall correctly), you should use the one-parameter cubic z^3 + (c - 1)z - c. Without thinking about it, I just dumped that into the Mandelbrot program in place of z^2 + c, and was soon happily cranking out lots of pictures that looked like cacti. I thought Dewdney might find it amusing, so I sent him some. I was surprised when I saw my name mentioned in his column ... ... and also embarassed. Because I showed Mike the stuff, and when he asked me what I did, he said "That's not right". See, I just put the cubic in place of the quadratic, so the program was still iterating z = 0. While you do get pictures, they aren't the "right" pictures from the dynamical point of view. The reason you iterate z = 0 with the quadratic is that it's a critical point of f(z) = z^2 + 1. By analogy, for the cubic you should iterate the critical points (plural) and (I hope I don't screw this up!) see if *at least one* escapes. (If I'm wrong, then you see if *both* escape; unfortunately, I know nothing about dynamics. As I said, I don't work in the area!) The derivative for the cubic is 3z^2 + (c - 1). So you need to set this equal to 0 and solve for z (which gives two complex square roots, which gives two critical points). You iterate these guys, not z = 0. Thus, you'll be iterating different points, depending on the current value of c. So I fixed my program and got new pictures which don't look like cacti --- not surprisingly, they look more like the quadratic M-set --- and quickly wrote Dewdney and told him I screwed up. But he never got a chance to print a correction, though I don't believe the original article actually said in detail how the set was generated. (If it had, I'm sure any number of mathematicians would have written in to point out that it was the wrong set.) I guess people read the column and just assumed you did the same thing as with the quadratic. I got bored with making pictures of fractals after two or three years. (A lot of other mathematicians got bored as well. As an amusing example, the October 1992 issue of the American Mathematical Monthly has a picture of the Mandelbrot set on the front cover. Inside, it says: "Cover: The Mandelbrot set. Neither it nor the word fractal is mentioned anywhere in this issue of the Monthly, except on the inside front cover." (Kind of like 10 years of the "X-Files", I guess.) (As an aside, the last pictures I did were from a paper by Grebogi, Ott, and Yorke. Not fractals, but some of the best black-and-white wallpaper ever! I've never seen those pictures since, so maybe when I have time I'll dig up the program and put it up on my page so people can play.) Anyway, I'm chagrined to find something apparently named after me, when as a mathematician I know it's the "wrong" object! I would greatly appreciate it if you let people know ... though I guess most are just happy that the thing makes pretty pictures, huh? :-( Feel free to copy this to others if it helps to correct this. Oh ... do any of those fractal-generating programs actually do the cubic, but the *correct* way? If not, you could do a favor for the people who write these things by letting them know. (Maybe go ask a dynamical systems person first whether you want *at least one* or whether you want *both* critical points to escape in order to color the point c. Don't take my word for it --- as you can see, I'm not a good source for this!) I hope this somewhat lengthy explanation helps. Bruce Ikenaga Department of Mathematics Millersville University Millersville, PA 17551

4 3

Kleinian Group formulas - More pars
by Sylvie Gallet 28 May '02

28 May '02

M5KLN02 { ; . t= 0:02:22.43 ; Copyright Sylvie Gallet, May 26, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=klein.frm formulaname=mod5klein_group passes=1 center-mag=-7.3926/-0.316566/0.1738033/1/-52.500000000000014\ 2/-1.23373533611470521e-014 params=2/0.6/1.5/0.5/0/1.5/1/1 float=y maxiter=1023 proximity=3.45 outside=fmod periodicity=0 sound=off colors=000<182>000000000000000<10>0A00B00C00D00E0<3>3H04I06J\ 1<20>ejMgkNimO<3>orSpsTrtU<5>svdswftwg<2>txmuyouyqvzs000<2>0\ 00 } M5KLN03 { ; . t= 0:05:24.23 ; Copyright Sylvie Gallet, May 26, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=klein.frm formulaname=mod5klein_group passes=1 center-mag=-31.7027/62.311/0.01391957/1/-30.0000000000000533\ /-2.50563458870090017e-014 params=2.9/0.58/1.5/1/0/1.51/0.85/0 float=y maxiter=1023 proximity=3.45 outside=fmod periodicity=0 sound=off colors=000<181>000000000000000<10>0900A00B00C00D0<3>2G03H04I\ 0<21>ejMgkNimO<3>orSpsTrtU<5>svdswftwg<2>txmuyouyqvzs000<2>0\ 00 } ----------------------------------------------- E-mail: Sylvie_Gallet(a)CompuServe.com Web site: http://www.fractalus.com/sylvie/homepage.htm -----------------------------------------------

2 1

outside=tdis
by Ricardo M. Forno 28 May '02

28 May '02

I downloaded developers' version 20.0.9, which I understand is the last, but outside=tdis doesn't work in it. Morgan Owens' formulas posted recently use this feature. What am I doing wrong?

1 0

FOTD 27-05-02 (Sausages [6])
by Jim Muth 27 May '02

27 May '02

FOTD -- May 27, 2002 (Rating 6) Fractal visionaries and enthusiasts: We're at the end of a crackling lightning storm this Monday morning here at Fractal Central. The rain has stopped falling but the cats are still hiding. Luckily, all the utilities, especially the e-mail, are still functional. I know that the e-mail is working because I have just received a letter from Bruce Ikenaga, originator? of the mysterious but famous, (for devoted Fractint users), Ikenaga function. I have not yet read the rather lengthy letter, but at first glance it appears to explain the mystery surrounding the 'function', which, as I recall, Mr. Ikenaga once denied writing. When I have read the letter and determined that it contains nothing which Mr. Ikenaga would prefer to be kept private, I will forward it to the list. Today's image was created by a formula that mixes various portions of four different negative powers of Z: -1.2, -2, -2.8, and -6, and adds 1/C. The parent fractal created by this mixture is shaped like a crescent moon, with today's midget located on the north shore of the largest bud. I named today's image "Sausages". It's not a very classy name, but a string of sausages is the first thing that came to mind as I studied the image. I rated the image at a 6, the rating I usually apply when I can't decide. With the parameter file's render time of 13 minutes, running it is not the most efficient way to see the sausages. A far more efficient method is to download the completed image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Sunday here at the Fractal Central was warm and humid, with a high temperature of 79F 26C and humidity to match. Thunder-storms threatened in the evening but never materialized. The cats spent a lazy day lounging on the porch in the hazy sun, sniffing at the aroma of the neighborhood cook- outs, which occasionally wafted by. When a careless sparrow landed on the porch railing, Tippy made a move to stalk it, but decided the result would not be worth the effort, and returned to sleep. The yard work that lies before me, however, most definitely will be worth the effort -- if I get it finished that is. And the way to finish a job is to start at the beginning, so I'd best get moving. My only escape would be for the rain to continue all day, but that does not appear likely. Until the 30th, take care, and place your faith in fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Sausages { ; time=0:13:41.80--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3 function=recip passes=1 center-mag=-3.70474245107962100/+0.657760841842085\ 30/3.069827e+010/1/120.005849754697749/0.010984664\ 4080361863 params=4/-1.2/-2/-2/1.5/-2.8/-0.8/-6/0.\ 9900694240234/0 float=y maxiter=1000 inside=0 outside=tdis symmetry=none periodicity=10 colors=0000Ug0Ue0Ue0Ud2Ud2Ua2Ua2Ua2U_4U_4UY4UY4UW4\ UW4UU7UU7US7US7UQ7UQ7UN9UN9UN9UL9UL9UJCUJCUHCUHCUE\ CUECUCEUCEU9EU9EU7EU7EU7HY9J_9Ja9Ld9Ng9Ni9QlCSnCSq\ CUsCWuCWwCYzE_zE_zEazEdzEdzEezHgzHgzHizHlzHlzHizEi\ zEizEizEizEizCizCizCizCgzCgz9gz9gz9gz9gz9gz7gy7gw7\ gw7eu7es4eq4eo4eo4en4el2ei2eg2dg2de2dd2da0d_0d_0dY\ 0dW0dU0dU0aS0aQ0aN0aL0aL0aJ0aH0aE0aC0_C0_90Z70Y40X\ 20W20W00U00T00Q00R00R20R70RE0TJ0VQ0XV0ZZ0_c0_h0_o0\ au0_s0Ys0Yq0Wq0Wo0Uo0Un0Sn0Sl0Ql2Qi2Ni2Li2Lg4Jg4Je\ 4He4Hd4Ed7Ea7Ca7C_79_79Y97Y94Y94W92WC2UC0UC0SC0SC0\ QE0QE0NE0NE0NE0QH0QH2QH4QH7QH9SHESHHSHJSHLSHNUHQUH\ UUHWUHYUH_WHaWHdWHgWHiWHlYHnYHoYHqYHuYHw_Hy_Hz_Hz_\ Hz_HzaHzaHzaHzaHzaHzaHzdJzdLzeNzeQzgSzgUzgWziYzi_z\ lazlazldynewngwoiuolsqnqqoqqqossnssluuluwiuygwzewz\ eyzdyzazzazz_zzYzzWzzWzzUzzSzzQzzQzzNzzLzzNzzLzzLz\ zJzzJzzJzzHzzHzz0Ui0Ui0Ug } frm:MandelbrotMix3 {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] homemade watch
by Bodo Schäfer 26 May '02

26 May '02

hi everybody, >I also found a "fractext.exe" on a German site. The >automatically-translated page said: I don't know this site but since I am German, I can provide Information as follows . . . > Fraktale: presumably Deutches for "fractals". quite so ! > apple males: not sure about the males, but the word for apple > (apfel) also means "ball". Maybe it works out to something > like "spherical projections" ;-) 'apple males' is the incorrect translation for 'Apfel-Maennchen'. 'apple-man' is a German figurative for mandelbrot-set. > almond bread: literally "mandel brot". Now you know what > his name *really* is! 'course we do . . . > dissolutions: probably "resolutions". seems to make sense greetings from Germany, Bodo ________________________________________________________________ Keine verlorenen Lotto-Quittungen, keine vergessenen Gewinne mehr! Beim WEB.DE Lottoservice: http://tippen2.web.de/?x=13

4 5

Kleinian Group formulas - Pars
by Sylvie Gallet 25 May '02

25 May '02

Hi All, I really enjoyed playing with the new formulas! - Sylvie I4KLN01 { ; . t= 0:02:11.44 ; Copyright Sylvie Gallet, May 25, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=fractint.frm formulaname=inv4klein_group passes=1 center-mag=73.5131/-118.653/0.002078673/1/70/-3.778227730677\ 48585e-014 params=1/1.67/0/0.505 float=y maxiter=1000 inside=0 decomp=256 periodicity=0 cyclerange=0/255 sound=off colors=qtz<16>gozfozfozenzenzdnzcmz<11>JVkHTjFRhDQgBOf9Md<10\ >7FV6EU6ET6DS6CR5BQ<10>23F13E12D11C00B<148>003003002<2>00200\ 3015<7>06J06L07N<3>0AU<4>PVhU_kZcn<3>suz<2>ruz } I4KLN02 { ; . t= 0:02:10.27 ; Copyright Sylvie Gallet, May 25, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=fractint.frm formulaname=inv4klein_group passes=1 center-mag=0.507222/0.443677/0.06591993/1/30.000000000000042\ 6/-2.50563458870090017e-014 params=0.99/1.9/0/0 float=y maxiter=1000 inside=0 proximity=2 outside=fmod periodicity=0 cyclerange=0/255 sound=off colors=000006<4>006006005osz<12>gozfozfozenzenzdnzcmz<11>JVk\ HTjFRhDQgBOf9Md<10>7FV6EU6ET6DS6CR5BQ<10>23F13E12D11C00B<140\ >003003002<2>002003015<6>05I06K06M<3>0AU<4>PVhU_kZcn<3>suz<6\ >osz } I4KLN03 { ; . t= 0:01:12.72 ; Copyright Sylvie Gallet, May 25, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=fractint.frm formulaname=inv4klein_group passes=1 center-mag=16.0055/-0.000584484/0.690905/1/-29.9999999999999\ 609/-1.01391117723892421e-013 params=1/4/0/0 float=y maxiter=1000 inside=0 proximity=2 outside=fmod periodicity=0 cyclerange=0/255 sound=off colors=000<8>D60E60G70<3>LA0UA0<4>c50<3>k10m00nA0<3>um0ww0wu\ 0<3>xj0xg0xd0<3>zU0<10>dA0b80`60Z40X20U00<9>I00H00F00<2>C00A\ 00A00<28>100100000<71>005005004<28>003003003<3>003000<9>6006\ 00700<3>A00<4>ZA0<4>wK0wQ0wW0xa0<2>xmCyqGyuKzyOzy_zxkzww } I4KLN04 { ; . t= 0:02:05.73 ; Copyright Sylvie Gallet, May 25, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=fractint.frm formulaname=inv4klein_group passes=1 center-mag=0.0683063/-0.118293/19.72787/1/-30.00000000000036\ 59/2.29385954675365156e-013 params=1/4/0/0 float=y maxiter=1000 inside=0 proximity=2 outside=fmod periodicity=0 cyclerange=0/255 sound=off colors=000<8>D60E60G70<3>LA0UA0<4>c50<3>k10m00nA0<3>um0ww0wu\ 0<3>xj0xg0xd0<3>zU0<10>dA0b80`60Z40X20U00<9>I00H00F00<2>C00A\ 00A00<28>100100000<71>005005004<28>003003003<3>003000<9>6006\ 00700<3>A00<4>ZA0<4>wK0wQ0wW0xa0<2>xmCyqGyuKzyOzy_zxkzww } I4KLN05 { ; . t= 0:02:58.78 ; Copyright Sylvie Gallet, May 25, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=fractint.frm formulaname=inv4klein_group passes=1 center-mag=-0.758199/-1.30697/5.875157/1/142.500000000000028\ /1.31075705844807544e-014 params=2.18/3.6/0/0 float=y maxiter=1000 inside=0 proximity=2 outside=fmod periodicity=0 sound=off colors=000<163>003003003003003003004<8>005005004<44>00200100\ 1<3>000<4>K00P00S20V40<3>gH3jL4mP5pU7rZAtcEugJvkOwpUxu_ywlzz\ z } I4KLN06 { ; . t= 0:06:47.44 ; Copyright Sylvie Gallet, May 25, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=fractint.frm formulaname=inv4klein_group passes=1 center-mag=191.022/-164.014/0.02784725/1/140.000000000000057\ /-8.86721251980304714e-014 params=1/3/0/0 float=y maxiter=1000 inside=0 proximity=2.35 outside=fmod periodicity=0 sound=off colors=L22O44<9>L22K22K22<10>F00F00E00D00<4>B00A00900<3>7006\ 30620600<3>400300200<3>000630<92>kjilkjlkj<8>rrpssqttr<2>vvt\ wwuwwt<10>wwiwwhwwgwwfvvdwwc<26>fU6eT5eS3dR2cP0<24>UB4UA4U94\ <3>S75R66R66<11>O44 } M4KLN01 { ; . t= 0:01:11.13 ; Copyright Sylvie Gallet, May 25, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=fractint.frm formulaname=mod4klein_group passes=1 center-mag=0.0376176/1.29648/0.05679751/1/-127.4999999999999\ 86/2.58335020042466112e-014 params=1/2/3/4/0/1 float=y decomp=256 periodicity=0 sound=off colors=000<2>P0F<9>PHcPJfPLh<3>PSs<5>WhvXjwYmw<2>`vybyzeyz<3\ >sxzwwzF0Pzzz<3>rrvpptnnr<41>MMSMMRLLR<3>IINHHMGGL<43>222222\ 111<113>000 } KLNTL01 { ; . t= 0:02:35.66 ; Copyright Sylvie Gallet, May 25, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=fractint.frm formulaname=klein_tri_lattice passes=1 center-mag=-1.26480702043964400/+5.27055699730365900/175.678\ 6/1/4.99999999999930367/5.12714870559705105e-014 float=y maxiter=1023 inside=255 decomp=256 symmetry=xyaxis periodicity=0 sound=off colors=000xo4<3>xm0wl0wl0<3>vi0zz0<9>ra0q_0pX0<2>mQ0lN0jM0<7\ >QA0N80L70<3>A00<10>400300200<2>000000111<87>ssstttuuuuuuvvv\ <58>xxwxxwxxw<2>xxwyyvzzw<4>zypzyozymzxlzxjzxh<21>xqBxpAxp8x\ o7xo5 } M5KLN01 { ; . t= 0:03:10.14 ; Copyright Sylvie Gallet, May 25, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=fractint.frm formulaname=mod5klein_group passes=1 center-mag=-0.447835/-1.25027/14.61321/1/155.000000000000142\ /-2.03170813506403647e-013 params=1/0.6/1/1/0/1.5/2.5/0 float=y maxiter=1023 proximity=4 outside=fmod periodicity=0 sound=off colors=000<132>006006005<49>003003003<3>003000<10>07E08F08H0\ 9I0AJ0BL<26>bltcmueowfpxhrz<15>zzz }

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Re: [Fractint] FractInt under Windows XP Pro
by nick.grasso＠hrads.com 24 May '02

24 May '02

Paul N. Lee wrote: >>>I recently was in a conversation with someone about running FractInt under Microsoft's Windows XP Pro edition. And was told that they experienced a few problems at first, but now seems to be functioning quite fine.<<< I have been trying to get Fractint to work on Windows XP with no luck so far. My video card is a Dell OEM with the ATI Radeon chip. I am using the ATI generic 'reference' drivers. I am not using the Dell drivers because they don't support 1152x864. Windows XP also has built-in drivers for this chip, but I don't use them because they cause my PC to not wake up from standby mode. I have a DOS program called vgatest.exe and if I run it in a full screen DOS session, it displays all the VESA 256 color modes OK. I have fractint set to come up in 320x200x256 mode, which it does, but when I hit the Del key and pick an Auto-detect VESA mode, it starts to draw the fractal then locks the PC up. I have to do a cold boot. When it starts to draw the fractal, it looks like it is still in 320x200x256 mode. I have tried a few things but it is difficult to experiment since the PC locks up each time. I tried various Compatibility modes to no avail (but these seem to be for earlier Windows versions, not DOS). I am using the latest 20.0 official release. Does anyone think the latest developer's release would be different? Tim, if you are listening, do you have any idea why vgatest.exe would work, but not fractint? On another note, has anybody tried Virtual PC? It supposedly allows any DOS SVGA program up 1600x1200x256 to run (it emulates an S3 chip using DirectX). I have read several reviews saying that it works great but haven't heard of anyone running fractint on it. Virtual PC is $200, but you can get a free, full featured 45 day trial from their website: http://www.connectix.com Any further information would be greatly appreciated. Nick

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FOTD 24-05-02 (Hexagons and Circles [7])
by Jim Muth 24 May '02

24 May '02

FOTD -- May 24, 2002 (Rating 7) Fractal visionaries and enthusiasts: To begin, I will answer a few questions about the FOTD CD that must be causing unlimited concern to the members of the list. :-) Q -- When will the CD be ready? A -- Before the end of (northern hemisphere) summer if all goes well. Q -- Will there be a charge for the disk? A -- Yes -- blank disks are not free. Q -- How much will the charge be? A -- I haven't decided. Q -- Will the disk have a graphic-user-interface? A -- At this point, no. Q -- What kind of indexing will the disk have? A -- That depends on how much time I have to work on it. Q -- Will the Fractint program be included on the disk? A -- Probably not. The notice that the program may not be sold is still at the bottom of the Fractint opening credits screen. And those who would want the disk will probably have a more recent version of the program by the time they receive the disk. Finally, those who have recently discovered fractals have probably done so with one of the Windows programs, and would have little interest in a DOS program. The disk is intended to be a convenience rather than a commercial success. Q -- Are the above answers fixed in stone? A -- No! As for today's image, I must confess a bit of thievery. I found today's fractal image while noodling with a formula named Klein_tri_lattice that was posted recently to the Fractint list. I have no time to check through my old mail to see who wrote the original formula, but I give thanks regardless. Since the formula has no changeable parameters, what I have done basically amounts to tweaking someone else's fractal. Normally I never tweak the images of other fractalists, but today's tweak makes such a striking image that I could not keep it to myself. I named the image "Hexagons and Circles". I gave it this name because the densest packing of circles in a plane is in the shape of a hexagonal grid. The rating of 7 seems appropriate. With a run-time of under five seconds on most machines, today's parameter file is one of the all-time fastest. The completed GIF image will still be available for quick download on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> With total sun and a temperature of 77F 25C, the fractal weather Thursday was ideal for man and cats alike. The man spent the day working; the cats spent the day resting and having fun. Today promises to be a repeat, so I'd best get busy with the work. Until Monday the 27th, take care, and see you then. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ HexagonsAndCircles { ; time=0:00:05.55--SF5 on a P200 reset=2002 type=formula formulafile=kleintri.frm formulaname=Klein_tri_lattice passes=1 center-mag=-0.00254816/0.00115498/0.5537159 float=y maxiter=1023 inside=255 proximity=40 outside=fmod symmetry=xyaxis periodicity=0 colors=000Ld`GTTC`Ozzzzzzxvxrpp`X_mliggaaaVXYO903D\ 0UIPZUDCPMFviirfdmdajaYf`Va_Q_XOVVJC0xLDaz9ApJDDSA\ LTDX40V90VC0TF3TI6TL9SOCSQF06V0AS3DQ7GODLMIOJOQI7J\ vFOgMQTLpaMjYOfTPaPQYLrzzmvzjrsgmmdif`d_Y`TVXMCYdF\ X`GXYJVVLVSMVPPTMQTJ0Jv0Mm3OdCQXLSOc0IaM3YP7VSCDQ0\ TxJSoISgIS`GQjzSfxSaiSYVg00c60_D3VMAmzQizOfvMaoL_g\ JV`I0`l0_f1Ya7XYCXTIVPOTLJr7MiAP`DSSvSToSTiSTcSTYS\ TSSTMVVOTTLTTJSTIudMoaLj`Jf_J`XIXVGz7zuFmfMXzz`zzY\ vxVrsSlmQfgOacLXYIju0fo0cj0`f4Ya9VYDg00A9rDClGFfJI\ `LLXOOQQQLX0SV0PV6OTCMTIJSOIOrxPmpPiiQdaQ`VSXO0sc0\ o_1jV7fSFaOMYJY0IV9GyD0dPx0dC0aD9_FJXG0z01u36p6Al7\ FfAJaCOYFzmuoffc_T0uO7jLIaIzzimoV9vzCrzFoyGjrJgjMc\ aO`VQXOJz0Oo96aTA`QD_PGYOJXLMVJPTILxTMsQOoPOlOPgMQ\ cLQ`JSXI0uI1pG6mG9iGDfGIcGL_GPXGJCLLFJMIJOLIPOIQQG\ zCxzFpxIioLagOV_QOzYGzXGzXGuVGoVGiVGcTGYTGPGzQLpQO\ dSQSI9Xmvzgszcpz_msVjmPgf } frm:Klein_tri_lattice(XYAXIS){ ang=pi/3 r=1/2 rr=r*r z=pixel t1=sin(ang) t2=tan(ang) t3=exp(flip(ang)) : inside=0 m = round(imag(z)/t1) n = round(real(z)-imag(z)/t2) c0=n+m*t3 c1=n+(m-1)*t3 c2=n+(m+1)*t3 c3=(n-1)+m*t3 c4=(n+1)+m*t3 if(|z-c0|<rr) z=r*conj(r/(z-c0))+c0 inside=1 elseif(|z-c1|<rr) z=r*conj(r/(z-c1))+c1 inside=1 elseif(|z-c2|<rr) z=r*conj(r/(z-c2))+c2 inside=1 elseif(|z-c3|<rr) z=r*conj(r/(z-c3))+c3 inside=1 elseif(|z-c4|<rr) z=r*conj(r/(z-c4))+c4 inside=1 endif inside} END 20.0 PAR-FORMULA FILE==================================

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FractInt under Windows XP Pro
by Paul N. Lee 24 May '02

24 May '02

I recently was in a conversation with someone about running FractInt under Microsoft's Windows XP Pro edition. And was told that they experienced a few problems at first, but now seems to be functioning quite fine. Here are two different emails (posted with permission) that state some of the specifics about the Property settings for FractInt under Win-XP: _______________________________________________________________________ From: "Steven A. Hessler" <shessler1(a)attbi.com> Date: Thu, 23 May 2002 15:23:42 -0500 Fractint (V 20.0) works on my computer under WinXP Pro, using a Diamond Viper 550 video card, which uses the Nvidia compatible Riva TNT chipset. It Has 16mb video memory installed. (WinXP drivers used are NV4.sys and NV4.INI.) No Diamond-released XP drivers exist, although some Riva TNT generic XP drivers Released by third parties DO appear to work properly if installed, although They are NOT digitally signed by MS. (I never noticed any difference in performance of XP when using the generic drivers, which I found by searching the internet.) Fractint is started using a desktop icon. The memory options are conventional-- The Initial Environment is set to AUTO. No EMS is used. No XMS is used. Uses HMA is checked. MS-DOS protected-mode (DPMI) memory is set to AUTO. Under SCREEN settings, Fast ROM emulation and Dynamic memory allocation are Both checked. It's set to start up in Full Screen mode. Compatibility mode is NOT active. The Fractint video drivers that work are the SVGA/VESA AUTODETECT drivers (SF2-SF7). VESA STANDARD INTERFACE (SF8-SF9) also appear to work. Saving a fractal to GIF file works, saving the fractal normally. ALL OF THESE DRIVERS FUNCTION USING 256 COLOR MODE. Although some of the VESA True-Color drivers appear to work, they in fact appear to create fractals Using only one color-- blue. Experimenting with some of the EMS or XMS memory settings does not seem to Have any effect one way or the other on the program's performance or on the Performance of the video drivers. Before V. 20.0 came out, I also experimented with the last V19.x Release. It appeared to perform identically. Steve H. _______________________________________________________________________ _______________________________________________________________________ From: "Steven A. Hessler" <shessler1(a)attbi.com> Date: Thu, 23 May 2002 18:08:28 -0500 I just downloaded the developer's version of Fractint, and much to my Amazement, all the VESA True-Color video drivers suddenly work properly Under XP Pro. ......(snipped other stuff)..... Regards, Steve H. _______________________________________________________________________ Sincerely, P.N.L. -------------------------------------------------------------- http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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New Gallery by "O"
by Paul N. Lee 23 May '02

23 May '02

Greetings, For those unfamiliar with "O", then this will be something unique. For everyone else, this will be a location to see around twelve hundred of O's creations. The new Domain and web site have been available for a couple of months now. Not everything is quite complete, a few of the images are missing and hopefully will be made available as soon as possible. But there are at least 1,160 graphics which should keep most anybody busy for a few hours of browsing: http://www.o3-designs.com/ Hope you can visit and enjoy the view!! :-) Sincerely, P.N.L. -------------------------------------------------------------- http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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fractint on mac
by Alex Dukay 23 May '02

23 May '02

I've purchased a MAC and I want to know whether anyone has had success running fractint with the program VPC (virtual PC) on a MAC? Can it be done? I would like some advice before installing VPC. Thanks, Alex

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Sorry for the double posting...
by Gerald K. Dobiasovsky 22 May '02

22 May '02

...somehow I managed to leave a copy of the already sent mail in the queue. Gerald

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FOTD 15-05-02 (Mandelia [6])
by Jim Muth 22 May '02

22 May '02

FOTD -- May 15, 2002 (Rating 6) Fractal visionaries and enthusiasts: As has been obvious for some time, I am fascinated by things that cannot be comprehended by the human mind. When these things are irrational, some on the philofractal list feel that I am indulging in fantasy, but none can dispute that the Mandelbrot set and its associated Julia sets comprise a single four-dimensional object that in a sense most certainly does exist, yet cannot be comprehended by the human mind. This 4-dimensional object is sometimes called the Julibrot figure. Depending on the direction and location in which this 4-D figure is sliced, either Julia sets or perturbed Mandelbrot sets will appear. But in addition to producing Julia and Mandelbrot sets, the Julibrot can be sliced in other directions which produce hybrid sets that are neither Julia nor Mandelbrot sets, but combine the features of both. Today's image is one of these hybrid sets. I could have named the image "Julibrot", but that word has become hackneyed, so I named the image "Mandelia", a name which combines the names of both families of sets and also has a nice sound to it. I rated the image a 6. To produce today's image, I began with the Julia set of Seahorse Valley, which normally appears as a chain of empty bays, but I did not slice the Julibrot in exactly the Julia direction. Instead, I double rotated the slice 1/100 degree and 1 degree from the Julia direction. This tiny rotation produces a tremendous difference in the resulting image. (Curiously, the values of the rotation are quite critical this close to the Julia direction.) The overall shape of the fractal is that of the Julia set of Seahorse Valley. But the chain of bays is no longer empty. Instead of a dull, blank inside, we see an inside filled with detail quite unlike any normally seen in Julia or Mandelbrot sets. The valley itself appears at the exact center of the image, and the great spirals that lie in the area are also in evidence, appearing where the many unadorned valleys of the pure Julia set would normally lie. I have tilted the image to give it a more dynamic feeling, and colored it with the basic equal-iteration-band method. I used the basic coloring method to assure that the unusual effects in the image are actually a part of the fractal and not a result of a fancy coloring system that distorts and sometimes totally hides the original fractal. Due to the unusually high maxiter and the periodicity setting of 15, both of which are necessary, the parameter file is a rather slow one, taking 25 minutes on my machine. But Paul and Scott are here to save such frustration, and will soon have the completed GIF image file posted to their web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> from where it may be downloaded with ease. The fractal weather Tuesday was chilly (64F 18C) and very windy, with heavy threatening clouds that finally released a damaging rain squall at 7pm. When the squall passed, a glorious double rainbow appeared. (All rainbows are double, but the second bow, which lies outside the main bow, is usually too faint to be seen.) Then the sun set peacefully. The dynamic duo, who were still shell-shocked from the hailstorms of Sunday and Monday, dashed for cover when the wind started roaring and things started flying around again, and didn't reappear for several hours. Due to a power failure Sunday evening, I am a bit behind on the FOTD CD. But a half-hour extra work today will make up the shortfall. And it's now time to get busy. Until next time, take care, and it all depends on which direction you view your fractals. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Mandelia { ; time=0:25:37.91--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=flip/ident passes=t center-mag=3.19189e-016/6.66134e-016/0.99\ 3388/1/55/3.88578058618804789e-016 params=89/89.99\ /2/0/0/0/-0.75/0 float=y maxiter=75000 logmap=yes inside=0 periodicity=15 colors=000N7PL8SL9SKGSJ9TI\ CUHDVGEWEFXCGYAH_8L_6P_4Wa2_a0ca0ha0nc3tc9ycDzcFzf\ HzfJzfLzfNzfPzfRzfUzfWzfUz_UzUUzNRzHRzBRz5_z0fv0mn\ 0tf0zY0zR0zJ0zD0zH0tL0fN0RR1FWB3YJ7cFBjBDn9Hv5Jz3N\ z0Pz0Uz0Wz0Yz0Yz5YzB_zJ_yP_tWrnBzj0zh0zz0zz0zz0zz3\ zv7zrBzmFzhJzcNz_RzWWzR_zNczJfzHhzHhzHhzHhzHjzHjzH\ jyHjvHmtHmrHmnHmmDjjBhj7fh5ch3af0_f0_c0Ya0Wa0U_0R_\ 0PY0NY0Nj5YyUhzttzzzzzyzzrzzjzzcvzYrzRmzchzlcyjlwj\ tvjyumzsnzqrznrzktzitzfvycvtaymayh_za_zY_z__aa_Hc_\ 0f_0hY0jW0mU0nT0rS9tRJvQUyPPzOLzRHzUDzXBz_7vb3re0n\ h0jk0fn0cq0_t0Ww0Uz0Nz0Hy0Dv07t01r00n00m00j00h00f0\ 0c00a00_00YLYWzWUyURrRPmWPhYPc_P_aPWfRUhRPjRLmRHrU\ FtUBvU7yU3zU1nW3fY3YY3P_3Ha39a3J_FUYPcWanUmyRyfYvR\ cvBjt0rt0yr0zr0nh0ea1gUBhNNhHYc9jU3vK0zA9z0Jz0Uz3c\ zDnz9mz5mtAmjHmaLmWOjNRjFUj9Xj1_j0bh0eh0hh0kh0nh0q\ j0tm0wn0zr0zt0zv0zy0zz0zz0zz0zz0zz0zt0zm0zf3zf3zf } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] At it again...
by Andrew Coppin 22 May '02

22 May '02

>From: "Morgan L. Owens" <packrat(a)nznet.gen.nz> >Reply-To: fractint(a)mailman.xmission.com >To: fractint(a)mailman.xmission.com, fractint(a)mailman.xmission.com >Subject: Re: [Fractint] At it again... >Date: Tue, 21 May 2002 10:25:27 +1200 > >At 00:14 21/05/2002, Franktal Gallery wrote: >>>From: "Morgan L. Owens" <packrat(a)nznet.gen.nz> >>> >>>I think it's probably more likely due to the difficulty of manufacturing >>>optics, mirrored spheres, and CCDs/film emulsions to the required >>>precision/resolution. >> >>No, what I meant was, if you build a physical mirror >>ball stack, with a physical camera mounted inside >>(no matter how precise/small), the resultant picture >>would be modified by the infinite reflections of the >>camera itself. So, you'd need a virtual camera to >>make sure there's no perturbation introduced. > >Oh, right; very true - the same situation in Andrew's case, of >course, where his own head would keep getting in the way of his view of >the infinite corridor. But there's no "uncertainty principle" here. > >Morgan L. Owens >"'Cos right before my eye" Yes, it does take a lot of effort to find a spot where I can SEE infinite reflections of myself (my head is small, but my hair is not). It also attracts unwanted attention from the other shoppers for that matter... Andrew "Well, what else is a guy do to when forced to go shopping with mum? :S" _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com

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homemade watch
by Guy Marson 21 May '02

21 May '02

Hi fractinters, homeworkers.. although the numbers are not correctly positioned, zhis is dedicated to my daughter.. watch-1 { ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=uhr-mand.frm formulaname=uhr-mand center-mag=-0.10261656595166480/+0.94415252797943690/757.5809/1/7.999999\ 99999890132/9.29110954839273973e-013 float=y maxiter=250 inside=0 logmap=old colors=000w02<5>d0Aa0CZ0D<3>M0II0KG0I<3>708506303000<2>01612913B14D14F<6\ >39V3AX3BZ<2>4De5Eh4Kg4Of3Sd<3>2ba2e`1g`<3>1oZ0pY0rY0tX0vW0vX<12>0TG0RF0\ PE<3>0F80C70A6<2>032000202<3>B0CD0FG0HI0K<4>Z0Da0Ce0A<2>o05s04w01y00<3>y\ N0zS0zY0<3>zt0yy0zu0<3>zZ0zT0zN0<3>z00<6>d0Aa0CZ0D<3>M0II0KG0H<3>5063030\ 00<3>11A11C21F<2>31L31O42Q42T42V<3>63d63g63i69i5Gh4Mf<3>2Zb2ab2ca<3>1k_1\ mZ0oZ0qY0rX0tX0vX0vX<12>6TK7RJ7PI<3>9FE9CDAAC<2>B39C08C09<3>G0GH0II0KL0J\ O0HS2GV0E<3>h08l06o05<2>z00<4>zT0zY0zc0<2>zt0yy0zu0<9>z00 } watch-3 { ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=uhr-mand.frm formulaname=uhr-mand center-mag=-0.10285122098288750/+0.94403293733755530/1.08674e+009/1/2.99\ 99988845146679/-0.000451242073825117163 float=y maxiter=28460 inside=0 logmap=2846 colors=0002jS<7>6TK7RJ7PI<3>9FE9CDAAC<2>B39C08C09<3>G0GH0II0KL0JO0HS2GV0\ E<3>h08l06o05<2>z00<4>zT0zY0zc0<2>zt0yy0zu0<3>zZ0zT0zN0<3>z00<5>g09d0Aa0\ C<3>P0HM0II0K<3>90B708506303000<2>01612913B14D14F<6>39V3AX3BZ<2>4De5Eh4K\ g4Of3Sd<3>2ba2e`1g`<3>1oZ0pY0rY0tX0vW0vX<12>0TG0RF0PE<3>0F80C70A6<2>0320\ 00202<3>B0CD0FG0HI0K<4>Z0Da0Ce0A<2>o05s04w01y00<3>yN0zS0zY0<3>zt0yy0zu0<\ 3>zZ0zT0zN0<3>z00<5>g09d0Aa0C<3>P0HM0II0K<3>809506303000<4>11C21F21H31J3\ 1L<3>42V52Y53_<3>63i69i5Gh4Mf<3>2Zb2ab2ca<3>1k_1mZ0oZ0qY0rX0tX0vX0vX<3>2\ mT } frm:uhr-mand { ; ; 'periodicity=0' and 'passes=1' recommended x=real(scrnpix)/real(scrnmax), y=(imag(scrnmax)-imag(scrnpix))/(rea\ l(scrnmax)*0.75), z=x+flip(y) x1=1.5*x chr11 = y<x1+0.245&&y>x1+0.23094&&y>-x/1.5+1.26333||(x>0.48491&&x<0\ .49271) x2=2.5*x chr22 = abs(cabs(z+(-0.51266,-0.95305))-0.01305)<0.0039&&(y>0.95305\ ||y>-x/1.22571+1.3713)||(y<1.22571*x+0.31021&&y>1.22571*x+0.29787&&\ y<-x/1.22571+1.3713)||y<0.9178&&x>0.49571&&x<0.52961 test1 = chr11||chr22&&y>0.91&&y<0.97 chr13 = y<x1+0.252&&y>x1+0.23794&&y>-x/1.5+1.24867||(x>0.47491&&x<0\ .48271) chr24 = abs(cabs(z+(-0.50266,-0.94505))-0.01305)<0.0039&&(y>0.94505\ ||y>-x/1.22571+1.35515)||(y<1.22571*x+0.31446&&y>1.22571*x+0.30213&\ &y<-x/1.22571+1.35515)||y<0.9098&&x>0.48571&&x<0.51961 test2 = chr13||chr24&&y>0.902&&y<0.962 chr15 = y<x1+0.46&&y>x1+0.44594&&y>-x/1.5+1.06667||(x>0.29491&&x<0.\ 30271) chr16 = y<x1+0.42144&&y>x1+0.40738&&y>-x/1.5+1.08381||(x>0.32062&&x\ <0.32842) test3 = chr15||chr16&&y>0.84&&y<0.9 chr17 = y<x1+0.4635&&y>x1+0.44944&&y>-x/1.5+1.055||(x>0.28791&&x<0.\ 29571) chr18 = y<x1+0.42494&&y>x1+0.41088&&y>-x/1.5+1.07214||(x>0.31362&&x\ <0.32142) test4 = chr17||chr18&&y>0.833&&y<0.893 chr19 = y<x1-0.11&&y>x1-0.12406&&y>-x/1.5+1.32||(x>0.67491&&x<0.682\ 71) test5 = chr19&&y>0.84&&y<0.9 chr110 = y<x1-0.1065&&y>x1-0.12056&&y>-x/1.5+1.30833||(x>0.66791&&x\ <0.67571) test6 = chr110&&y>0.833&&y<0.893 chr111 = y<x1+0.485&&y>x1+0.47094&&y>-x/1.5+0.81||(x>0.16491&&x<0.1\ 7271) chr012 = abs(cabs(z+(-0.19266,-0.71305))-0.01305)<0.0039&&y>0.71305\ ||(abs(cabs(z+(-0.19266,-0.68695))-0.01305)<0.0039&&y<0.68695)||(((\ x>0.17571&&x<0.18351)||(x>0.20181&&x<0.20961))&&y>0.68695&&y<0.7130\ 5) test7 = chr111||chr012&&y>0.67&&y<0.73 chr113 = y<x1+0.4885&&y>x1+0.47444&&y>-x/1.5+0.79833||(x>0.15791&&x\ <0.16571) chr014 = abs(cabs(z+(-0.18566,-0.70605))-0.01305)<0.0039&&y>0.70605\ ||(abs(cabs(z+(-0.18566,-0.67995))-0.01305)<0.0039&&y<0.67995)||(((\ x>0.16871&&x<0.17651)||(x>0.19481&&x<0.20261))&&y>0.67995&&y<0.7060\ 5) test8 = chr113||chr014&&y>0.663&&y<0.723 chr215 = abs(cabs(z+(-0.80695,-0.71305))-0.01305)<0.0039&&(y>0.7130\ 5||y>-x/1.22571+1.3714)||(y<1.22571*x-0.29051&&y>1.22571*x-0.30285&\ &y<-x/1.22571+1.3714)||y<0.6778&&x>0.79&&x<0.8239 test9 = chr215&&y>0.67&&y<0.73 chr216 = abs(cabs(z+(-0.79995,-0.70605))-0.01305)<0.0039&&(y>0.7060\ 5||y>-x/1.22571+1.35869)||(y<1.22571*x-0.28893&&y>1.22571*x-0.30127\ &&y<-x/1.22571+1.35869)||y<0.6708&&x>0.783&&x<0.8169 test10 = chr216&&y>0.663&&y<0.723 chr917 = abs(cabs(z+(-0.15695,-0.47695))-0.01305)<0.0039&&y<0.47695\ ||abs(cabs(z+(-0.15695,-0.50305))-0.01305)<0.0039||(x>0.1661&&x<0.1\ 739&&y>0.47695&&y<0.50305) test11 = chr917&&y>0.46&&y<0.52 chr918 = abs(cabs(z+(-0.14695,-0.46695))-0.01305)<0.0039&&y<0.46695\ ||abs(cabs(z+(-0.14695,-0.49305))-0.01305)<0.0039||(x>0.1561&&x<0.1\ 639&&y>0.46695&&y<0.49305) test12 = chr918&&y>0.45&&y<0.51 x3=0.7*x chr319 = abs(cabs(z+(-0.83389,-0.47695))-0.01305)<0.0039||abs(cabs(\ z+(-0.83389,-0.50305))-0.01305)<0.0039&&(y>-x3+1.08677||y<x3-0.1067\ 7||x>0.83389) test13 = chr319&&y>0.46&&y<0.52 chr320 = abs(cabs(z+(-0.82389,-0.46695))-0.01305)<0.0039||abs(cabs(\ z+(-0.82389,-0.49305))-0.01305)<0.0039&&(y>-x3+1.06977||y<x3-0.1097\ 7||x>0.82389) test14 = chr320&&y>0.45&&y<0.51 chr821 = abs(cabs(z+(-0.19695,-0.26695))-0.01305)<0.0039||abs(cabs(\ z+(-0.19695,-0.29305))-0.01305)<0.0039 test15 = chr821&&y>0.25&&y<0.31 chr822 = abs(cabs(z+(-0.18995,-0.25995))-0.01305)<0.0039||abs(cabs(\ z+(-0.18995,-0.28605))-0.01305)<0.0039 test16 = chr822&&y>0.243&&y<0.303 x4=1.8*x chr423 = y<x4-1.134&&y>x4-1.15006&&y>0.27||(x>0.80335&&x<0.81115)||\ (y>0.2622&&y<0.27&&x>0.78&&x<0.81715) test17 = chr423&&y>0.25&&y<0.31 chr424 = y<x4-1.1284&&y>x4-1.14446&&y>0.263||(x>0.79635&&x<0.80415)\ ||(y>0.2552&&y<0.263&&x>0.773&&x<0.81015) test18 = chr424&&y>0.243&&y<0.303 x7=2.75*x chr725 = y<x7-0.74743&&y>x7-0.77025||y>0.1422&&x>0.3&&x<0.3318 test19 = chr725&&y>0.09&&y<0.15 chr726 = y<x7-0.73518&&y>x7-0.758||y>0.1352&&x>0.293&&x<0.3248 test20 = chr726&&y>0.083&&y<0.143 chr527 = abs(cabs(z+(-0.6789,-0.1089))-0.015)<0.0039&&(y<0.1089||x>\ 0.6789)||(x>0.66&&y>0.12&&x<0.6978&&(x<0.6678||y>0.1422||(y<0.1278&\ &x<0.6789))) test21 = chr527&&y>0.09&&y<0.15 chr528 = abs(cabs(z+(-0.6719,-0.1019))-0.015)<0.0039&&(y<0.1019||x>\ 0.6719)||(x>0.653&&y>0.113&&x<0.6908&&(x<0.6608||y>0.1352||(y<0.120\ 8&&x<0.6719))) test22 = chr528&&y>0.083&&y<0.143 chr629 = abs(cabs(z+(-0.50695,-0.07305))-0.01305)<0.0039&&y>0.07305\ ||abs(cabs(z+(-0.50695,-0.04695))-0.01305)<0.0039||(x>0.49&&x<0.497\ 8&&y>0.04695&&y<0.07305) test23 = chr629&&y>0.03&&y<0.09 chr630 = abs(cabs(z+(-0.50695,-0.06605))-0.01305)<0.0039&&y>0.06605\ ||abs(cabs(z+(-0.50695,-0.03995))-0.01305)<0.0039||(x>0.49&&x<0.497\ 8&&y>0.03995&&y<0.06605) test24 = chr630&&y>0.023&&y<0.083 test=test1||test3||test5||test7||test9||test11||test13||test15||tes\ t17||test19||test21||test23 test0=test2||test4||test6||test8||test10||test12||test14||test16||t\ est18||test20||test22||test24 z=c=pixel: z=z*z+c |z|<=4&&test0==0 } have fun, Guy

3 7

FOTD 21-05-02 (Cutoff Disconnected [6])
by Jim Muth 21 May '02

21 May '02

FOTD -- May 21, 2002 (Rating 6) Fractal visionaries and enthusiasts: Do not give up hope. The FOTD CD is past the halfway point, and sometime this summer the 1,700 or so fractal images and discussions will be available for distribution. Even better news is that, when the CD is completed, the ongoing FOTD will return to the daily schedule, while hopefully increasing in quality. The midget at the center of today's image, which exists in the fractal created by the formula (Z^3)+0.4(Z^5)+C, is located in the suburbs of a larger midget in a cut-off feature deep in an un-named valley of its bloated parent fractal. Since the feature in which today's midget lies is cut off from the main body of the fractal, the midget itself is cut off from its surroundings. I needed to include the <mathtolerance=/1> entry in the parameter file because of the magnitude of the image, which, at close to 9*10^12, is in the borderline range where strange things begin to happen. In fact, strange things are already happening. The pattern surrounding the midget is infinitely disconnected. Regardless of how close to the actual shore-line of the midget a particular feature lies, that feature will be disconnected from the main body of the midget. The situation is somewhat similar to that of the Newton's images, where the areas leading to different roots lie adjacent to each other with no space between them, yet at no point do they actually touch. The boundaries between the basins are fractal in nature. I have named today's image "Cutoff Disconnected", a redundant name that emphasizes the nature of the midget at the center. I rated it a 6, a rating I have been using quite a lot since cutting the frequency of the FOTD's by 2/3. The image is nice, it is interesting, it is curious, but such words really mean nothing. IMO, today's image is worth no more than the present rating. With a render time in the vicinity of 20 minutes, the parameter file of today's image is a bit of a drag to run. Wise fractalists, (that is everyone), will let Paul and Scott do the rendering, and download the completed GIF image from one of their web sites. Paul's site is at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's is at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Monday here at Fractal Central was mostly sunny, but with occasional cloudy periods. The chilly temperature of 59F 15C combined with the breaks in the periods of sun kept the dynamic duo of fractal cats dashing in and out all afternoon. As for myself, I've got to dash off to finish some important work so that I can get back to the fun work on that FOTD CD, which despite fears is progressing just a bit behind schedule. I shall return on the 24th with another fractal to amaze and delight even the mathematically challenged. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ CutoffDisconnected { ; time=0:22:23.97--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=ident passes=1 center-mag=+0.09846970716854085/-0.977478678397672\ 90/8.71082e+012/1/-144.990106256018947/-0.00765988\ 837549030216 params=1/3/0.4/5/0/0/0/0 float=y maxiter=2000 inside=0 logmap=446 periodicity=10 mathtolerance=/1 colors=000ONTRQWTTZWVaZYd``gccjee\ lggmhinjkpkmqmnrnntpouqpvspxtpzuozrowpornomlphjqdh\ rafs_dsYbtV`uTZvQXwOVxMTyJRzHPzF_ze`wdardcmbehagc`\ ic_kcZmdYoeXqgWshVujUwkTxlSneOdZKVSGAADAAERNETOEWP\ EYQF`RFbSFeTFhUGjVGmWGoXGrYHtZHw_Hy`HHWJJXMLXOMXQO\ XSQXURXWTXYVX_WXaYXc_Xe`XgTVaMUWFTR8SL1RG4OJ7MLAKO\ CIQFGTIDVKBYN9_Q7bS5hQ6cP6cO6bM6bL6aK6aI6`H6`G6_E6\ _D6ZC6ZBBbBFfBJiBNmBRpBVtBZwD`uEbtFdsGeqHgpJioKkmL\ llMnkNpiPrhQsgRueSwdTxcRq`PkYNeVL_TJUQHONFILGKMGMM\ GNMGPMGQMGSMGTMGVMGWMGYMGZMG`MGaMGcMGdMI`LJXLLTLMQ\ LOMLPIKRFKSBKU7KV4KT4IS4HR4FQ4EO4CN4BM4AL48K47I45H\ 44G42F41E40MgXHbPCZI7UB2Q4AUDHYLOaUVdaSb`Qa_O`ZM_Y\ KZXIYWFXVDWUBVT9US7TR5SQANNEILJDIN9GO7BR8CU9DXAE_A\ FbBGeCHhCHkDInEJqEKtFLwGMzIMwKLuMKrOKpQJnSJkUIiWHf\ YHd_GbaG_cFYeEVgETiDRkDTmHUmKWmNXmQYmT_mX`m_bmbcme\ dmhbmgamf`me_mdZmcYmbWmaVm`Um_TmZSmYRmYMmQ } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

1 0

Re: [Fractint] At it again...
by Franktal Gallery 20 May '02

20 May '02

>From: "Morgan L. Owens" <packrat(a)nznet.gen.nz> > >I think it's probably more likely due to the difficulty of manufacturing >optics, mirrored spheres, and CCDs/film emulsions to the required >precision/resolution. No, what I meant was, if you build a physical mirror ball stack, with a physical camera mounted inside (no matter how precise/small), the resultant picture would be modified by the infinite reflections of the camera itself. So, you'd need a virtual camera to make sure there's no perturbation introduced. Regards, Miguel > >At 02:29 20/05/2002, Franktal Gallery wrote: > >>Andrew, you might like to check out my ray-traced fractals >>made from infinite reflections inside a stack of mirrored >>spheres. I think these pictures show something impossible >>to reproduce in the real world, because of the perturbation >>introduced by a real camera. This seems related to the >>uncertainty principle, I guess.... The virtual camera >>overcomes this obstacle. _________________________________________________________________ MSN Photos is the easiest way to share and print your photos: http://photos.msn.com/support/worldwide.aspx

3 2

Fwd: Re: [Fractint] At it again... (threecircles1 fix)
by Morgan L. Owens 20 May '02

20 May '02

>I've just started on another where each pixel is coloured according to how >many reflections a ray starting from that point goes through before >escaping the system, but at the moment it's still a bit buggy: Oh, of course. That's what happens when I'm not reading what I'm typing. In threecircles1 the line direction=cos(theta)+i*sin(theta) ; We'll use a vector representaion ; of the direction should of course be direction=cos(theta)+(0,1)*sin(theta) ; We'll use a vector representaion ; of the direction Morgan L. Owens "I'm so sorry, I was miles away."

1 0

Second test
by JimMuth＠aol.com 19 May '02

19 May '02

this is the second test

1 0

test (par included)
by Franktal Gallery 19 May '02

19 May '02

This is a test message. A par is included to comply with netiquette ISO standards. I need to see if my messages are reaching the list (I'm not receiving the usual copy). Regards, Miguel --- A_Love_Supreme { ; by Miguel Fliguer - 1999 ; uses A0 ; Palette: MIGMULTI.MAP ; Title from John Coltrane's masterwork reset=1960 type=formula formulafile=miguel.frm formulaname=a0 function=sqrt/recip/sqr/cotanh center-mag=-0.56828087873239030/-0.16055600848866020/1278.823/1/119.978/\ 0.035 float=y logmode=fly decomp=256 colors=eVM021010000220<24>wwu<9>fYNeVKeVK<3>ZL6XI2VF0<10>wU0<22>QD0OC0OC\ 0OC0<7>w00<22>OO0<22>ww0<27>II0HK2<12>2tq0wu0ut<16>0FT<18>0Uu<36>033 } frm:a0 {; (c) by Miguel Fliguer z=c=pixel: z=fn1(z/fn2(z/fn3(z/fn4(z))))+c |z|<4 } _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com

1 0

Test
by JimMuth＠aol.com 19 May '02

19 May '02

Is the list working?

1 0

Re: [Fractint] At it again...
by Franktal Gallery 18 May '02

18 May '02

Andrew, you might like to check out my ray-traced fractals made from infinite reflections inside a stack of mirrored spheres. I think these pictures show something impossible to reproduce in the real world, because of the perturbation introduced by a real camera. This seems related to the uncertainty principle, I guess.... The virtual camera overcomes this obstacle. Best regards, Miguel Fliguer . Buenos Aires, Argentina Franktal Gallery - http://www.geocities.com/franktal2002 >From: "Andrew Coppin" <orphi69(a)hotmail.com> ><snip> >I've come up with the "hall of mirrors" analogy. Have you ever been to a >department store where they have mirrors on the columns supporting the >roof? >If you stand between two columns (assuming both have mirrors), you can see >an infinite number of reflections of yourself! But, of course, the mirrors >are always slightly greenish (never any other colou... mmm....) and never >completely flat. > >The Julia sets are the same. It seems that the infinite progression of >spirals/forks/dust are mirror images of one single such feature. _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com

1 0

FOTD 18-05-02 (The Blue Light [6])
by JimMuth＠aol.com 18 May '02

18 May '02

FOTD -- May 18, 2002 (Rating 6) Fractal visionaries and enthusiasts: The FOTD CD progresses, the rain falls, it's Preakness festival Saturday here in Fractal Land, and all else is well. (A Preakness is a horse race that tries to be another Kentucky Derby!) But the FOTD is about fractals, not horses. Today's image is a flowery affair which I found in the fractal that results when the formula Z^(-6)+6Z^(-1.6)+(1/C) is iterated. This parent fractal is an indescribable affair, with bays of all shapes and sizes, and lots of places that might harbor interesting scenes. (I leave it to the math experts to figure what all those bays represent.) Today's minibrot is located near the southern edge of the largest bay, actually in an area that at first glance appears to hold little promise. The area appears so hopeless in fact that I almost passed it by. Only an area of vague symmetry drew me to investigate further. And when I did investigate, I was glad that I had not passed by. I named the picture "The Blue Light". There is no obvious reason why I chose this name; I simply like its sound. I rated the image at a 6 because there is really nothing exceptional about it. Perhaps the best feature of today's image is its speed, rendering from the parameter file as it does in well under one minute. As always, those who would rather download than render may pick up the pre-rendered GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Friday here at Fractal Central was near perfect, especially for the cats who wanted to be comfortable outdoors. Generous sun and a temperature of 81F 27C kept them happy in the yard all afternoon. Thinking he was once again a kitten, Tippy scampered up a holly tree, but the bird he was chasing flew away long before he reached the branch where the bird had perched. A heavy rain shower passed over in the evening, but by that time the dynamic duo had settled for the night in their favorite indoor spots. This morning the rain is continuing, and there's much work to do and only limited time in which to do it. So until Tuesday the 21st of May, take care, and search for truth. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ The_Blue_Light { ; time=0:00:20.43--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=b center-mag=-0.28394429430300750/-1.090882416624821\ 00/2939.972/1/57.4999999999925038/2.42871001088218\ 463e-011 params=1/-6/6/-1.6/0/525/0/0 float=y maxiter=265 inside=255 logmap=8 periodicity=10 colors=00000000000002606H0AT0Ad08o08sUQzGTzRbzdkzq\ vzzzzzzzzzzzzzzszzdzzPxzAuz0qz0mb0z80zEku4zu0zs0zs\ 8sdVLPdPPmRPuVPzXPzZPvgTioVXvXJz`6zb0zd0zV0zL0zC2z\ 24z0Az6GqHLZTPHd`EXkAPv6Hz4CuNHidNXvTLzXRzLXzAbz0g\ z0kz0gz0ds6`iJX`XTTiH`L8e00k0Es0Rx2dzGqzTszbuqivgs\ xXzzNzzEzz4zzNzzdzzuzzzzzzzzzzzzzzzzzqzzkzzmzzozzq\ zzszzvzozzbzzPzzCzz0zzAzzJzqTzbbzNkz8Azd0zz2zxVzov\ zggzkVzoHzs2zv0zz0zz0zm0z`0zN0z82z06z0Ez0Jz4PzGXzP\ bz`gzkmzuxz0sz0oz0zzzzzzzzuszkizbbzTizEqz0xz0Nz40z\ P0zT0zV6zZCz`JzbPzeXzgbzigzdmz`szVxzRzzNzzHzzEzzAz\ z6zz2zz0zz0zz0zz0zz0zz0zz0zz00zP0zZ6zeGzmPzuXzzZzv\ Zzq`zm`zgbzdbzZbzV0z00z40zH0zV0zg0zu0zk0zb0zT0zJ0z\ A0zL0zX0zg0zs0zz0zz0zzzzzzzzzzzzzzzzzzzzzzzzzzzzxz\ zzxzzqzzizzbzzVzzNzzJzgGz8Cz0Jz0Rz0Zz0ez0mz0uz0zz0\ xzCxzTxzixzxgzbTzHEz00z00z00z00z00z00z00z00z00z00z\ o0z00zooz0ozooz0ozoCzC000 } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 18-05-02 (The Blue Light [6])
by Jim Muth 18 May '02

18 May '02

FOTD -- May 18, 2002 (Rating 6) Fractal visionaries and enthusiasts: The FOTD CD progresses, the rain falls, it's Preakness festival Saturday here in Fractal Land, and all else is well. (A Preakness is a horse race that tries to be another Kentucky Derby!) But the FOTD is about fractals, not horses. Today's image is a flowery affair which I found in the fractal that results when the formula Z^(-6)+6Z^(-1.6)+(1/C) is iterated. This parent fractal is an indescribable affair, with bays of all shapes and sizes, and lots of places that might harbor interesting scenes. (I leave it to the math experts to figure what all those bays represent.) Today's minibrot is located near the southern edge of the largest bay, actually in an area that at first glance appears to hold little promise. The area appears so hopeless in fact that I almost passed it by. Only an area of vague symmetry drew me to investigate further. And when I did investigate, I was glad that I had not passed by. I named the picture "The Blue Light". There is no obvious reason why I chose this name; I simply like its sound. I rated the image at a 6 because there is really nothing exceptional about it. Perhaps the best feature of today's image is its speed, rendering from the parameter file as it does in well under one minute. As always, those who would rather download than render may pick up the pre-rendered GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Friday here at Fractal Central was near perfect, especially for the cats who wanted to be comfortable outdoors. Generous sun and a temperature of 81F 27C kept them happy in the yard all afternoon. Thinking he was once again a kitten, Tippy scampered up a holly tree, but the bird he was chasing flew away long before he reached the branch where the bird had perched. A heavy rain shower passed over in the evening, but by that time the dynamic duo had settled for the night in their favorite indoor spots. This morning the rain is continuing, and there's much work to do and only limited time in which to do it. So until Tuesday the 21st of May, take care, and search for truth. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ The_Blue_Light { ; time=0:00:20.43--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=b center-mag=-0.28394429430300750/-1.090882416624821\ 00/2939.972/1/57.4999999999925038/2.42871001088218\ 463e-011 params=1/-6/6/-1.6/0/525/0/0 float=y maxiter=265 inside=255 logmap=8 periodicity=10 colors=00000000000002606H0AT0Ad08o08sUQzGTzRbzdkzq\ vzzzzzzzzzzzzzzszzdzzPxzAuz0qz0mb0z80zEku4zu0zs0zs\ 8sdVLPdPPmRPuVPzXPzZPvgTioVXvXJz`6zb0zd0zV0zL0zC2z\ 24z0Az6GqHLZTPHd`EXkAPv6Hz4CuNHidNXvTLzXRzLXzAbz0g\ z0kz0gz0ds6`iJX`XTTiH`L8e00k0Es0Rx2dzGqzTszbuqivgs\ xXzzNzzEzz4zzNzzdzzuzzzzzzzzzzzzzzzzzqzzkzzmzzozzq\ zzszzvzozzbzzPzzCzz0zzAzzJzqTzbbzNkz8Azd0zz2zxVzov\ zggzkVzoHzs2zv0zz0zz0zm0z`0zN0z82z06z0Ez0Jz4PzGXzP\ bz`gzkmzuxz0sz0oz0zzzzzzzzuszkizbbzTizEqz0xz0Nz40z\ P0zT0zV6zZCz`JzbPzeXzgbzigzdmz`szVxzRzzNzzHzzEzzAz\ z6zz2zz0zz0zz0zz0zz0zz0zz0zz00zP0zZ6zeGzmPzuXzzZzv\ Zzq`zm`zgbzdbzZbzV0z00z40zH0zV0zg0zu0zk0zb0zT0zJ0z\ A0zL0zX0zg0zs0zz0zz0zzzzzzzzzzzzzzzzzzzzzzzzzzzzxz\ zzxzzqzzizzbzzVzzNzzJzgGz8Cz0Jz0Rz0Zz0ez0mz0uz0zz0\ xzCxzTxzixzxgzbTzHEz00z00z00z00z00z00z00z00z00z00z\ o0z00zooz0ozooz0ozoCzC000 } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] FOTD 15-05-02 (Mandelia [6])
by Jim Muth 18 May '02

18 May '02

FOTD -- May 18, 2002 (Rating 6) Fractal visionaries and enthusiasts: The FOTD CD progresses, the rain falls, it's Preakness festival Saturday here in Fractal Land, and all else is well. (A Preakness is a horse race that tries to be another Kentucky Derby!) But the FOTD is about fractals, not horses. Today's image is a flowery affair which I found in the fractal that results when the formula Z^(-6)+6Z^(-1.6)+(1/C) is iterated. This parent fractal is an indescribable affair, with bays of all shapes and sizes, and lots of places that might harbor interesting scenes. (I leave it to the math experts to figure what all those bays represent.) Today's minibrot is located near the southern edge of the largest bay, actually in an area that at first glance appears to hold little promise. The area appears so hopeless in fact that I almost passed it by. Only an area of vague symmetry drew me to investigate further. And when I did investigate, I was glad that I had not passed by. I named the picture "The Blue Light". There is no obvious reason why I chose this name; I simply like its sound. I rated the image at a 6 because there is really nothing exceptional about it. Perhaps the best feature of today's image is its speed, rendering from the parameter file as it does in well under one minute. As always, those who would rather download than render may pick up the pre-rendered GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Friday here at Fractal Central was near perfect, especially for the cats who wanted to be comfortable outdoors. Generous sun and a temperature of 81F 27C kept them happy in the yard all afternoon. Thinking he was once again a kitten, Tippy scampered up a holly tree, but the bird he was chasing flew away long before he reached the branch where the bird had perched. A heavy rain shower passed over in the evening, but by that time the dynamic duo had settled for the night in their favorite indoor spots. This morning the rain is continuing, and there's much work to do and only limited time in which to do it. So until Tuesday the 21st of May, take care, and search for truth. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ The_Blue_Light { ; time=0:00:20.43--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=b center-mag=-0.28394429430300750/-1.090882416624821\ 00/2939.972/1/57.4999999999925038/2.42871001088218\ 463e-011 params=1/-6/6/-1.6/0/525/0/0 float=y maxiter=265 inside=255 logmap=8 periodicity=10 colors=00000000000002606H0AT0Ad08o08sUQzGTzRbzdkzq\ vzzzzzzzzzzzzzzszzdzzPxzAuz0qz0mb0z80zEku4zu0zs0zs\ 8sdVLPdPPmRPuVPzXPzZPvgTioVXvXJz`6zb0zd0zV0zL0zC2z\ 24z0Az6GqHLZTPHd`EXkAPv6Hz4CuNHidNXvTLzXRzLXzAbz0g\ z0kz0gz0ds6`iJX`XTTiH`L8e00k0Es0Rx2dzGqzTszbuqivgs\ xXzzNzzEzz4zzNzzdzzuzzzzzzzzzzzzzzzzzqzzkzzmzzozzq\ zzszzvzozzbzzPzzCzz0zzAzzJzqTzbbzNkz8Azd0zz2zxVzov\ zggzkVzoHzs2zv0zz0zz0zm0z`0zN0z82z06z0Ez0Jz4PzGXzP\ bz`gzkmzuxz0sz0oz0zzzzzzzzuszkizbbzTizEqz0xz0Nz40z\ P0zT0zV6zZCz`JzbPzeXzgbzigzdmz`szVxzRzzNzzHzzEzzAz\ z6zz2zz0zz0zz0zz0zz0zz0zz0zz00zP0zZ6zeGzmPzuXzzZzv\ Zzq`zm`zgbzdbzZbzV0z00z40zH0zV0zg0zu0zk0zb0zT0zJ0z\ A0zL0zX0zg0zs0zz0zz0zzzzzzzzzzzzzzzzzzzzzzzzzzzzxz\ zzxzzqzzizzbzzVzzNzzJzgGz8Cz0Jz0Rz0Zz0ez0mz0uz0zz0\ xzCxzTxzixzxgzbTzHEz00z00z00z00z00z00z00z00z00z00z\ o0z00zooz0ozooz0ozoCzC000 } 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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At it again...
by Andrew Coppin 18 May '02

18 May '02

On 15/05/02, Morgan L. Owens wrote... over 9x2^10 octets of stuff! 8-0 Thanks for that mate - my head hurts so much! :S As regards the 4D generalisations of M and J sets... aren't they just simple surfaces of rotation of the ordinary complex versions? (Hmmm... some day I've GOT to download the POVRay source code and find out how the hell it renders 3D slices of the 4D Julias...) While I'm here, I thought I'd just report some of my recent fractal antics. I've been busily revising for my final year exams, but in between I've done some fractal work... Not content with Julia sets, after much experimentation I've persuaded WinAmp's AVS to draw (linear) IFS! (Figuring out the correct blit settings was highly non-trivial I can tell you!) As with the Julia sets, the trick is finding good patterns to apply the mapping to... I found that if I draw white graphics, and apply different colour filters to each transformation of the system, the results are really quite pretty! I also did some work with POVRay, drawing graphs for forwards and backwards iterations of the quadratic mapping (with Z-depth indicating iteration count), trying to work out where those complex patters derrive from. I mean, z => z^2 is a very simple function; it's just a big troff! (Oh dear... too much UNIX :S) The Julia set reflects this - it's a circle. Adding the c term only moves the center of the thing... and yet this creates amazingly complicated patterns. Why? Through my WinAmp experiments, it has become clear that ANY patters that has the quadratic mapping applied to it turns up these wonderful patterns. (Unsuprising really...) Also, my POVRay work has shown that the adjasent points on the graph which look so like they are images of each other, are in fact derrived from distant points. (Internally, the Julias seem to be a lot less symmetric than you might think!) I've come up with the "hall of mirrors" analogy. Have you ever been to a department store where they have mirrors on the columns supporting the roof? If you stand between two columns (assuming both have mirrors), you can see an infinite number of reflections of yourself! But, of course, the mirrors are always slightly greenish (never any other colou... mmm....) and never completely flat. The Julia sets are the same. It seems that the infinite progression of spirals/forks/dust are mirror images of one single such feature. (To look at it the other way - the orbits of distant points are ending up in the same vicinity. That's the fun part - the forward transformation of the individual orbits can be seen as the reverse transformation of the bailout boundery...) Erm... am I making sense here? 8-| OK, well anyway, I've also been investigating the Julia sets embedded in M. (Apparently these are quite a well known feature - as I discovered when I first mentioned them on this list!) It seems many an explorer knows that if you tunnel into the center of just a mini Julia, you find 2, 4, 8, 16... groups of the pattern outlining the equipotential curves of a minibrot (how deep depending on how close to the parent minibrow you found this minijulia in the first place). Well... I've been exploring the minijulias of the largest minibrot (the lowest-period one on the negative stem on the M set). Here every minijulia is scuered with a beautiful curving line. And at every major junction of this line, a minijulia sits. The one in the center leads (eventually) to a minibrot, as described above. However If you zoom into other parts of the minijulia, the minijulias you find dotted around the various junctions (and it's a nightmare to try to index them!) don't follow the equipotential curves of a minibrot. The outer most ring isn't a ring. Typically that are S-shaped groups, or just chaotic (but beautiful) "clusters", who's underlying pattern is difficult to understand. I'm still a long way off finding the pattern in all this... To anyone who thinks that M has been completely explored and holds no mysteries any more, I say KNICKERS! B^P OK, now I *am* jibbering... I'm gonna stop typing now... might send a PAR of the mini Julia patterns in a while tho... Thanks. Andrew. _________________________________________________________________ Join the worlds largest e-mail service with MSN Hotmail. http://www.hotmail.com

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At it again... Pars!
by Andrew Coppin 18 May '02

18 May '02

Have a look at this lot... (I mean... if you're bored that is!) Mini-Julia { ; A typical mini Julia in M. reset=2002 type=mandel center-mag=-1.74710622469804600/+0.00137745649736071/44635.92 params=0/0 float=y maxiter=65536 inside=255 sound=off } Spiral-Cross { ; A non-typical mini Julia arrangement! reset=2002 type=mandel center-mag=-1.74711451785152400/+0.00138682610202126/1.089744e+007 params=0/0 float=y maxiter=65536 inside=255 sound=off } Spiral-Cross-Z { ; The minibrot as it's heart... reset=2002 type=mandel center-mag=-1.74711452819077400/+0.00138682821036616/2.391468e+008 params=0/0 float=y maxiter=65536 inside=255 sound=off } Spiral { ; Another unusual arrangement. reset=2002 type=mandel center-mag=-1.74709858222257700/+0.00138213246963899/7390053 params=0/0 float=y maxiter=65536 inside=255 sound=off } Spiral-Z { ; ...and it's minibrot reset=2002 type=mandel center-mag=-1.74709858052979200/+0.00138213299873782/1.154696e+008 params=0/0 float=y maxiter=65536 inside=255 sound=off } Twin-Spiral { ; It goes on... reset=2002 type=mandel center-mag=-1.74710019324498000/+0.00138058047460226/4.658619e+009 params=0/0 float=y maxiter=65536 inside=255 sound=off } Double-S { ; It gets stranger... reset=2002 type=mandel center-mag=-1.74711328280191700/+0.00138630427456312/1.417572e+009 params=0/0 float=y maxiter=65536 inside=255 sound=off colors=000<87>000000000<3>000w00<25>C00A00800<2>200000003<8>00b00f00j<3>\ 00z<9>`bOdfKhjG<3>wz0<9>xObyKfyGj<3>z0z<9>O0OK0KG0G<3>000<41>oooppprrr<3\ >www000<14>000 } Mini-Julia2 { ; Another mini Julia. reset=2002 type=mandel center-mag=-1.76904186275559900/+0.00315554134874867/64710.86 params=0/0 float=y maxiter=65536 inside=255 sound=off } Sausage { ; Curiouse... reset=2002 type=mandel center-mag=-1.76904179326671400/+0.00315920536912995/1.12082e+011 params=0/0 float=y maxiter=65536 inside=255 sound=off } Sausage2 { ; [Ditto!] reset=2002 type=mandel center-mag=-1.76904179326680700/+0.00315920536933926/1.12082e+012/0.9999 params=0/0 float=y maxiter=65536 inside=255 sound=off } Thanks. Andrew. _________________________________________________________________ Send and receive Hotmail on your mobile device: http://mobile.msn.com

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intestines
by M J Benkers 15 May '02

15 May '02

A rather weird fractal. The formula I used, gave an uninteresting picture, but after some experimenting I got something very interesting. Mary Stultorum infinitus numerum est. intestines { ; 0.00.23 on P200 ; Version 2000 Patchlevel 9 reset=1910 type=formula formulafile=robklep1.frm formulaname=DivMandel1 center-mag=+0.29840252942018640/+0.659471884253001 80/47.85979 params=2/0/0/0/0/0 float=y maxiter=32000 bailout=500 inside=0 potential=255/511/0 decomp=256 formula:DivMandel1 (XAXIS) {; c = z = pixel: z = (z^2+c)/(z^p1-c) + c; |z| <= 4 }

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Re: [Fractint] Mandellace
by M J Benkers 15 May '02

15 May '02

>Stultorum infinitus numerum est. What? There are so many fools, you can't count them......... :-)))))) It's in the bible (Ecclesiastes 1:15). Mary ---------------------------------------------------------------------------- Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com

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Re: [Fractint] FOTD 12-05-02 (Galactic Arm [7])
by Multiple Bogeys 15 May '02

15 May '02

>The bad feature of images such as today's, which consist totally >of trapped inside points, is their slowness. Today's image >requires over an hour to render on my tired old P200 machine. >It will render faster on a state-of-the-art screamer, but the >easiest way to see the image is to let Paul and Scott do the >rendering and download the completed image from either of their >web sites. A state-of-the-art screamer like my new 1526MHz Athlon? ;-) >73F ... 22.75C? ... Those are nearly the same, 73F being 22.777777... Celsius...Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com

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Re: [Fractint] Mandellace
by Multiple Bogeys 15 May '02

15 May '02

>Stultorum infinitus numerum est. What?Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com

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Re: [Fractint] FOTD 30-04-02 (Frenetic [7])
by M J Benkers 14 May '02

14 May '02

> >You need to go to the following location and download the 20.2.04 >version to get the most current Developer's release: > Thanks! Mary

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Re: [Fractint] FOTD 30-04-02 (Frenetic [7])
by M J Benkers 13 May '02

13 May '02

>Being colored with the outside=tdis option, Well, the version of Fractint (20.0) that I use, doesn't know this option! Mary

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FOTD 12-05-02 (Galactic Arm [7])
by Jim Muth 12 May '02

12 May '02

FOTD -- May 12, 2002 (Rating 7) Fractal visionaries and enthusiasts: With today's image we embark on a trip to interstellar space. It's enjoyable to be able to do this on a computer, since the way man is going, no one will ever be able to do it in person. (We won't lack the know-how; we'll lack the resources.) Our trip takes us to an arm of the local galaxy -- let's call it the Orion arm -- from where we see ourselves surrounded by clouds of nebular gas and nascent stars. All around us is a vast emptiness. Yet the emptiness is not the nothingness that it first appears to be, (vacuum energy?), for on this trip we have been given additional senses. We have the senses to perceive magnetic fields as well as gravitational fields. Since these new perceptions would likely appear to us in a manner we cannot now imagine, I have translated them into vision, which we can imagine. So, in my fancy, today's image, dark and somber as it is, shows the star-lanes and energy fields of a very densely populated area of our Milky-Way Galaxy. With this in mind, I named the picture "Galactic Arm". The rating of a 7 is optional. Actually, the image is one of an 'evaporated' midget, which has ceased to exist, but whose ghost has been revealed by illumina- ting it with the ghost-busting <bof60> inside fill. (A <fmod> fill would also have worked.) The very simple fractal formula Z-(1/Z)+(1/C) created the original midget, which I killed when I raised the escape radius to one-googol plus one-hundred. (The one-hundred is built into the M-Mix2 formula, though it has no effect on the final result.) The bad feature of images such as today's, which consist totally of trapped inside points, is their slowness. Today's image requires over an hour to render on my tired old P200 machine. It will render faster on a state-of-the-art screamer, but the easiest way to see the image is to let Paul and Scott do the rendering and download the completed image from either of their web sites. Paul's site is at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's is at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather, (Is there any other kind?), Saturday here at fractal central was ideal. What could be better than a temp- erature of 73F, unless it was a temperature of 22.75C? The cats spent the entire afternoon in the sun of the yard, frolicking like tired kittens. And no, Tippy did not catch any more sparrows. As for myself, it's Sunday, it's Mother's day, and I'm going to treat myself to a well-deserved rest from work on both the CD and the stuff that I expect to bring profit. But I still might sneak in a fractal or two when the obligatory social activity has been accomplished. Regardless, until next time, take care, and try to decide whether fractals are really real or are real merely because we decide they are. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Galactic_Arm { ; time=1:10:15.64--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=-1.65751903104643300/+1.790625615929802\ 00/100087.5/1/-152.5/-3.13505964244509272e-009 params=1/1/-1/-1/0/1e+100/0/0 float=y maxiter=1500 inside=bof60 logmap=yes periodicity=10 sound=off colors=000uiqrhoogmlfliekfdiccgabeZacX`aV__SZYQYWO\ WULUTJSSGQSEORJAMJ9K00800B00D00G00J00L00O00R00T00W\ 00Z00`00a00b00c00d00e00e00f00g00h00i00j00j00k00k00\ k00k00l00l00l00l00l00m00m00m00m00m00h00c00_00V00Q0\ 0M00W00e00o00l00i00f00c00`00Y00V00S00P00M00P00R00T\ 00V00X00Z00T00O00I00D00800C00G00J00N00R00U00Y00a00\ d00h00l00o00m00k00i00g00e00c00a00_00Z00X00W00V00U0\ 0S00R00Q00P00O00N00M00L00K00J00I00H00G00F00E00D00C\ 00B00A00C00E00F00H00I00K00L00Q00V00_00d00i00n00s00\ w00r00n00j00f00b00Y00U00Q00M00I00E00m00o00q00g00Y0\ 0Z00_00_00`00a00a00b00b00i00g00e00c00a00_00Y00X00Z\ 00_00`00a00b00c00d00f00g00h00i00j00k00l00k00k00k00\ k00k00k00k00k00k00f00a00X00T00O00J00F00A0050010070\ 0C00H00M00R00W00a00f00k00p00u00z00t00o00j00e00_00V\ 00Q00L00G00F00F00F00E00E00E00I00L00O00R00V00Y00`00\ c00g00j00m00p00s00`00J00M } 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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Mandellace
by M J Benkers 12 May '02

12 May '02

A new picture from the Netherlands! It's made with cubic in the fractint.frm file (9.48.68 on a Pentium 200). By the way, there are a lot of nice pictures to construct with this formula. Mary Stultorum infinitus numerum est. mandellace { reset=1910 type=formula formulafile=fractint.frm formulaname=Cubic center-mag=-0.02295512076302016/+2.845707937164529 00/1.76006e+007/1/-32.\ 499 params=0/0/0/0/0/0 float=y maxiter=5000 inside=0 colors=000KKa<4>MMeNNfOOg<28>ggxhhxiiy<28>xxzxxzyy zyyzzzz<28>zcczbbzaa<4\ >xYYxYYwXXvWW<21>iFFiEEhDD<30>M11L11K00<25>4003002 00200100<3>001002113<2\ 3>66I66I66J<24>JJa }

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homemade watch
by Bill Jemison 10 May '02

10 May '02

I always thought that it looked like some naked guy sitting on the scanner. <Interesting ... it doesn't really look _that_ much like a person, but <it's quite frequently described as one - apple-man, it seems; or snowman <(with an aerial sticking out of his head) - even though the figure has <to be turned on its side from its convenetional orientation for the <description to make sense!

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Re: [Fractint] Mary Benkers, New person on the list
by M J Benkers 10 May '02

10 May '02

> I liked your picture in the M-set very much Don't ask me how I made it! It can't remember what I did to make it, it's too long ago! Mary

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FOTD 09-05-02 (Spider-Man Delbrot [7])
by Jim Muth 09 May '02

09 May '02

FOTD -- May 09, 2002 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal has been created by iterating the deceptively simple fractal formula -1(Z)-(1/Z)+C, an expression that at first glance would appear to result in no fractal at all when iterated. But things are not always as they appear in the world of fractals, and today's image is a perfect example of the ability of fractals to create something from nothing. I named today's image "Spider-Man Delbrot". The spider-web effect around the central midget inspired the name. The new Spider-Man movie likely played a part also. I decided to give the image a rating of an above-average 7. Whether this rating is deserved is up to the individual to decide. In this particular image I departed from the usual FOTD equal- iteration-band outside-coloring algorithm and tried the alternate outside=summ. The result was not much of an improvement, but the improvement was enough to cause me to temporarily change my usual coloring method. The parameter file renders in 19 minutes on a quaint old P200 machine. The image file downloads from Paul's site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> in far less time. The news for those waiting with bated breath for the FOTD CD to appear is good and bad. The good news is that the CD is making progress; the bad news is that I continue to find new things that need to be done to make the disk easy to use. The latest task is to change the names of the fractal image files from their present cryptic 8-letter DOS names to names which are the dates on which the images appeared. I can either change the names of the image files or place every day's discussion and image in a separate directory (folder). Right now, the files are organized into monthly directories. Whatever I do, the time required will be several additional days. Take a couple dozen of these unanticipated 7-day tasks and it's easy to see why the CD is taking so long. The fractal weather Wednesday started sunny and mild, but as the afternoon progressed, the clouds moved in. The temperature of 70F 21C must have been just what the cats ordered, because they spent most all day romping in the yard. Tippy set the day's high point when he showed up at the door with a sparrow in his mouth. This was the first bird he has caught in over a year. There's life in the old ex-tomcat yet. Now if Thomas can only catch something other than a ray of sunlight. . . . As for me, I've got work to do, both for money and in the preparation of the FOTD CD. The time will never be better to get started, so until next FOTD on May 12, take care and be happy. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Spider-Man_Delbrot { ; time=0:18:52.84--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+2.010171243979102/+0.1046890830356033/\ 106079.2/1/167.5/2.3982375016440294e-008 params=-1\ /1/-1/-1/0/525 float=y maxiter=1400 inside=0 outside=summ colors=000GFZUqhRnYQlOOjFNh5SZ0Qa0Nd0\ 0RJ0QM0OO0NQ0NS0MV0KX0JZ0Ia0Gb0Fe0Eh0Ci1Bl19n18p17\ s17t08s08q08p08n08m08l08j08i08h09h09f09e09d09b09a0\ 9`09Z09Y09X0BX0BV0BU0BS0BR0BQ0BO0BN0BM0BM3EO7GRBJU\ FKXKNZOQaSRdXUfaXieYli`nmbqqdssiism`sqRqmOpiNneMma\ KlYJjVIiRGhNFfJEeFCdCBeJ9fO8hU7hZ5id4ji3ln1lt1iu0h\ u0fw0ew0dx0bx0ax0`y0Zy0Yz0Xz0Vz0Uz0Sz0Rz0Qz0Nz0Mz0\ Kz0Jz0Iz0Gz0Fz0Ez0Cz0Bz09z08z07z05z04z03z05z18z49w\ 7Cs9EmBGiEIdGK`JMVMORNQMQSISUCVX8YY4ZZ8aZCd`Fe`Jha\ MiaQlbSmbXpdZqdbtdeuIXl0Nb0Md0Kd0Kd0Jd0Jd0Id0Id0Gd\ 0Gd0Fd0Fd0Ee0Ce0Ce0Be0Be09e09e08e08e07e07e08b08a09\ `09Z3BY4BX7CV8CU9ESCEREFQGFOIGNKGMMGKNIJQIIRJGUJFV\ KEYKCZMB`M9bN8dN7fO5hO4jQ3lQ1mQ0nS1pV1qY1s`3tb3ue3\ wh4xj4ym4zp5zs5zu5zx7zz7zz7zz8zz8zz8zzEzzIzzMzyQzw\ UztYyqaxnewliuimtfqsduqayp`zpaqpbfpbXpdMpdBtbGwaMy\ `Rz`VzZ`zYezYilXSQVB3U0Qe39Z0Gb0YZdRbI } 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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Mary Benkers, New person on the list
by Harold Lane 09 May '02

09 May '02

Mary, I am new to the Fractint list also - although I wrote a lot of programs to create fractals back when the graphics adapters commonly had a resolution of 320 x 200 with 16 colors! I am enjoying getting back to creating fractal images using Fractint. I liked your picture in the M-set very much. It has a nice Julia set-like quality to it. I especially liked your color map. It is very sophisticated - despite its apparent simplicity. How did you make it? One unusual aspect of your image and color map is that the mostly red outside edge of the 'island' of your image is adjacent to a blue surrounding field. Due to the fact that the eye focuses different colors at different depths in the eye, the 'island' in your image appears to hover 'above' (closer to your eye) than the blue surround. You have created a truly three dimensional image - as far as the eye is concerned! (This effect is enhanced somewhat if the room you view the image in is darkened and direct your gaze to the boundary between the red and blue. When the effect appears I can then refocus my attention to the entire island and it will remain hovering above the blue 'background'. ) Did you construct your color map in order to create this effect? Please let me know whether you are able to see this effect. Would others who create your image please let me know whether they can see this as well? Thanks I zoomed into the center of your image on the miniature mandelbrot set located there (Jim Muth calls this a 'Midget') and created another image using your color map. The file to create it follows. The image takes about 3-4 hours on a P400 using the 1024 x 768 x 256 disk video mode. (My Windows 98 machine actually uses Expanded Memory instead of the disk.) I increased the maxiter to 10,000 to insure an accurate coastline to the mini-brot. I don't believe that the high maxiter is the cause of the long creation time. I believe it is because in most of the image the actual number of iterations it takes to color the pixel is large. Also, periodicity testing inside the 'lake' of the M-set should keep the number of iterations from reaching 10,000 there. [Can anyone confirm those two conjectures?] The 'island' in my image resembles a starfish with eight arms. Just within it is the outline of another 'starfish' with 16 arms. Within it is one with 32 arms, etc. I can just begin to make out some of the arms of the starfish with 256 arms with the image rendered at 1024 x 768. I don't recall being able to see a period doubling of that high an order before - and I look every time I see this doubling in a minibrot. I believe that Guy's expression in his message to you: "...a more performant version of FractInt..." means that it will create images more quickly. :-) - Hal Lane USA mandelischia_midg{ ; Zoomed into the center of mandelischia_coli.par ; Orig par by Mary Benkers NL, midget by Hal Lane USA ; Fractint Version 2002 Patchlevel 3 (20.02.3) reset=1910 type=mandel passes=1 center-mag=-1.8605739577363196/-9.3407056855e-7/8.742819e+012 params=0/0 float=y maxiter=10000 inside=0 distest=1/71/1024/768 sound=off colors=000uux<2>xxyzzzyyz<42>GJeFIeEHdDGdBEc<25>BCOBBOBBN<2>BBLAAKCDK<8>\ YcF_fFaiE<3>kuC<9>OSHMPIKMI<3>AAK<9>f48i36m35<3>z00<9>zbbzffzjj<2>zvvzzz\ xvw<6>mRbkN_jIX<3>c0K<5>l8Hm9GoAFpBErDE<3>xIBzKAzMB<8>zjMzlOzoP<3>zzU<9>\ TVYQSZNPZ<3>9C`ADaBEc<42>ttw } >Hello, > >I am new on the list. My name is Mary and I am >from the Netherlands. >I hope you do like my picture. It is somewhere on >the Mandelbrot set. It takes 6 min on my computer >(P200) to make it. > >Mary Benkers > >mandelischia_coli { ; some strange bacteria? >reset=1910 type=mandel passes=1 >corners=-1.8605739577489129/-1.860573957723912/-9.3407929358274632e-007/\ >-9.340605428307932e-007 params=0/0 float=y >maxiter=1500 inside=0 >distest=1/71/1280/1024 >colors=000uux<2>xxyzzzyyz<45>DGdBEcBEc<29>BBLAAKCDK<14>kuC<15>AAK<15>z00\ ><15>zzz<12>e5Oc0Kd1K<12>xIBzKAzMB<14>zzU<15>9C`ADaBEc<42>ttw > }

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Re: [Fractint] homemade watch
by Mark Christenson 08 May '02

08 May '02

At 03:39 PM 5/7/02 -0700, John wrote: >... >I also found a "fractext.exe" on a German site. The automatically-translated page said: > >"Fractal of extremes provides and stores bizarre and apparently coincidentally developed Fraktale in form of the well-known apple males over mathematical almond bread functions in different dissolutions. With the mouse you click a range of the Fraktals, which is then gezoomt and again computed. (Shareware, English)" > Fraktale: presumably Deutches for "fractals". apple males: not sure about the males, but the word for apple (apfel) also means "ball". Maybe it works out to something like "spherical projections" ;-) almond bread: literally "mandel brot". Now you know what his name *really* is! dissolutions: probably "resolutions". Glad to be of service, Bud

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FOTD 06-05-02 (A Broken Minibrot [5])
by Jim Muth 06 May '02

06 May '02

FOTD -- May 06, 2002 (Rating 5) Fractal visionaries and enthusiasts: The parent fractal of today's image was created by the iterated formula Z^(1.8)+C, and is shaped like a rotated and perturbed version of the classic M-set. The image is located in a broken elephant trunk of the fractured East Valley area of the parent. I named the image "A Broken Minibrot" because of the spirals which are so obviously broken. The image is of average quality and rates an average rating of 5. The breaks in image continuity are unavoidable with fractional exponents of Z, and are caused by the multi-valued nature of the complex log function. But the same multi-valued nature is not all bad, since it makes the resulting fractals infinite both on the surface as well as in their depth. The 14-minute render time can be reduced to a minute or two by going online and downloading the finished image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Though I took the day off on Sunday, the FOTD CD is progressing. A midsummer completion still looks likely, and anything worth having is worth waiting for. The all-important fractal weather Sunday here at Fractal Central was just what the fractal cats ordered. Well, maybe they didn't order it, but they certainly did enjoy it. Warm sun, light winds and a temperature of 68F 20C made conditions ideal for man and cat alike. Both the dynamic duo and myself spent a good part of the afternoon in the yard, the only diversion being when Tippy started rolling in the emerging catnip patch. Since all good things must eventually end, this day is just about on its last lap. It's near late-news time and I can't end the day without knowing the latest bit of bad news. So until next time on May 9, take care, and let's get some fractal into that fractal philosophy. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ A_Broken_Minibrot { ; time=0:14:36.56--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=+0.00817267703828271/+0.240493666992600\ 80/1.818109e+011/1/114.999944662658265/-1.10636886\ 913803578e-005 params=1.8/0/28.7/0 float=y maxiter=4500 inside=0 logmap=366 symmetry=none colors=0009F04D06F07F09F09G0AG0CG0DI0DI0FI0GJ0IJ0I\ J0JL0LL0LL0MM0OM0PM0PO0SO0VO0VP0WP0XP0XQ0YR0YS0ZS0\ ZS0ZS0YT0ZS0ZT1XV4VX7TYAQ_DP`GOaJLcMJdPIfSGhVDj_Cl\ aAmd7og6pj4rm1sp0us0vv0xy0yz0zz0zz0zz0zz0zx0zu0zr0\ zo1zl3zi4zfAzXGzOMzFSy6Yu0cr0do0fm0gl0gj0ii0jg0jf0\ ld0mc0ma0o_0pY0pX0rV0sT0sS1uQ3vP3xO4xM4yL6zI6zG7zF\ 7zD9zC9zAAz9Az7Cz6Cz4Dz0Cz3Dz6Dz9FzCFxFGuIGrLIoOIl\ QJiTJYSMaTLfVJjVIoXGsYGxYFz_Dz`Czg6zc9z`CzYDzVGzSI\ zPLzMMzJPzGSyDTyAXx7Yv4`u1as0dz0gs0fg0dY1cM4aA6fC7\ cC7aD9`D9YFAXFAVGCSGCQICPIDMJDLJFJLFILGFMGDMGCOI9O\ I7PJ6PJ3QL1QL0QL0OJ7LIGIGPGGgDFvADz3Cz6Dz9DzCDvDDo\ GDlJDgLDcOD`QFXTFTTFPTFLTFITFDTFATF6TF3YTSacu_foXi\ jTlfQo`OrXLuSIvOJvPJvPLvPLvQMvQMvQOxQOySPzSPzSQzTQ\ zTSzTSzVTzVTzVVzXVzXXzXXzYYzYYzY_z__z_`z_azY`z_`z_\ `z``z``za`za`za`zc`zc`zd`zd`zd`zf`zf`zg`zgMzJMzOLz\ QLzTLzXJz_JzcIzfGz4Dz3Cz1 } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END 20.0 PAR-FORMULA FILE==================================

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FOTD 03-05-02 (Eight Gold Keyholes [6])
by Jim Muth 03 May '02

03 May '02

FOTD -- May 03, 2002 (Rating 6) Fractal visionaries and enthusiasts: Today's fractal scene exists in an oversized parent fractal, way out on a filament that leads from a mandel-bud of the main bay and terminates in a ring-like feature. Many filaments converge on this ring, but only the one that comes from the bud has midgets along it. The terminal ring is mirrored in the eight rings, (I call them keyholes), that surround the midget in today's image. The formula of the parent fractal is Z^(-11)+6Z^(-1.1)+(1/C). This formula was iterated by the MandelbrotMix2 Fractint formula, which likely will replace the old M-Mix4 formula as my most often used formula. The speed of the new formula is the same, and the new one is more versatile. The blue-gold color scheme makes the image appear a bit better than its actual worth of average. I therefore rated it at a 6, which is the least possible above-average rating for a FOTD fractal. The 9-minute render time of the attached parameter file makes a download of the completed GIF image the marginally better choice. That download can be found at Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Thursday started with a heavy thunder-storm, followed by sun from 10am to 3pm. At 4pm, another heavy thunder- storm, this one with golf-ball-sized hail, passed over. Between storms it was warm and humid, with a temperature around 80F 27C. The fractal cats found enough time during the midday sunny period to romp in the yard, but when the hailstones started clattering, they dashed for cover and didn't come out for nearly an hour. As for myself, I've got work waiting and not enough time in which to do it. The best way I know of solving the problem is to get started, so that's what I'm about to do. And that FOTD CD, which has been languishing of late, still has a considerable amount of work to be done. The next FOTD will appear May 6. Until then, take care, and be philosophical. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ EightGoldKeyholes { ; time=0:09:07.33--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+428.8990414983479/-46.07822226439/272/\ 1/-15/-6.55149697686985277e-009 params=6/-1.1/1/-1\ 1.1/0/525/0/0 float=y maxiter=1500 inside=0 logmap=149 periodicity=0 colors=00000l00m00n01o02p\ 03q04r05s06t07u08v09w0Ax09y07z05x05z03u03x03r03q01\ m01j01f01d00a00Y10U10Q10N30J30F30D3095055015007007\ 00700700B00F30H70LB0PF0QL0UP3YS5ZW7cZBfdDhhFllJooL\ qpNrqLsqLtqLuqLvqLwqLwqLwoLwoLwoLroLroLmoLmoLmmLmm\ LmmLmmLimLimLfmLijNjhPlfQmdQoaSqZUsYUtWWvUYyQYzPZz\ NazLazJczFdzDdzBfz9hz7hzBjzFlzHmyLovPqsQqoUslYthZv\ dcxafyYhyUlzQozNqzJtzFxzByzDzzDzzDzzDzyDzvDztFzsFz\ qFzmFzlFzjFzhDzjBzlBzl9zm9ym7vo7sq5oq5ls3hs3dt1av1\ Yv0Ux0Qx0Ny0Jy0Fy0By07y09v0Bs0Do0Fl0Hh0Jd0Ja0LY0NU\ 0PQ0QN0SJ0UF0UB1YF1aP3dY5hf7loFoxNszUvzayzhzzfzzdz\ zdzzczzazzazzYzzUzzQzzPzzLzyHzyFzxBzx7zv5zv7zo9zhB\ taDmUFfNHaFJc7Ld0Nf0Ph0Pj0Sl0dm0fq0ht0jq0lo0mm0oj0\ qh0sf0tc0ta0vZ0xY0yY0zY0zY5zYFzYJzYNzYQzYUzYYzYazY\ dzYhzYlzYozYszYvzYyzYzzYzzYzzYzzYzzYzzYzzYzzYzzYzz\ YzzYzzYzzYzzYzzYzzYzzYzzYzzYzzYzzYzzYzzYzzYzzYzzYz } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 30-04-02 (Frenetic [7])
by Jim Muth 30 Apr '02

30 Apr '02

FOTD -- April 30, 2002 (Rating 7) Fractal visionaries and enthusiasts: I'm actually nearing the point where I'll be able to say that the completion of the FOTD CD is within sight. My original hope was to have the disc ready for distribution sometime this summer. Considering the way things are going, I may actually make it and be back to an FOTD every day sooner than expected. Today's image illustrates a lively scene in the fractal that results when the rather confusing formula -1(Z)-(1/Z)-(1/C) is iterated. In this case, the M-Mix2 formula, with its adjustable starting value of Z, draws the critical plane that the M-Mix4 formulas misses -- not that it makes much difference in the final appearance of the parent fractal. Being colored with the outside=tdis option, today's image is more than lively, it is downright "Frenetic", and that's what I named it. The sharply defined, almost sinister features and almost too-brilliant colors earned the image a rating of an above-average 7. Had it not been for the area immediately surrounding the midget, which seems to have run out of detail, the image might have rated an 8. The <tdis> algorithm often does this when applied to the outside areas of fractals close to high-iteration midgets. There is probably a way to work around it, though I have not yet looked for such a work-around. The render time from the parameter file of 6 minutes on a P200 machine can be cut by over half by downloading the finished GIF image from Paul's site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Monday here at Fractal Central was cloudy, blustery and chilly, with a temperature of 57F 14C which, combined with the winds, made the porch a bit too cold for the intrepid duo of housecats, who spent the day by the radiator, wishing the heat would come on a bit more often. A treat of mackerel kept them from becoming too testy. As for me, I'm going to spend the rest of the evening dozing in front of the TV, which will be showing a junky old sci-fi or horror thriller, which I will dredge up from my vast collection and which has long since lost its thrill. If I'm lucky I'll doze off fast; if I'm unlucky I'll get to watch the whole thing. Regardless, I'll return in three days with another thrilling chapter of the ongoing FOTD. Until that wondrous time arrives, take care, and ponder the hidden meaning of fractals. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Frenetic { ; time=0:05:57.34--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=-0.30415843043600430/+0.176317849078791\ 20/72998.29/1/-67.4999999992991775/-1.078220374095\ 55094e-009 params=-1/-1/-1/1/0/0/-2/0 float=y maxiter=1200 inside=0 outside=tdis periodicity=10 colors=000NchLciLckLclKenKepIerIetHfuHfwHfxFfzFhzE\ hzEhzEhzHezKczNbzQZzTYzWWzZTxbRweQwhNukLtnKtrHruFp\ wEpkKhbQbTWWIbO9hI1nC0z30x50u70t80p80n90kB2iC3fC5e\ E8bF9`HBYHCWIFTKHRLIOLLNNNKOOIQRFQTERVBTW9TVBRVCRV\ EQVFQVHQTIOTIOTKOTLNTNNRONRQLRQLRRKRTKQVKQWIQYIQYI\ QZHO`HObHOcFOeFLl9NhCOeFQbIQYLRVOTRRTOVVKYWH`WEcYB\ fZ7iZ3l`1pb0tb0wc0ze0zh0ze0zc0zb0zZ0zY0zW0zT0zR0zQ\ 2zO3zL5zK8zI9zFCzEEzCHzBIz8Lz7Nz5Qz2Rz1Tz0Wz0Yz0`z\ 0bz0ez0fz0iz0kz0lz0iw0hr1el7chBbcHZZLYVRWQYTLbRHhO\ ClN8tL3xI0zH0zB0zE0zF0zH0zI0zL0zN0zO0zQ0zT0zV0zW0z\ Y1z`2zb3zc3ze5zh7zi7zk8zl9zpBzrBztCzuEzzCzwEztEzpE\ zlEziEzhFzeFzbFzZFzWFzTFzRHzOHzLHzIHzFHzEIzBIz8Iz5\ Iz2Iz0Iz0Kz0Kz0Kz0Kz0Kz0Kz0Nz0Oz0Qz0Rz0Vw0Wt1Yp2Zn\ 3`e9YWEVOIRFNO8RL0WI0l90fC0`F0VI0OL0KO0ER28V32Y30`\ 50Z50Z70Y70Y71Y81W82W82V93V95VB5TB7TB7RC8RC9RC9QEB\ QEBOECOFEOFENHFNHFLHHLIIL } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] new person on the list
by RENRAD1＠aol.com 29 Apr '02

29 Apr '02

In a message dated 4/28/02 7:16:29 AM Pacific Daylight Time, emjeebee(a)tomaatnet.nl writes: << I am new on the list >> Hi! Welcome to the List, Mary, hope you're having fun with Fractint:)

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new person on the list
by M J Benkers 28 Apr '02

28 Apr '02

Hello, I am new on the list. My name is Mary and I am from the Netherlands. I hope you do like my picture. It is somewhere on the Mandelbrot set. It takes 6 min on my computer (P200) to make it. Mary Benkers mandelischia_coli { ; some strange bacteria? reset=1910 type=mandel passes=1 corners=-1.8605739577489129/-1.860573957723912/-9. 3407929358274632e-007/\ -9.340605428307932e-007 params=0/0 float=y maxiter=1500 inside=0 distest=1/71/1280/1024 colors=000uux<2>xxyzzzyyz<45>DGdBEcBEc<29>BBLAAKCD K<14>kuC<15>AAK<15>z00\ <15>zzz<12>e5Oc0Kd1K<12>xIBzKAzMB<14>zzU<15>9C`ADa BEc<42>ttw }

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FOTD 27-04-02 (Mandel Potboiler [5])
by Jim Muth 27 Apr '02

27 Apr '02

FOTD -- April 27, 2002 (Rating 5) Fractal visionaries and enthusiasts: Today's image was created with the MandelbrotMix2 formula, which is a more versatile version of the workhorse MandelbrotMix4 formula. The new formula has a new variable p4 parameter, which offers control of the starting point of Z. When p4 is set to 0,0, the new formula works exactly like the M-Mix4 formula, and has the same speed. I added the new parameter because many of the expressions I have been calculating with the M-Mix4 formula have more than one critical point, and I wanted the ability to explore these other critical starting points. So far, I have found little of interest in the other critical planes of the fractals I have explored, but the exploration has just begun, and some surprises are sure to appear. Since the p4 parameter of today's image is 0,0, the image could just as easily have been drawn by the M-Mix4 formula, which may be headed for a long-overdue retirement. I named the image "Mandel Potboiler" because, like a cheap romance novel, it is a rather pretentious image with a lot of surface sparkle but little depth. The bubble-like features also helped inspire the name. The surface sparkle gives the image a rating of an average 5; the lack of depth precludes a higher rating. The render time is under 7 minutes -- a bit slow for such an average image. But relief for impatience may be found on the web at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> where the pre-rendered GIF image will soon be posted. The fractal weather Friday here at Fractal Central was near perfect, resulting in near perfect fractal cats. With clear skies, warm sun, and a temperature of 66F 19C, the cats spent all afternoon on the porch. Tippy even started to stalk a robin that ventured dangerously close, but the bird saw Tippy coming and flew away well before Tippy was within pouncing range. Thomas watched the whole affair with interest. As for me, I've got work to do, both for money and for fun. And there's also that grass which was trimmed only six days ago but already is waving in the breeze again. And the FOTD CD also has a way to go yet. So I guess it's time to say farewell until next time, which will be here in two wags of Thomas's tail. Until the tail wags, take care, and enjoy the illusion. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Mandel-Potboiler { ; time=0:06:40.62--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+7.67992477588323/-1.18115358183837/156\ 42.22/1/-87.5/-2.9822114222533003e-010 params=5/-1\ .321/0.5/-13.21/-1.454/525/0/0 float=y maxiter=1200 inside=0 logmap=120 periodicity=10 colors=0005zU5z95yH5xN5wU5t_5rf5pl5lh5jf5fc5c_5_Y5\ YV5US5RO5NM5LJ5IHzzJxxIwtIurItmIsjIrgIocHm_HlYHkUH\ jQHhNHjLJkILlGNmDOoARpNSr5VxVWtG_udcucfwmjwzlxujyu\ gyrfzoczkbzh_zdYzbWzZUzWSzSQzQOzONuONpNMkNMfMLaMLW\ LJSLJNJIIJIDIH8IH2HG0HG0HG0GH2EI6DJCCJGCLJAMO9MS8N\ W6O_6Ob5Sc4Wd4_f2cg1gh1kj0ok0sf2lb4gY5bU8YO9SLANHD\ ICED8G82I20J00L00M05M6ANDGNJJNQHWMEdJDmGAwD9zADzEH\ yHLwJNtMRpQVmSZkVahYddahbcl_foYhsUlwRozOrzMtwJtrHt\ lEtfCta9tW6tdCsmHswMrzQrrRrcSrQUrDUr6_f1dW4fS5gQ6h\ N9hLAjICkGElDGlAHm8Jo5Lp2Mp0Or0Qs0Rs0Yj1baAhSJmJSt\ Aay1hp9agHVZONQVHHb98j20p09h2Hb8OVEWOJdIOlAVt4_z0d\ w0gs2ho4jk6lf8mbAoZCrVEsQGtMIwIJxEMvANr9Jm9Hm9Em9C\ m99m8cz8cz8cz8cz8czCczE1mH5mJ8mNCzQEzSHzVLzZNzaRzc\ UzfWzhUzkSzlRzoQzrOzsNzuLzwJzyIzzHzzGzzEzzDzxGzoIz\ gJzZMzQOzIQzIOzGMzLlzJjzHhzGfzEdzCbzAaz9Zz6Yz5Vz4U\ z5Uz5Uz6Uz6Uz1Uz2Uz2Uz4Uz } 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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test
by Mark Christenson 24 Apr '02

24 Apr '02

This is only a test. Really.

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FOTD 24-04-02 (Scherzo [8])
by JimMuth＠aol.com 24 Apr '02

24 Apr '02

FOTD -- April 24, 2002 (Rating 8) Fractal visionaries and enthusiasts: Today's fractal is a picture of a midget in the Z^sqrt(3)+C fractal, a fractal that is infinite both in surface extent and in its depth. The particular midget in today's image is located in a cut-off fragment of a spiral elephant-trunk located in the East Valley area of the parent fractal, which is shaped surprisingly like the classic M-set. This midget is one of the more interesting ones I have found in the range between the linear non-fractal Z+C and the ultimate fractal Z^2+C. The MandelbrotBC1 formula is a great help in getting the most out of fractals in this range. If the image on one level of the logarithmic spiral shows little of interest, I merely go up to the next level by adjusting the real(p2) parameter. I named the image "Scherzo", a word that describes a lively and humorous musical composition. It was the first word that came to mind, and has little to do with the actual appearance of the fractal. Because it is perhaps the most satisfactory midget I have yet found in these under Z^2 fractals, I rated it a lofty 8, a rating that might be a bit liberal. An extra feature of the image is that it renders from the parameter file in under 5 minutes. But 5 minutes can seem an awfully long time when one is waiting for a fractal to finish and other things need to be done. Relief for impatience is at hand in the form of the completed GIF image, which is available on the W.W.Web at Paul's site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Tuesday here at Fractal Central was brisk and breezy, with a temperature of 55F 13C. But a strong sun peeking between the clouds gave enough warmth on the porch to keep the fractal cats happy for over an hour. My happiness did not arrive until I had most of the day's work behind me. And then I was happy. I'll be even happier when today's work is behind me. But the greatest happiness of all will come when the FOTD CD is finished and if it proves to be a success. I'm currently involved in re-writing many of the short stories I have written over the past 20 years. When reading my own writing some 10 to 20 years after I wrote it, I sometimes wonder how I could have written something so trite, and then there are the all-too-few times when I wonder how I could have written something so good. Regardless, the next ongoing FOTD will appear on April 27th. Until then, take care, and hold your breath. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Scherzo { ; time=0:04:43.20--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=recip passes=1 center-mag=-0.21378685445671390/-0.076303594971113\ 36/337296.3/1/-162.5/-1.8837750803690767e-010 params=1.73205/0/30.69/0 float=y maxiter=1800 inside=0 logmap=130 symmetry=none periodicity=10 colors=000L00P30S60V70_A0aD0dF0gG3jGCmILpISrI`uJix\ JpzLyzLzzLzxazpszizzdzz`zzXzzUzzOymJxcFuZAsW6rJ1oM\ 0mP0lS0jT1c`DYfPQm`LslDzx7zz1zy1yo1ld1`X1OM1CC1031\ 0970FC9LILQMVXSfaUpfUzcUpZUgUUaPUWKTQFSKASE0QQ0QQ0\ QQ0PQ0PP0PP0OP0OP0OO0MO0MO0MO0LM0LM0LM0LM9WgCeuYTi\ TKmO7p03z9FzOPzc_zrizofzldzjazg`zfYzcXz`Tz_SzXPzVO\ z_SxaXud`ridolijomgsrdvvayz_ssVomSjgPfaMaXJYQGSJDO\ DAJ77F14A01600400400400300300300100100100000000000\ 00000000000000000000000000000000000000000000000000\ 0000000000000000000000000000000000000TzDSyCSxCSxCQ\ vCQvAQuAPsAPsAPrAOr9Op9Op9Mo9Mm9Mm7Ll7Ll9LjAJjCJiD\ JgFIgGIfIIfJGdLGdMGcOFaPFaQF`SD`TD_VDYXCYYCX_CX`AV\ aCVcETdHSfJSgMQiOQjRPlTPmVOoWMpYMrZLs_Lu`JvaJxbIyc\ GzdGzeFzfFzgDzhDziCzjAzkAzl9zn9zp7zq6zr6zt4zz4zz3z\ z3zz1zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0\ zz0zz0zz0zz0zz0zz0zz0zz0z } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END 20.0 PAR-FORMULA FILE==================================

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FOTD 21-04-02 (On the Negative Stem [7])
by Jim Muth 21 Apr '02

21 Apr '02

FOTD -- April 21, 2002 (Rating 7) Fractal visionaries and enthusiasts: The image-rerendering stage of the FOTD CD preparation is complete, as is the organization of the FOTD discussions. What I now need to make the disk a big seller (25 copies) is something extra. I already have hundreds of fractals that I produced before I started the FOTD in April 1997. I also have scores of short and not-so-short stories on science-fiction, philosophical and mystical themes that I have been writing at intervals over the past 20 years. But I still need something extra to make the disk move out like water at a marathon race. Cat pictures might be just the thing . . . Today's image is from my archives. I found it over a year ago while I was working on fractal images that resemble lizard skin. The name "On the Negative Stem" describes the location of the midget in the image. And doesn't the term 'negative stem' sound better than 'negative tail'? After a moment's consideration, I rated the image a 7. The unusually powerful textures garnered that above-average rating. The 7-minute render time is a bit slow, so a download may be the better choice. The download can be found at Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Saturday here at Fractal Central featured lots of clouds and warm temperatures around 82F 28C. The cats must consider such conditions ideal because they were outdoors from 10am until sunset, which is just before 8pm at this time of year. They behaved all the time like angels, one of the few days this has ever happened. As for me, it's just past 11am and I must get moving. Until next time, take care, and don't get abstracted by the abstract features of fractals. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ OnTheNegativeStem { ; time=0:07:23.58--SF5 on a P200 reset=2001 type=formula formulafile=allinone.frm formulaname=mandelbrotmix4 function=recip passes=1 center-mag=-0.78591456586991960/+1.210154351001015\ 00/2.009572e+011/1/27.5021443003626942/-0.00178625\ 504485115105 params=-0.6/-0.85/0.06/-8.5/-2.16/525 float=y maxiter=1500 inside=0 logmap=138 sound=off colors=0000000000000000000000000000000000000000000\ 00000000000640B93GD8NIFSNLXQQaVXh_cmbhrgnyquzuzzzz\ zzzzzzszzizzazzSzyIzw8zs0zr4zm8zhBucFnZIgULbPPXKSQ\ FVLAZE4a80d30h00k00n00k00h80fJ0cV0af0ai0al0ap0as0a\ w0ax0az3az4az6azAazBazDczBczAdxAds8dn6fg6fb4fY3hS3\ hN1hI1kL4nO6pQAsUBwXDyYGzaIzbLzfNziPzkSznUzpVzXSzE\ Qw0Nr0Lk0Gd0D`08U04N00I30B804B00E03QD6acAlz`zZ`zP`\ zF`z4`z0`w0ar0al0ag0ad0c_0cV0cS0cN0dI0dE0d90d40f10\ f00f00f00i00k60nG0pO0sX0uf1yn1zx1zz1zz1ux6mgAcSDVB\ G`4Kc0Nf0PrzVwzUzzSzzSzzQzzPzzPzzNzzLzzLzpZhYkPGwK\ JpGLkDOdAQ`6UU3VP0YI0_F0bV0dk0YzDOza0zc1zd3za4z`4z\ Z8zV9zUBzSDzQEzSGzSIzUJyULrVNiVOcXQXXSQZUKZVB`X4`Y\ 0a_0aa0Sb0Kd0Bf03g00i00k00l00n00p10r30s40u60w80xA1\ zB3zD4zF6zG8zI4zL1zN0zP0zQ0zU0zV0zX0zZ0z`Kz6VzAfzD\ zzdzzdzzfzzfzzfzzfwzZrzSnzKizDdz4az0Qz8GzG6zPUzdpz\ hnzVmz0kz3iz8hzDfzIdzLczQ } 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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Fractal Universe Calendar 2004
by gumbycat 18 Apr '02

18 Apr '02

This is a final call for images! The April 30 deadline is almost here! Please submit your fractal artwork for consideration for inclusion in the Fractal Universe Â® Calendar 2004 now. All the information you will need is detailed on the following website: http://www.fractalforum.com/fc2004 Please make your submissions and any additional enquires you may have via the contact form on the above website. Thanks and good luck! Linda Allison and Tina Oloyede xxxxxxxxxxxxxxxxxxxxxxxxxxx Fractal Forum http://www.fractalforum.com xxxxxxxxxxxxxxxxxxxxxxxxxxx

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FOTD 18-04-02 (Ensign [7])
by Jim Muth 18 Apr '02

18 Apr '02

FOTD -- April 18, 2002 (Rating 7) Fractal visionaries and enthusiasts: I named today's image "Ensign". I had no real reason for giving it such a name -- with as much as I have to do, I simply could think of nothing better. I rated it at a 7, which I believe is the highest rating to have been given a FOTD since I cut the FOTD schedule to one every 3 days. (When the CD is ready, the FOTD will return to its normal every-day schedule.) The parent fractal was created by the simple formula: -5(Z^(-1.1))-8(Z^(-11))+(1/C), a formula that creates a grossly oversized double-negative fractal. As is the case with many of these oversized double-negative fractals, most of the interest lies relatively near the origin, where the fractal takes on a critical appearance. Most of today's parent fractal appears to be a non-critical area where midgets are unlikely to be found, but there is the usual small area of interest near the origin. The point I chose to check for midgets lies at the end of a filament extending from a mandel-shaped bud. Of course, in fractals the filaments have no end. No matter how close the zoom-in point lies to the 'end' of a filament, by the time a midget is reached, the image has been magnified so much that a near infinity of even smaller midgets can be seen lying farther out on the filament. The trick lies in finding a midget that is close to but not beyond the limit of resolution. As a matter of passing interest, starting with a bloated parent fractal thousands of times the size of the default screen does not give a greater range of sizes to explore. The large size merely shifts the decimal point to the right without increasing the range of precision. Today's render time of just under five minutes is worth the satisfaction of doing it for oneself. Those who are already satisfied with themselves can find the rendered image posted to the two FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather here at Fractal Central Wednesday was ridiculously hot. The blazing sun and incredible afternoon city temperature of 102F 39C made life on the porch far too uncomfortable for the cats, who passed the heat of the day lying under the air conditioner, trying to catch as much cool air as possible. While the cats were trying to keep cool, I spent the day trying to get as much work done as possible so that I can advance the FOTD CD, which is progressing but still has a way to go. (Those who claim that I will never finish the CD will be given ample chance to eat their words when the disk is ready.) As for me, it's hot again today, the cats are already testy, and I've got a pile of work to get out of the way -- or at least to start. So until next time, which will be on April 21, take care, and be where the action is, but don't become a casualty of the action. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Ensign { ; time=0:04:42.81--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-2.53422952923341000/-2.428182368486123\ 00/5.617065e+007/1/62.5/1.20480510572285038e-006 params=-5/-1.1/-8/-11/0/0 float=y maxiter=900 inside=0 logmap=88 periodicity=15 colors=00070E80EA0EB0ED0EE0EG0EH0EJ0EK0EM0EN0EP0EQ\ 0ES0EV1EY4E_7JbAMeDQfGViJYlMbnPeoTfoXfq`hqchqhirki\ rokrrkvvrzzrzzzzzzzzzzzzlzrezuXzxPtzGoz8kz1fz0ez0e\ z0Tz0Jq18e10THzzNznSz`XzPbzBfz0kz0cz2XlJQY_oqbzzez\ zczxbzr`zl`wf_t`YoVXlPXiJVeDTb7S_1SS0`M0hG0o80x20z\ 00zzz0zz0zz0zz0xz0tz0qz0nz0kz0hz0YuTPrzNtzNuuNwrMx\ nMzkMzfKzbKz_KzVJzSJzNJzJHzGHzBHz8XAzVDqTGcSJQ7T`0\ ck0Tf8JcJ8`P5iT4q_2xc1zh0zT8rEGY0PD0X00_00b02e08h0\ Ek0Jn0Pq0Vt0_w0ez0iz0`z5TzBMzHEzN7zT0z_0ze7nTKbJYS\ 8kG0x50oB2fHGYNTQSfPVhNXhMYhK_iJ`iHciGeiEfkDhkBikB\ kkGihJifNieQicTibYi``i_ciYhiXkiVniToeQq`PrXMrSKtPJ\ uKGuGEwBDx7Az58z77z84zA2zB1zD2zE2zH4zK4zN5zQ5zT7zX\ 7z_8zb8zeAzhAzkAwnBtqBqtBnwBkzDhzDezDczDYzMXz`XzBP\ zHHzNAzS2zY0zc0zhVznQzhKzPQzKVzH`zDez8kz4oz1uz0zz0\ zz0zz0wz0iz1Yz8KzH7zP0zX0zS0zN0zK0zG0zD0z80z40z10z\ 00z00z00z02z0Bz0Kz2Tz8bzE } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 15-04-02 (Discus [6])
by JimMuth＠aol.com 15 Apr '02

15 Apr '02

FOTD -- April 15, 2002 (Rating 6) Fractal visionaries and enthusiasts: If all goes well, before the day is finished, I will have finished re-rendering the last of the FOTD fractal images in SF6 format. This will complete the largest single project in the preparation of the FOTD CD. Several more large tasks remain to be accomplished, but now that the major task is finished, it will be downhill the rest of the way. Today's image, which was created by the workhorse MandelbrotMix4 formula, is an exploration of the fractal that results when 0.1 part of Z^(-9) is added to 1 part of Z^(-0.9), and the sum added to (1/C). I named the image "Discus" when that word came to mind as I was studying it. I rated the image a 6 when I left the room and returned a few minutes later to find it waiting on the screen. The 6-minute render time is nominal, but even this can be bypassed by visiting one of the FOTD web sites and downloading the completed GIF image from there. The web site URL's are: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Sunday was summer-like here at Fractal Central, with lots of sun and a temperature of 77F 25C. A brief light shower around sunset did nothing to spoil the cats' day. Of course, by sunset the dynamic duo had already enjoyed a full day in the yard. At one point, Tippy the tabby started feeling intrepid and ventured two doors up the hill. The sound of a can of tuna being opened brought him hurrying back where he belongs. Thomas, the oversized yellow-orange one, kept a watchful eye on Tippy as Tippy ventured away, ready to leap to the defense if Tippy had gotten into trouble. Luckily for Thomas, Tippy needed no help. And if I don't get my day's work done, some unpleasant things are sure to happen. Until next FOTD on April 18, take care, and whatever happened to catastrophe theory? Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Discus { ; time=0:06:01.03--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+228.9267420799002/+28.2204563662475/1.\ 774846e+009/1/22.533825173915968/-0.05346987079465\ 01886 params=0.1/-9/1/-0.9/0/0 float=y maxiter=1000 inside=0 periodicity=10 mathtolerance=/1 colors=000euHbu1_z4Yz6Uz9SzCPzEMzEUz4_z0gz0mz0zzHz\ zUzxezppzjzzezzYzzSzzMzz0pz01z00z00r00U014EK0U_0jp\ HzezzYbr_1S_01_0MK0g40z00z00z00z_0zb1zb9reHbePKgU4\ gYH__USbgKbuEMzU9zg0zx0zz9zxbzmzzbzx0zrEjp1Mj00g00\ b00_0zK006040HM0be0zu0zr0zr0zz00z00z00z00z01z04z09\ z0Cz0Hz0Kz0Pz0Sz0Yz0_z0bz0gz0jz0pz0rz0xz0zz0zz0rz0\ gr0Yb0MM0C60100000400C40K60S90bE0jH6rKEzPMzSUzUbz_\ jzbrzezz_uzYpzSjzPezK_zHUzESzMPzUez_KzgHzmEjuC_zCP\ z4bz0pz0zz0zz0zz0z0zz0Pz00z00z00z90zH0zS0z_0zj0zr0\ zz0zz0zz0zz0zz0zz1zz1zp4z_4zK6r46j09_09S0EP0KP0PP0\ UM0YM0bM0gM0mK0rK0uK0zK0zH0zH0zH0zH1zM4zP4zS6zY9z_\ 9zbCzeEzjEzmHzpKzuKzxMzzMzzUzx_zrezmmzgrzbxzYzzSzz\ MzzHzzCzz6zzEzzKzzSzzYrzemzjeur_pxSjzMezH_zPUzUPz_\ KzeEzm9zr4zx0xz0uz0rz0pz0mz0jz0gz0ez0bz0_z0bz0ez0g\ z0jz0mz0px0rr0uj0xb1zU4zP9zHEz9Hz1Mz0Pz1Uz4Yz9bzCe\ uEjrKmmMrgumzpuzmuzjumguY } 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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Fractal Laboratory Screen Saver updated
by Thore Berntsen 15 Apr '02

15 Apr '02

The new version can be found at: http://home.online.no/~thbernt/fraclab.htm Thore Berntsen

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FOTD 04-12-02 (Cosmic Nursery [3])
by JimMuth＠aol.com 12 Apr '02

12 Apr '02

FOTD -- April 12, 2002 (Rating 3) Fractal visionaries and enthusiasts: Today's fractal shows what happens when a near-linear expression such as Z^1.009+C is iterated. As can be seen from the image, not too much actually does happen, other than a scattering of fragments that barely present a theme. After standing back from the screen, trying to recall what it is that the image reminds me of, I remembered the famous picture of the dust pillars of a stellar nursery which was taken by the space telescope. I quickly decided on the name "Cosmic Nursery". The image could equally represent the last rays of the setting sun striking the snow-capped peaks of a mountain range to the east. In this case, I would have named the image something like "Mysterious Mountains". But names cannot make an image, and today's image has little other than its name going for it. As a result, I could rate the result of today's brief effort no higher than a 3. The wannabe great image can be viewed by running the attached parameter file, which will take 1/2 hour, or by visiting one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> and downloading the finished image from there. The fractal weather Thursday was quite pleasant, with warm sun, gentle breezes, and a temperature of 64F 18C. These are cat- pleasing conditions. The cats showed their pleasure by sleeping most of the afternoon. Like all cats, the older they get, the less they romp and the more they sleep. As for me, I'm entering a critical phase of the FOTD CD preparation. As Murphy's law would dictate, the more critical the phase of preparation, the greater the amount of other things to be done. And I'm still keeping the ongoing FOTD's coming on schedule, appearing every day of the month evenly divisible by 3. The next FOTD will appear April 15. Until then, take care, and don't be distracted. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Cosmic_Nursery { ; time=0:35:35.62--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-8.63091810918206500/-4.757995359907572\ 00/239.0022/1/177.5/7.32838095762744501e-012 params=1.009/0/359.5/3100 float=y maxiter=12000 inside=0 logmap=520 colors=000rhZrh_rhZrgZrgZrgZqf\ ZpfZofZneZmeZleZkdZjdZidZhcZhcZgcZgcZfbZfbZfbZfbZe\ aZeaZeaZe`Zd`Zd`Zd_Zd_Zc_Zc_Zb_Zb_Za_ZaZZ`ZZ`ZZ_ZZ\ _ZZZZZZZZYYZYYZXYZXYZWYZWYZVYZVXZVXZVXZVXZVXZUXZUX\ ZUWZUWZUWZUWZUWZUWZUWZTVZTVZTVZTVZTVZTVZTVZTUZTUZS\ UZSUZSUZSUZSUZSTZSTZSTZSTZRTZRTZRTZRSZRSZRSZRSZRSZ\ RSZQSZQRZQRZQRZQRZQRYQRYQRYQQYPQYPQYPQYPQYPQYPQYPP\ YPPYPPYOPYOPYOPYOPYOOYOOYOOYOOYOOYNOYNOYNNYNNYNNYN\ NYNNYNNYNNYMMYMMYMMYMMYMMYMMYMMYMLYMLYLLYLLYLLYLLY\ LLYLKYLKYLKYLKYKKYKKYKKYKJYKJYKJYKJYKJYKJYJJYJIYJI\ YJIYJIYJIYJIYJIYJHYIHYIHYIHYIHYIHYIHYIGYIGYIGYHGYH\ GYHGYHGYHFYHFYHFYHFYHFYGFYGFYGEYGEYGEYGEYGEYGEYGEY\ HFXHFXHFXIFXIFXIFXIFXJFXJFXJFWJFWKFWKFWKFWLGWLGWLG\ WLGWMGWMGVMGVMGVNGVNGVNGVNGVOGVOGVOHWPHXPHYPHZPH_Q\ H_QH_QH_QH_RH_RH_RH_SH_SH_SH_SH_TH_TH_TH_TH_TH_UG_\ UG_UG_UG_UG_VG_VG_VG_VF_VF_WF_WF_WF_WF_WF_WF_ } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END 20.0 PAR-FORMULA FILE==================================

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Re: Fractint digest, Vol 1 #106 - 2 msgs
by Gavin Ritz 12 Apr '02

12 Apr '02

Hi Anyone, got a simple programme (idiots version) to work out the fractal dimension? kindest gavin fractint-request(a)mailman.xmission.com wrote: > Send Fractint mailing list submissions to > fractint(a)mailman.xmission.com > > To subscribe or unsubscribe via the World Wide Web, visit > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint > or, via email, send a message with subject or body 'help' to > fractint-request(a)mailman.xmission.com > > You can reach the person managing the list at > fractint-admin(a)mailman.xmission.com > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of Fractint digest..." > > Today's Topics: > > 1. Re: Re: FOTD Anomaly (Programmer Dude) > 2. Semi-OT: Problem with Fractal Labs screensaver (David Jones) > > --__--__-- > > Message: 1 > Date: Wed, 10 Apr 2002 11:42:01 -0500 > From: Programmer Dude <cjsonnack(a)mmm.com> > To: fractint(a)mailman.xmission.com > Subject: Re: [Fractint] Re: FOTD Anomaly > Reply-To: fractint(a)mailman.xmission.com > > Multiple Bogeys: > > > I had been given to understand that Jim Muth posts separate versions > > to the two lists, sometimes with added philosophical musings in the > > Philofractal one, and that your Web site uses the latter version and > > Scott's the former. > > I believe that was true at one time, but is no longer the case. > > It would be easy enough to simply compare some pages at the two > sites, would it not? > > -- > |_ CJSonnack <Chris(a)Sonnack.com> _____________| How's my programming? | > |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | > |_____________________________________________|_______________________| > > --__--__-- > > Message: 2 > From: "David Jones" <gnome(a)hawaii.rr.com> > Organization: Alias Jones and Jones > To: fractint(a)mailman.xmission.com > Date: Wed, 10 Apr 2002 18:30:39 -1000 > Subject: [Fractint] Semi-OT: Problem with Fractal Labs screensaver > Reply-To: fractint(a)mailman.xmission.com > > Sorry, but can't track down the web site. But the > Fractal Labs screen saver that was (IIRC) recently > mentioned on this list, decided to generate an access > violation at address 0005d5f83 by trying to read > address FFFFFFFF. Using W95A, ELSA GLoria > Synergy card with most recent drivers for it. > > David > gnome(a)hawaii.rr.com > > --__--__-- > > _______________________________________________ > Fractint mailing list > Fractint(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint > > End of Fractint Digest

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Semi-OT: Problem with Fractal Labs screensaver
by David Jones 11 Apr '02

11 Apr '02

Sorry, but can't track down the web site. But the Fractal Labs screen saver that was (IIRC) recently mentioned on this list, decided to generate an access violation at address 0005d5f83 by trying to read address FFFFFFFF. Using W95A, ELSA GLoria Synergy card with most recent drivers for it. David gnome(a)hawaii.rr.com

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Re: [Fractint] Re: FOTD Anomaly
by Multiple Bogeys 10 Apr '02

10 Apr '02

> Since most of Jim's FOTD postings contain the following lines in the > Header information: > To: fractint(a)mailman.xmission.com > CC: philofractal(a)lists.fractalus.com > I do not understand why you would bother going to visit my hosting of > the FOTD. It is obvious to an intelligent person that there is no > special version of the FOTD to the PhiloFractal List. I had been given to understand that Jim Muth posts separate versions to the two lists, sometimes with added philosophical musings in the Philofractal one, and that your Web site uses the latter version and Scott's the former. If this is not the case, then there has been a misunderstanding. I see no reason to insult my intelligence here. Also, I don't recall seeing a Cc: header on any FOTDs. Perhaps Hotmail's crummy system doesn't show them to me, or perhaps this is something new. >> Scott's site doesn't include it, and I'm not >> subscribed to the other list. > Why not just subscribe to the other List I already am subscribed to one moderate-traffic list and one high-traffic list. I'd much rather not add another one just to read a particular subset of the postings, especially when that subset is available elsewhere. Also, since when does this list force a poster to edit the reply-to to send replies back to the list? (Yeah I know -- reply-to munging's been the subject of holy wars. I'm just curious why this list would change its policy in that area.)Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com

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