March 2004 - Fractint - mailman.xmission.com

Here are a few pearls stitched onto some lace.
by Hal Lane 20 Mar '04

20 Mar '04

Here are a few pearls stitched onto some lace. This region is a zoom out near Jim Muth's 19-3-04 FoTD - Semaphore; One color map location was set to black to get a dark background. - Hal Lane ######################### # hallane(a)earthlink.net # ######################### START 20.0 PAR-FORMULA FILE================================ Lace_and_pearls { ; Hal Lane 3-19-04 ; CPU=P400 1024x768 t=0:01:45 ; Near Jim Muth's Semaphore ; 19-3-04 FoTD reset=2003 type=formula formulafile=pastengo.par formulaname=slicejulibrot4 passes=1 center-mag=0.00245812/-0.147774/7.843562 params=89.63/90.33/89.72/90.31999999999999/-1.7435/4\ e-005/0.00019/0.07388/2.003/0 float=y maxiter=6000 bailout=9 inside=fmod proximity=0.02 logmap=50 periodicity=10 sound=off colors=000000NKL<2>QKJRKMSKO<3>WNYXN_YObZPd<3>_Sm<3>\ NcsJfuGivDlxAny<7>TuzVvzXvz<2>cyzeyzgxy<3>lvwmuvnuv<\ 3>sst<4>xG7<3>PFZGFdII_KczLPPWTJ<3>dKOfIPhGRjESlCT5M\ O<8>c`QfaQjcQ<3>yiQ<3>ocKmaJk`H<3>bVC<6>nIBoGBqEB<3>\ w7B<3>SXYKbbLd`<5>QoTRqRRsQ<3>UzL<3>OnMNkMLhM<3>GYMh\ rBdlE`gHmbK<3>mHWmCZm7a<5>mDfmEgmFg<3>mJj<2>mWI<3>mT\ WnSZpSb<3>uPovPruLhtIZuFQvCGw97x8Cy8H<3>z6ZzDVzKR<2>\ z`Gz`CzdjzZazTU<3>zSfzSizTe<3>zWUzXRzXNz`8zYK<3>z`8z\ UF<3>z_7zKYzLv<5>zTYzUTzVP<3>z_9zCOzLHzTBzAS<3>zKJzN\ HzPF<3>zZ7zvn<5>zcBzJj } frm:SliceJulibrot4 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } END 20.0 PAR-FORMULA FILE================================== --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.634 / Virus Database: 406 - Release Date: 3/18/04

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FOTD 19-03-04 (Semaphore [6])
by Jim Muth 19 Mar '04

19 Mar '04

FOTD -- March 19, 2004 (Rating 6) Fractal visionaries and enthusiasts: There is a very unusual rectangle in the Z^(2.003)+C Julibrot. It is located in the Julia set with a C-value of -1.7435 at Z-coordinates of 0.00019,0.07388 and a magnitude of around 75. I have several times mentioned this nearly-perfect rectangle in my FOTD discussions, and since the two most recent FOTD's took me to the general area, I decided to take a peek at the rectan- gle while I was there. The rectangle is quite critical. If imag(C) is changed even 0.0001 from zero, the near-perfection is lost. In today's image, the value is changed only 0.00004 and already strange things are happening. I aided the strange happenings by rotating the view less than one degree from the exact Julia orientation. As a result of my tweaking, the once near-perfect rectangle has been changed into what can be best described as a semaphore flag. (What ever happened to the days when they actually communicated with those things?) The lower right half of the rectangle is filled with reddish high-iteration outside stuff, while the upper left half is composed of trapped inside points given life by the 'fmod' inside fill. Several other inside fills would have worked nearly as well. The "SliceJulibrot4" formula that generates today's image is a generalization of the "SliceJulibrot2" formula to any power of Z. It is a new formula, which I have not previously posted. I named the image "Semaphore" and rated it at a 6. When the render time of 7 minutes is considered, the overall value equals an 82. Rendering may be avoided entirely by downloading the finished GIF image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Thursday was not too cold and not too cloudy. It was also not windy, and as a result, the fractal cats had almost two hours of quality time in the yard. When they came in, they settled down without demanding their usual treat of tuna. Rain fell during the night, but it has already moved off. If the clouds move out, the cats will have a fair chance at another good day. The work that I must finish is about average. It's 10:30am and time to get started, so until next FOTD, take care, and be lively. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Semaphore { ; time=0:07:16.94--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 passes=1 center-mag=0/0/77.51938 params=89.63/90.33/89.72/9\ 0.32/-1.7435/4e-005/0.00019/0.07388/2.003/0 float=y maxiter=6000 bailout=9 inside=fmod proximity=0.02 logmap=50 periodicity=10 colors=000MKMNKLOKKPKJQKJRKMSKOTKRULTVMVWNYXN_YObZ\ Pd_Qf_Ri_Sk_SmWVoTYpQ`rNcsJfuGivDlxAnyDozFpzHqzKrz\ MrzOszQtzTuzVvzXvz_wzaxzcyzeyzgxyhwxiwxkvwlvwmuvnu\ vptuqturstssttkjuc`vWRwOHxG7oFEfFLYFSPFZGFdII_KczL\ PPWTJYRK`PLbNNdKOfIPhGRjESlCT5MO9OPDQPHRPLTPOUPSWP\ WYP_ZQc`QfaQjcQneQrfQvhQyiQvgOtfNrdLocKmaJk`HhZGfY\ EdWDbVCdTBfRBgPBiNBkLBlJBnIBoGBqEBsCBtABv8Bw7BoEHg\ KN_RSSXYKbbLd`Mf_NhYOjXOlWPnUQoTRqRRsQSuPTwNUyMUzL\ SwMRtMPqMOnMNkMLhMKeMIbMH_MGYMhrBdlE`gHmbKmXNmSQmN\ TmHWmCZm7am8bm9cmAdmBdmCemDfmEgmFgmGhmHimIjmJjmO`m\ SRmWImVMmUPmUTmTWnSZpSbqRerQhtQluPovPruLhtIZuFQvCG\ w97x8Cy8Hz7Lz7Qz6Vz6ZzDVzKRzPNzVJz`Gz`CzdjzZazTUzS\ YzS`zSczSfzSizTezUbzV_zVXzWUzXRzXNz`8zYKzZHzZEz_Bz\ `8zUFzWDzXBzZ9z_7zKYzLvzNqzOmzPizQezSazTYzUTzVPzXL\ zYHzZDz_9zCOzLHzTBzASzDPzFNzILzKJzNHzPFzSDzUBzX9zZ\ 7zvnzrgzo`zlVziOzfIzcBzJj } frm:SliceJulibrot4 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } END 20.0 PAR-FORMULA FILE==================================

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roarbit.par ... puzzles?
by SherLok Merfy 19 Mar '04

19 Mar '04

I know better than to bother with subjects where my address is repeated. But someone sent me something that said "you" in the subject and referred to puzzles. I deleted it, and this is perhaps part of the reason why mailing lists typically repeat their _own_ name. It's rare for a subject to require that word. They are usually not sentences, though, so it was a mistake. Out_Of_Orbit { ; Animation. Border tracing _treats_ periodicity, ; too. How would you check if the white line is dithered? ; Default map is too sticky in FRACTINT. reset=2003 type=mandel passes=b periodicity=-11 showorbit=yes center-mag=-0.765332/6.66134e-016/0.7772216/1.4732/90/3.88578058618804\ 789e-016 params=0/0 float=y maxiter=255 fillcolor=1 sound=beep colors=000<4>00000000zzz0000<4>000z000zzz0zzz00zzz0zyy00yyy0yxx00xxx0x\ ww00www0www00www0wvv00vvv0vuu00uuu0utt00ttt0tss00sss0sss00sss0srr00rrr\ 0rqq00qqq0qpp00ppp0poo00ooo0ooo00ooo0onn00nnn0nmm00mmm0mll00lll0lll00k\ kk0kkk00kkk0kjj00jjj0jii00iii0ihh00hhh0hhh00hhg0ggg00ggg0gff00fff0fee0\ 0eee0edd00ddd0ddd00ddc0ccc00ccc0cbb00bbb0baa00aaa0aaa00```0```00``_0__\ _00___0_ZZ00ZZZ0ZYY00YYY0YYY00XXX0XXX00XXX0XWW00WWW0WVV00VVV0VUU00UUU0\ UUU00TTT0TTT00TTT0TSS00SSS0SRR00RRR0RQQ00QQQ0QQQ00QQP0PPP00PPP0POO00OO\ O0ONN00NNN0NNN00MMM0MMM00MML0LLL00LLL0LKK00KKK0KJJ00JJJ0JJJ00III0III00\ IIH0HHH00HHH0HGG00GGG0GFF00FFF0FFF00EEE0EEE00EED0DDD00DDD0DCC00CCC0CCC\ 00BBB0BBB00BBA0AAA00AA909990099909880088808880077707770077606660066606\ 550055505440044404440033303330033202220022202110011101000 } Default { ; I wouldn't jeneralize the formula, because ; it illustrates significance of sign. ; Try other methods of rendering. ; Try different periodicity thresholds. reset=2003 type=formula formulafile=roarbit.par formulaname=club_lambda function=zero/ident passes=t center-mag=-0.274835/8.88178e-016/0.7025121/1.214/90/0 params=3/0 float=y maxiter=255 fillcolor=1 periodicity=-1 sound=beep showorbit=yes; colors=(a)orbit.map colors=000<4>00000000zzz0000<4>000z000zzz0zzz00zzz0zyy00yyy0yxx00xxx0x\ ww00www0www00www0wvv00vvv0vuu00uuu0utt00ttt0tss00sss0sss00sss0srr00rrr\ 0rqq00qqq0qpp00ppp0poo00ooo0ooo00ooo0onn00nnn0nmm00mmm0mll00lll0lll00k\ kk0kkk00kkk0kjj00jjj0jii00iii0ihh00hhh0hhh00hhg0ggg00ggg0gff00fff0fee0\ 0eee0edd00ddd0ddd00ddc0ccc00ccc0cbb00bbb0baa00aaa0aaa00```0```00``_0__\ _00___0_ZZ00ZZZ0ZYY00YYY0YYY00XXX0XXX00XXX0XWW00WWW0WVV00VVV0VUU00UUU0\ UUU00TTT0TTT00TTT0TSS00SSS0SRR00RRR0RQQ00QQQ0QQQ00QQP0PPP00PPP0POO00OO\ O0ONN00NNN0NNN00MMM0MMM00MML0LLL00LLL0LKK00KKK0KJJ00JJJ0JJJ00III0III00\ IIH0HHH00HHH0HGG00GGG0GFF00FFF0FFF00EEE0EEE00EED0DDD00DDD0DCC00CCC0CCC\ 00BBB0BBB00BBA0AAA00AA909990099909880088808880077707770077606660066606\ 550055505440044404440033303330033202220022202110011101000 } Club_Lambda { ;Try inversion. Simplified since last post of it. z=fn1(pixel), c=fn2(pixel): z = z*z -conj(z) +c |z| <= real(P1) }

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FOTD 18-03-04 (Rising Alleluias [7])
by Jim Muth 18 Mar '04

18 Mar '04

FOTD -- March 18, 2004 (Rating 7) Fractal visionaries and enthusiasts: After I found the twin midgets in yesterday's image, I did a bit more exploring in the same area and turned up the scene that appears in today's image. I named the picture "Rising Alleluias" because of the eight elements surrounding the central midget, which appear, at least to me, like overweight people raising their arms in praise. I cannot say what the people are praising. It could be the immense and unlimited worlds of fractals, or the equally great physical universe, or perhaps the religious figure of their choice. It could even be science, which developed the machines that first revealed the worlds of fractals, and which some consider to be almost a religion. More thoughts along this line are included in the version of the FOTD that appears on the philofractal list. I rated today's image, which renders in under 7 minutes, at a 7, which gives an overall value of 104. The rendering stage can be eliminated by letting Paul do the rendering and downloading the finished image from his FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Wednesday remained cloudy and chilly here at Fractal Central. The temperature of 39F 4C was a bit too chilly for the cats' ears, and they spent the day wishing. In the evening a treat of tuna eased their frustration. My frustration will ease when the work I have scheduled for today is finished, and that will happen about 4 hours after I start. Then I'll take a trip to one of the infinite worlds of fractals. In 24 hours I'll return with whatever I find there. Until then, take care, and prepare for the best. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Rising_Alleluias { ; time=0:06:43.98--SF5 on a P200 reset=2003 type=manzpower passes=1 center-mag=-1.7\ 43238677909744/+0.00011432724916339/1.458905e+008/\ 1/177.5/-2.35020439424138416e-005 params=0/0/2.003\ /0 float=y maxiter=2000 inside=0 logmap=194 colors=000MDLNEMOHNPGNQHORIPSJRTKRVLSXMSZNSbOUdPWg\ QWjRVmRSoRQsSOvSLxSJzSGwWKtZOrbQodUmgWjj_hmbeoecsh\ `vkZxnczshzwkzzmzznzzozzpyzqzzrzzszztzzuzzvzzwzzxz\ zrzzmzzVzzbtziozqmzxczzVzwPzoJzgCz_6rR0hK0ZH0UG6UF\ CUAZUFdPKcKPhGUnHZuJcyKEdSLU_SJh_7oY5iW2cU0YS0RQ0L\ P0FR0CS4BVAAWF8YL7_Q6`W5b`2dg1ek0gr0iw0jz0kz0mz0nx\ 5ns8ooEqjJqeMrbRsYWsS_tOdvKivFmwArw6voJwhVx`gyUszO\ zzRxwUssWnoZik`chcZdgU`iPYkJUnEQq8Ms4Jv0FcZULzgKzh\ KzhKxhKvhKsiKqiKniKkiKijKgjKdjKbjK_jLYhLVgLSdLRcLP\ bMM_MLZMJWMGVMFUg6Wz0Yz8`zHdzQgz_jzhmzqqzyszttvotq\ jtmgthbtcYvZSvVPvQKvLFvHBvJEwJGwJJwJLwJOwJQxKSzKZz\ KczKgzKizKkzKnxPmrSkmWjh_icch_hgVkeQodLscGtbCt`Es_\ ErZEqYEoWEnVEmUEkUEjUFiUFhUFgUFeUFdUFcUFdUFeUEgUEh\ UEiUEjUCkUCmVCnWCoYBqZBr_Bs`Btb7vc5wd2xe0ye0ze0ze0\ ze6zeBzeHzeOzeSzeGze5ze6ze6ze7ze7ze8ze8zeAzeAzeBze\ BzeCzeCzeEzeEzeEzeMzeRzeY } END PARAMETER FILE=========================================

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FOTD 17-03-04 (The Twinship of Twins [4])
by Jim Muth 17 Mar '04

17 Mar '04

FOTD -- March 17, 2004 (Rating 4) Fractal visionaries and enthusiasts: The day started with a bang here at Fractal Central, when I opened my e-mail box and discovered that I had just won 3 million-dollar lotteries that I have no memory of entering. Talk about good luck -- it doesn't get any better than this. Now I'll be able to give up working and devote all my time to finding more fractals. ;-) Now on to today's fractal. I recently was asked if such a thing as twin fractals exists. I'm not sure about twin fractals, but twin midgets certainly do exist. A pair of them is illustrated in today's image. The twin midgets are located in the Z^(2.003)+C Mandeloid. This Mandeloid is part of the Julibrot that holds the near-perfect rectangle that I occasionally distort and use as a FOTD image. The parent Mandeloid is almost indistinguishable from the classic Mandelbrot set, the major difference being found in the area of the main stem, which has split into fractal dust. Today's image is located in this dust. Though the midgets in the image are close together, their basins of attraction do not interfere with each other. A major discon- tinuity that lies between them isolates them. Sometimes, the basins of closely-spaced midgets do overlap, and sometimes the midgets themselves merge, but in these cases, it is always corresponding parts of both midgets that come together. Two main stems can merge, or two East Valleys, but never an East Valley and a main stem. The two large twin midgets in today's image lie in a field of smaller midgets, some of which are quite attractive, surrounded by networks of fractal railroad tracks. The Julia sets of this area can also be unusually attractive, but that's another story. I named today's picture "The Twinship of Twins". The name doesn't make too much sense, but it has a nice sound to it. The rating of 4 is just a bit below average. Combined with the render time of near 4-1/2 minutes, this gives an overall value of 90. The rendering may be avoided entirely by downloading the finished image from Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A steady windy rain that fell all day Tuesday here at Fractal Central, and a temperature that never rose above 34F 1C, kept the fractal cats solidly confined to their indoor shelves by the windows. Their moods were not as bad as might be expected however. Most likely, as they gazed out at the miserable weather, they were thankful that they were not one of the homeless cats who have no place to go on such miserable days. In the evening I gave them a small treat of tuna as a reward for their good behavior. Today is starting cloudy and cold, but it is dry. We shall see how the day goes. For me it's just another day with work to be done and fractals to find. The next fractal will appear here in 24 hours. Check then for something you have never seen before. Until 24 hours have passed, take care, and almost all FOTD fractals are things that have never been seen before. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Twinship_of_Twins { ; time=0:04:25.18--SF5 on a P200 reset=2003 type=manzpower passes=1 center-mag=-1.51984679271885400/+0.011001816585014\ 69/5927.148/1/-100.000000000060254/3.5317263002987\ 4313e-011 params=0/0/2.003/0 float=y maxiter=3200 bailout=9 inside=0 logmap=40 periodicity=10 colors=000K8qJ9nJ9kI9iI9fI9dH9aH9ZG9XG9UG9SF9PF9ME\ 9KE9HE9FD9CD99C97C94C92BB5BC7BDABECBGEBHHBIJBJMBKO\ BMQBNTAOVAPYAR_ASaATdAUfAViAXkAYmAZpA_r8axA`tB_pC_\ lDZhEZdFY`GYXHXUIXQJWMKWILVEMVANU6OU3TXAYZGa`NfbTk\ d_ofethlxjrwipvhnuhlugktgisfgsffredqebqdapd_ocYobX\ nbVmaTmaSl`Qk`Ok_Nj_LiZJiZIh`NhaRfWSeQTdKUcEVb8Wa3\ Wb5Rb6Nc7Ic9EdA9dB5fF4gI4iM4jP4lT4mW4nZ4pb4qe4si4t\ l4vp4ws4xv4NadQceSdeVffXgf_ifajgdlgfmgiohkphnrhpsi\ suitwluviuuguueutcvsavs_vrYvqWwqUwpSwoQwoOxnMxmKxm\ IxlGxlEujHriKphNmgPkfSheVfdXcc_`bbZadW`gU_jRZlPYoM\ XrKWtJXqIYnHYkGZhF_eE_bD`_CaXBaUAbR9cO8cMBbLEbLHcL\ JdLMeKPfKRgKUhKXiK_jJakJdlJgmJinJhoIhpIhqHhrHhsGht\ GhuFhvFiwEjxEkyDlzDmzCnzCozBpzBqzArzAsz9tz9uz8vz8w\ z7xz7yzAzzDzzGzzJzzLzzOzzRzzUzzWzzZzzazzdzzkzzfzzb\ zzZzz_zzVzzRzzNzzJzzFzzGzzHzzOzzNzzMzzMzzLzzKzzJzz\ JzzIzzHzzHzzOzzUzz_zzezzk } END PARAMETER FILE=========================================

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FOTD 16-03-04 (Paddles [6])
by Jim Muth 16 Mar '04

16 Mar '04

FOTD -- March 16, 2004 (Rating 6) Fractal visionaries and enthusiasts: In a recent FOTD I wrote that almost all midgets in fractals created by the MandelbrotMix* series of formulas (formulae for the over-educated) are variations of the quadratic Mandelbrot set. Note that word 'almost'. Today's image shows a midget that most definitely is not quadratic, but cubic. And to top off the strangeness, the midget does not appear to be fully defined, almost as though it were cut in a non-critical plane. The pattern around the midget is perfectly defined however. This appearance of an imperfect cubic midget is far from the strangest scene I have stumbled upon in my adventures in fractal land. I have actually found perfect cubic midgets side-by-side in the same frame with midgets of the 6th order. A FOTD that appeared several years ago illustrates the scene. At the moment, the particular image is lost, but I would like to find it for further investigation. For some reason, the real(p2) parameter of today's image, which determines the amount of Z^5 to be subtracted from Z^3, is extremely critical, as it is in all fractals that I have so far found which contain higher-order midgets. I named the image "Paddles". The three prominent arms remind me of the paddle blades of an old-fashioned windmill. (Old-fash- ioned always seems to be more picturesque.) I rated the image at a 6, which is above average, but not outstanding. When the image's short render time is considered, its overall value comes in at a hefty 357. In a recent letter to the fractint list it was asked what I mean by a plane oriented halfway between the Mandelbrot and Julia orientations in the Z^2+C Julibrot. I am really not sure. The more I think about it, the less certain I become as to what I mean. I'll have more to say about this in the next FOTD that uses the Julibrot formula. I also recently was asked whether there is such a thing as twin fractals. I am not sure what the writer means by twin fractals, but there certainly are twin midgets. A pair of them will appear as tomorrow's FOTD. Though today's image is a fast one, the minor annoyance of running the included parameter file can be eliminated by downloading the completed image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The fractal cats, Thomas the lazy oversized orange and Tippy the thin wiry tabby, had one of their best days ever on Monday. It was one of those days when everything that could go right in the world of cats did go right. The weather was sunny, with a temp- erature of 63F 17C, but the big excitement came when a squirrel came too near Tippy, who appeared to be asleep. Tippy suddenly lunged and for a moment got his jaws on the squirrel's tail. Luckily for both the squirrel and Tippy, the squirrel pulled free and scampered up a holly tree, where he scolded loudly before going back to his hole. Thomas actually became alert during the scuffle. When they came indoors, I treated them to chicken, which they enjoy even more than tuna. But today is starting cold and rainy, and the two fractal cats are already turning sulky. We'll see how it goes. For me, it looks to be an average day. And if all goes well, the fractal I find will be above average. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Paddles { ; time=0:01:40.79--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.4615028914331138/0/9778.83/1/-90/3.8\ 857805861880479e-016 params=1/3/-0.21/5/0/0 float=y maxiter=2000 inside=0 logmap=25 periodicity=10 colors=000h0hh0hh0hh5hhAhhFhhKhhPggUffZeecddhc`k4V\ f9PbDJYIESMTLLZCKYHPYLTYPXXU`XYdXahWglWlpWqtYqrZrq\ _qoaznbulcpkdpj16l28m3An4Co5Ep5Gp6Iq7Kr8Ms9Ot9QtAS\ uBUvCWwCYwGTrKOnOJjREfV9bZ4Za0VZ5SWAPTFNQKKNPIKUFH\ YDFRNEKXCDeB6oA0xH6vNCtUIr_OpfUnl_lsejyjhvgiseiqci\ n`ilZiiXigViiWjjWjkWjlXkmXkoXkpYlqYlrYlsZmuZmvZmw_\ nx_ny_nz_nuakqbimcfiedefbag_YhYUjWQkTMlRImPEZRBKT8\ 6VAARBENCIJELGFPCGT8HW5G_4Fb4Ee3Dh3Cl2Bo2Ar19u1Ct2\ Fs3Ir4Lr5Oq6Rp7Uo8Wo8VmAVlCVlDVmFVnGUoIUpJUqLUrNUs\ OTtQTuRTvTTwUTxWTyXdzdpzlkzmgznczo_zpWzqSzrOzsKztG\ zuOzdWzOcz7bzAbzDbzGazJazMazP`zS`zU`zX_z__zb_zeZzh\ ZzkZzmPz5Pz7Pz9PzBPzDPzEPzGPzIPzKPzMPzNPzPPzRPzTPz\ VPzWSzXUzYXzZZz_az`cz``zZYzYVzWSzVPzUMzSJzRGzQWzaj\ zmhzhgzdez`dzWczSazO`zJZzFYzBXz7Uz6Sz5Pz5Nz4Lz4Iz3\ Gz3Ez2Bz29z17z17z17z17z16z16z16z16z16z16z16z15z0Zz\ hbzkeznizqlztpzwszzrzyqzx } 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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Tracing Negativ Periodicity
by SherLok Merfy 16 Mar '04

16 Mar '04

If you're like me, then you hit 't' at the spash screen of FRACTINT instead of believing in default fractals or complaining about maps that disappear whenever you switch fractal types. It's worth noting that it's FRACTINT that defines negative periodicity, and it means "show your work". A picture is worth a hundred lies, so I'll mention that before I start: Methods { ; A look at the internals of tesseral, border ; tracing, and diffusion at the inversion of where x=1/3. reset=2003 type=mandel passes=t center-mag=-0.533722/6.10623e-016/0.9699869/1.5686/-90/-1.233735336114\ 70521e-014 params=0/0 float=y maxiter=255 fillcolor=2 inside=255 invert=0.47/-0.33333333333333333/0 periodicity=-2 colors=0zzzzz00zz0zz0Wz00zV0zz0<3>0z00zV0zz<3>00zV0zz0z<3>z00<3>ze0zo0\ zz0Wz00z0<3>0ze0zo0zz<3>00zV0zz0z<3>z00<3>ze0zo0zz0<3>Lz0Bz00z00zV0zz<\ 3>0Lz0Bz00z<3>z0zz0Wz00<3>ze0zo0zz0<3>0z0<3>0ze0zo0zz<3>0Wz0Oz0Gz08z00\ z<3>z0zz0Wz00<3>zz0Wz00z0<3>0zz<7>0Rz0Nz0Iz<3>00z<3>z0z<3>z0Lz0Bz00zV0\ zz0<3>az0Wz0Qz0<3>0z00zV0zz<3>0Lz0Bz00z<3>e0zo0zz0z<3>z00<3>ze0zo0zz0<\ 3>Lz0Bz00z00zV0zz<3>0az0Wz0Qz<3>00zV0zz0z<3>z00zV0zz0<5>Wz0Rz0Lz0<3>0z\ 0<5>0zV0z_0ze<3>0zz<3>00zV0zz0z<3>z00<3>ze0zo0zz0Wz00z0<3>0zP0zV0z`<3>\ 0zz<3>000 } Bogus, my cat, was last seen evading American Foreign Policy on a rocket destined to annoy Marvin The Martian. I had a joke about "advanced connect the dots" in high school that I thot was funny, so little did I know that the mathematic art form could safely be called "Advanced Paint By Number" to piss off the blondes who thot they knew all about that. In the above "methods", you would see three critical rejions; White On Blue: First Escapees. Black On Blue: Rejion of unlikelyhoods. Yellow On Blue: Rejion of dispute. [Negativ periodicity is required to make border tracing work in this example, so if you zoom or pan this fractal to where border tracing yields what could be mistaken for a dubl fawlt, then try a more pessimistic number.] The rejion of dispute is the only part that rendering this fractal with passes=diffusion will highlight. Border tracing will highlight all of the mandeloids (physically on the outside, while mathematically on the inside of an inversion), while tesseral makes for a clear-cut reminder that this is art in the midst of analytic minds -- where geers and artsies work together with bounded chaos. This rejion is yellow on blue. If a bug is here, then it looks kinda cool, so maybe THIS should be the default parameters, no matter what you think of periodicity checking. Perhaps periodicity should be moved to the X-screen, while one of the doo-dads like biomorph or decomp (that don't seem to apply to orbital fractals, either) can move to Y. Synchronous Orbits? That's so close to the bleeding edge that it doesn't work with inversions. Now, as an excercise for the reader, which means I'm too lazy to answer the question myself: Why does border tracing require colour number zero?

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for jim muth
by David Lowenstein 15 Mar '04

15 Mar '04

since I am a twin of my brother hugo, are there such thing as twin fractals? -david

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FOTD 15-03-04 (Eggplant on your Face [5])
by Jim Muth 15 Mar '04

15 Mar '04

FOTD -- March 15, 2004 (Rating 5) Fractal visionaries and enthusiasts: Today's brief diversion takes us to the fractal created when the negative square root of 2 is combined with 1/4 part of 1/100th of the negative sign of the beast. With all this negativity going for it, the resulting fractal must be beastly indeed. If not beastly, the image is certainly mystical. Stretching to infinity as it does, the square root of two is as close to eternity as one could come while still on earth. And as for that mystical 666 beast, the less said about him the better. The name I gave the image is "Eggplant on your Face", which has nothing at all to do with the appearance of the image. I think I was listening to my standard morning fare of talk radio when the totally irrelevant phrase came to me. And since I can't seem to concentrate on the fractal of the day, it might be time to say I rated it at a 5, with a value of 53, and end the discussion, which seems to be going nowhere anyway. As always, the pre-rendered image is available for viewing and download on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The clouds hung around most all day Sunday here at Fractal Central, but the temperature reached 50F 10C, which was mild enough to let the cats to enjoy their needed time outdoors. They ended the day happy. Today is starting even warmer, and the sun is bright. It looks like another good day. For me, it will not be a good day until the work is finished. And that time is yet several hours off. Until next FOTD, take care, and one of these days I might actually learn enough math to claim to be a mathematician. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ EggplantOnYourFace { ; time=0:09:24.64--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.80348715162360600/-0.266042032269169\ 20/8.291078e+008/1/-17.5/7.15007914269885636e-005 params=1/-1.414213562373/0.25/-6.66/0/0 float=y maxiter=1200 inside=0 logmap=167 periodicity=10 colors=000zXLxVLy0LvSLt0LqRLl0Pi0Se8VbEXaL__QaXWeY\ `fVei_jlaoofspiysmzupzxszztzxtzwuzuuztwzswzqxzpxzo\ zzmzzlzzkzzizzhzzfzzezzczzazz`zz`zvPzrAzn0wm2pm9im\ FcjH_gIVeIQcKL`LHZLAWN5UNA`YHShKkpIioHgoFdoFdoCaoA\ ZoAXm9Wm7Um7Sm5Qm2Om1Mm1Ll0Jl0Hl0Fl0El0Cl0Alxdzqgz\ lixfjt`mqVnmmoimqemsamtYmvUmxQmtPmsNmrLmqKAoIFnHKm\ FNkFSjCViA_g9ae7fd5ic2la2kZ5iX7iW9hUAfSCfRFeQHeOIc\ MKaLLaJN`HN_FP_EQYCSYAUX8VV5XV4YU2_S0`S0aQ0cQ0cX0a\ a5`hC_mH_sMYxRXzWXz`VzdUzgUzZXzR_qJ`h8cY0fP0ham0_n\ 0Xo0Uq0Qs0Nt0Kv0Hx0Cy09z05z11z10z10z20z20z20z90zF0\ zI0zN1zQ2zV5z_9zaAyfCyiFxmIvqKttLsxNszQvxSxuVzsXzp\ _zm`zkczhezefzaYzQQqCHg07X09Z09Z09Z09Z5A`9A`FA`IA`\ NC`QCaVCaYCaaFafFaiFcmFcpHctHcwHczHdzIdzIdzIdzIdzP\ izVmz_ozeszivzozztzwxztzzqzzozzqzzszztzzuzzwzzxzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzLzzLzzL } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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[Fractint] Hearts finalist. heartsf.par = whole message with snipped rambling.
by SherLok Merfy 15 Mar '04

15 Mar '04

I don't use "frm:formula_name", because that means you can't also run FRACTINT with "formulafile=heartsf.par" and expect to see your formulas. FRACTINT will let you try to run parameter specs. as formulas from such merged files, though. If you missed my QBASIC for blowing music _into_ Fractint, then you can reverse the enjineering with this formula, otherwise more QBASIC might come later with the other three formulas that I will use. My tuning is simple: whole numbered multiples of a source frequency. It doesn't matter what the source frequency is unless you want an orchestra to accompany the computer, because it's ratios that matter to the ear. My tune has literally changed. This one works quite nicely, but that's challenging, because it makes for a look very different from the basis equation: heartx, and I want more unity or commonality among the images than that. I wonder if PDF is sent to PostScript printers without rendition, because writing this stuff in PostScript and converting to PDF might let me compress my output (for cards) to what fits on a floppy (or takes less time to download than to render). If rendition of PDF is done on the host of the printer, then there's no problem, but if it's sent to the printer, then the FRACTALS must be very fast or they'll make it time out. It's tempting to explicitly copyright this work, even if it takes an hour and a half plus some editing on a box older than five years. It falls under collective works, but this doesn't: http://ecn.ab.ca/~brewhaha/img/hearts.jpg , so fair use rules apply, whatever that means with MicroSoft source code running around making a mess of everything else that doesn't work. _______ heartsH { ; Chrominance: Alter through mask of HeartsV as ; grayscale. reset=2003 type=formula formulafile=heartsf.par formulaname=hearty passes=d center-mag=0.00844324/-1.37358/0.3241387/1.2195 params=2/0 float=y maxiter=255 inside=0 colors=000z00zz00z00zV0zz0Wz00z<3>z0zz0Wz00<3>zz0Wz00z0<3>0zz<3>0Lz0Bz\ 00zV0zz0z<3>z0Lz0Bz00<3>zz0Wz00z0<3>0zz<3>0Lz0Bz00z<3>e0zo0zz0zz0Wz00<\ 3>ze0zo0zz0<3>0z00zV0zz<3>0Lz0Bz00z<3>z0z<3>z0Lz0Bz00<3>zV0zb0zj0zr0zz\ 0<3>0z00zV0zz<3>00zV0zz0z<3>z00<7>z_0zc0zh0<3>zz0<3>0z0<3>0ze0zo0zz0Wz\ 00z<3>P0zV0z`0z<3>z0zz0Wz00<3>ze0zo0zz0<3>Lz0Bz00z0<3>0zz<3>0Lz0Bz00z<\ 3>e0zo0zz0zz0Wz00<3>zP0zV0z`0<3>zz0Wz00z0<3>0zz0Wz00z<5>V0z_0ze0z<3>z0\ z<5>z0Wz0Rz0L<3>z00<3>zz0Wz00z0<3>0zz<3>0Lz0Bz00zV0zz0z<3>z0az0Wz0Q<3>\ z00<3>zzz } heartsV { ; Drop luminance through this "graymask" after raising 50%. reset=2003 type=formula formulafile=hearty.par formulaname=hearty passes=d center-mag=0.00844324/-1.37358/0.3241387/1.2195 params=2/0 float=y maxiter=255 inside=0 outside=atan; colors=(a)rainboh.map colors=000z50z70zB0<3>zJ0zL0zM0zN0zP0zR0<5>z_0z`0za0zb0zd0<14>zu0zv0zw\ 0zx0zy0<14>lz0kz0jz0<5>bz0az0`z0<4>Tz0Sz0Rz0Pz0Nz0Mz0Lz0Iz0Hz0Ez0Dz0Bz\ 0<2>0z00z30z70zB0zD0zH0zJ0zK0zL0zN<3>0zS0zT0zV0zX<4>0zc0zd0zf<14>0zu0z\ v0zw0zx0zy<8>0rz0qz0oz<4>0jz0iz0hz<8>0Xz0Vz0Tz<3>0Pz0Nz0Lz0Jz0Hz0Gz0Dz\ 0Bz<2>00z30z70zB0zD0zF0zG0z<4>P0zQ0zS0zT0zV0z<2>_0z`0za0zb0zc0z<3>h0zi\ 0zk0z<9>u0zv0zw0zx0zy0z<13>z0mz0lz0k<3>z0fz0dz0cz0az0`<4>z0Vz0Tz0S<3>z\ 0Lz0Jz0Hz0Gz0D<3>z04 } heartsS { ; Mask for stripes of fading. Maybe needs work. ; Perhaps wood grain, like on my skull. reset=2003 type=formula formulafile=hearty.par formulaname=hearty passes=d center-mag=0.00844324/-1.37358/0.3241387/1.2195 params=2/0 float=y maxiter=255 inside=0 proximity=1 outside=fmod colors=000zzz000zzz000000zzz000000000zzz000<3>000zzz000<5>000zzz000<4>\ 000<4>000zzz000<4>000<4>000zzz000<6>000<4>000zzz000<10>000<4>000zzz000\ <12>000<4>000zzz000<16>000<4>000zzz000<22>000<4>000zzz000<24>000<4>000\ zzz000<30>000<4>000zzz000<29>000 } Hearty { ; Formula. Needs arrays for speed. Cropped as above, ; about 30min. on 350MhzPII @ 1280x1024, ; more for atan and fmod. s=z=atanh(real(-1/pixel) +flip(imag(-.5/pixel))), iter=0, t=|P1|, mean= 24.15789473684211: imod=(iter/ 127 -trunc(iter/ 127 ))* 127 , ; imod=remainder(num_notes/iter) iter=iter+1, if(imod>-1 && imod< 8 ) note= 11 elseif(imod> 6 && imod< 19 ) note= 13 elseif(imod> 17 && imod< 22 ) note= 17 elseif(imod> 20 && imod< 27 ) note= 19 elseif(imod> 25 && imod< 34 ) note= 16 elseif(imod> 32 && imod< 41 ) note= 23 elseif(imod> 39 && imod< 52 ) note= 31 elseif(imod> 50 && imod< 55 ) note= 29 elseif(imod> 53 && imod< 60 ) note= 23 elseif(imod> 58 && imod< 67 ) note= 31 elseif(imod> 65 && imod< 74 ) note= 11 elseif(imod> 72 && imod< 85 ) note= 9 elseif(imod> 83 && imod< 88 ) note= 13 elseif(imod> 86 && imod< 93 ) note= 17 elseif(imod> 91 && imod< 100 ) note= 13 elseif(imod> 98 && imod< 107 ) note= 29 elseif(imod> 105 && imod< 118 ) note= 51 elseif(imod> 116 && imod< 121 ) note= 59 elseif(imod> 119 && imod< 128 ) note= 44 endif, z=s*(z-flip(note/mean))*(flip(note/mean)-z) |z| <= t } Heartx { ; Formula. The core of hearty. s=z=atanh(real(-1/pixel) +flip(imag(-.5/pixel))), iter=0, t=|P1|,: z=s*(z-(0,1))*((0,1)-z) |z| <= t }

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