April 2014 - Fractint - mailman.xmission.com

FOTD 27-04-14 (Saucer Convention [A10,M10])
by Susan Brown 27 Apr '14

27 Apr '14

FOTD -- April 27, 2014 (Rating A-10,M-10) Fractal visionaries and enthusiasts: Finally, after all these years, we have a FOTD that rates a double 10. And it took an invasion of flying saucers from outer space to earn this astounding rating. My first impulse was to name the image 'Saucer Invasion', but then I decided to give the aliens the benefit of a doubt, and not automatically assume they are war-like creatures. I finally decided that the aliens are here on nothing more threatening than a galactic convention, and named the image "Saucer Convention". The art rates the holy grail of a 10 because after hours of working on the 48-colors of the palette, I finally got the image to appear almost 3-D photographic. The math earns the same rating because I have no idea what is going on with the math, which appears to have something to do with both Mandelbrot images and Newton's method of finding roots. This could well be the only FOTD that will ever be posted rating a double ten. The flying saucers are all made of some burnished hi-tech copper-colored metal. Some of them resemble huge flying kettledrums, while others resemble thin, flattened dish-like craft, barely able to hold an intelligent alien. It's anyone's guess what the inhabitants of the saucers might look like. The saucers must be mother ships carrying fleets of smaller craft. How else could the many smaller groups flying in formations be explained? The image takes 3-1/4 minutes to calculate, which is likely a lot less than the time it took the saucers to reach the earth from their home worlds scattered throughout the galaxy, if not the universe. See the finished image instantly at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> The partly cloudy sky, chilly north winds and temperature of 57F 14C were fine for spring gardening here at Fractal Central today, though not quite so good for the fractal cats, who were unhappy about the chill and waited for the sunshine to become dependable, which never happened. The fractal humans were in kind of a down mood. The next FOTD will in all likelihood be posted 24 hours from now. If not, it will appear in 48 hours. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Saucer_Convention { ; time=0:03:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=mandnewt.frm formulaname=MandNewt12 passes=1 center-mag=+0.7897\ 049206/-0.0284320591/284405/1/107/0 params=-4.3808\ /-0.5139/-1.2595/1.0881/-0.811/2.519 float=y maxiter=250 inside=bof60 logmap=yes periodicity=0 colors=000yzzyxvxwrwumvshuqctlZshWreRqcQobPnaOm`Nl\ _MkZLjYKiXJhWIgVHfUGeTFdSEbRD`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} frm:MandNewt12 {; Jim Muth z=g=pixel, a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), e=real(p3), f=imag(p3): h=z^a+(g-1)*(z-b) j=c*z^d+g z=z-e*h/(f*j), 0.0000000000000000000000000000005 <= |h| } END PARAMETER FILE=========================================

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FOTD 25-04-14 (Koilon Bubbles [A-8,M-7])
by Jim Muth 26 Apr '14

26 Apr '14

FOTD -- April 25, 2014 (Rating A-8,M-7) Fractal visionaries and enthusiasts: Today's image lies in the parent fractal that results when 0.01 part of Z^(2) is subtracted from Z^(-2) on each iteration. This parent is gargantuan in size, though the unlikely escape radius of today's image cuts off most of it. This odd escape radius of 99.999 was carefully chosen to bring the scene of today's action as close as possible to the cutoff point, where the bubbles created by the 'fmod' outside option are as prominent as possible. The name "Koilon Bubbles" describes the bubble-like objects in the image, and points back to the time when empty space was assumed to be filled with an invisible substance called aether, which transmitted light waves. Some people, mostly occultists who called the aether 'koilon', also assumed that atoms were actually made of bubbles in this all-pervading substance that were held open by the creative power. Curiously, now that dark energy has come on the scene, this idea does not seem quite as goofy as when it was seemingly disproved by the theory of relativity. The art rating of an 8 is thoroughly earned, since I spent over an hour working up the custom coloring. The math rating of a 7 is earned because the un-truncated parent fractal extends apparently infinitely in both the outward and inward directions. The calculation takes 1-1/2 minutes -- fast enough to keep boredom at bay. And the web sites can avoid all calculation problems. Save a little effort by viewing the finished image on any one of the FOTD web sites at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Morning sun gave way to afternoon clouds and evening rain here at Fractal Central today. The temperature of 64F 18C was very near normal. The fractal cats were too busy tussling with each other to care very much about the outside conditions, though I did hear Jasmine chattering when a pigeon landed near the window. The humans, who are becoming ever more disgusted with politics and the mass media, had an average day. The next FOTD will be delayed until April 27, two days from now. Until that time arrives, take care, and beware of manipulative media exaggerations. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Koilon_Bubbles { ; time=0:01:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-4.439109860299364/-5.965792592977377/\ 2.5e+008/1/-42.5/0 params=1/-2/-0.01/2/0/-0.001/0/0 float=y maxiter=1000 inside=0 proximity=0.5 outside=fmod logmap=yes periodicity=6 colors=000zzzxyzwwzuuzsszrqzqozpmzokznizmgzkeziczg\ aze_zcYzaXz_WzYVzWUzVTzUSzTRxSQvQPqOOoMNnKMlILgGKe\ FKdDIaBHY9FX9FV7DT5BO3BM29K27I07F05D03B03905H27S39\ Z5Bc7Df9Fi9FiDIzFKzHMzIOzKQzKQzKQzKQzKTzKTzKTzKTzK\ VzKVxMVvMVqMXoMXnMXiMXgMYeMYaMY_MYYKX_KX_IXaIXaHXd\ HXdFXeFXeFXgDXgDXiBXiBXl9Xl9Xn9Xn7Xo7Xo5Xq5Xq3Xt3X\ t3Xt5Yq7Yo7Yn9YlB_iB_gD_gF_eF_dHaaIa_IaYKaXKaXMdVO\ dTOdQQdOTeMTeKVeKXeIXeHYgFYgD_gBagBag9di7ei5ei3gi2\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 0000000000000000000000000 } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, esc=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < esc } END PARAMETER FILE=========================================

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FOTD 24-04-14 (Return to Basics [A-7,M-3])
by Jim Muth 24 Apr '14

24 Apr '14

FOTD -- April 24, 2014 (Rating A-7,M-3) Fractal visionaries and enthusiasts: There is not much to say about today's image, which is a scene deep in the east shore line of the north branch of Seahorse Valley of the Mandelbrot set. Since the magnitude is at the limit of conventional math, arbitrary precision math will produce a slightly sharper rendering, but at the same time will increase the calculation time from 10 minutes to a day or more. I put some extra effort into the coloring, mainly by setting the logmap at a higher than proper value, which produces the large flat areas that I colored black. This earns the art aspect a respectable 7. The math however is pure Mandelbrot stuff. There is nothing wrong with this, but the trick is now over 30 years old and hardly worth a rating above a 3. The name "Return to Basics" reminds us that the Mandelbrot set is still the most basic of all fractals. The calculation time of 10 minutes is a rough average. Different machines run type=mandel fractals at widely different speeds. So avoid all uncertainty by visiting the web sites. Check the finished image on the FOTD web sites at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Despite the brilliant sun, the high temperature of 59F 15C and brisk wind from the north kept a feeling of late winter in the air here at Fractal Central today. The fractal cats, who now regularly tussle with each other, were too pre-occupied with their play to be concerned with the slight chill. The fractal humans simply got through the day the same as they have done on countless other days. The next FOTD will be posted in 24 hours. Until then, take care, and see you soon. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Return_to_Basics { ; time=0:10:00.00 SF5 at 2000MHZ reset=2000 type=mandel center-mag=-0.7499977505574\ 505/+0.00301634025810139/2.177347e+013/1/-40/0 params=0/0 float=y maxiter=750000 bailout=4 inside=0 logmap=-91500 mathtolerance=0.05/1 colors=000000000000xc7xeBxhFwjKwmOwoSwqWmwzrnfpmkn\ lpigidccESw9Tw4Uw5So6Qh7Oa8NV9LOAJHBHABG3SnjQjhOgg\ NdfLaeKZdQOnVEwcBcl8Kt60n96iBCdDI_FOVHUQJ_TBGU8KW6\ OX4SS6NO7JK8FGAAI668C2KQ1Wb1fo1im9lkHojPrhXugcndfh\ ahaZkWXmPUoJRrCOt6MvPbpgsjaaqXKxqc5nc6lK6jc6hc6fc6\ dg6bf6`f6wB5ag4wB5bY6w07jk8wS9p_BwOCqUDrREwLFwPGwU\ HwVIwVJwUKwVLwWMwXNwXOw_Pw_Qw_RwZSwZTwZUw_VpWWqWXr\ WYsWZtW_uW`vWavWbvWcvWdvWewWfwWgwWiwWjwWkwWlwWmwWn\ wcJwc_wcowcjwcewc`wcWwcXwcXwcXwcdwckwcRzcMzcIzcEzc\ Azc6zc8zcUzcOzcJzcEzc9zc4zcBzcHzcOzcUzm`zmfzm`zmWz\ mRzmMzmfzmzzmuzmqzmmzmhzmdzm`zmczmePmhJmjDmlTmggmb\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } END PARAMETER FILE=========================================

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FOTD 23-04-14 (It's Not Quadratic [A-7,M-6])
by Jim Muth 23 Apr '14

23 Apr '14

FOTD -- April 23, 2014 (Rating A-7,M-6) Fractal visionaries and enthusiasts: >From a distance the little minibrot at the center of today's image may look quadratic, but it certainly is not. It is of order 1.5 and lies in a parent fractal that resulted when I iterated the expression Z^(1.5)+C at a level 33 levels up the hyperladder with no function applied. The name "It's Not Quadratic" confirms the apparent discrepancy. This parent is shaped quite like the minibrot in the image, and is oriented so that the large period-2 bud points out to the south. Today's scene is located in a sprawling chaotic spiral just inland from the southeast shore line of the parent's main bay. I intentionally set the logmap about 25 levels too high. Doing this created a flat background that could be given any color I wished. For various reasons I chose solid black. The art rates a 7, mostly because of the flat black background. The math rates a 6, since the math trick is so old that it is hardly a trick any longer. The calculation time of 1-1/2 minutes is fast enough. But visit the web sites for an even faster way to view the image. The web sites are online at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Lots of clouds with only a few breaks of sun spoiled the day here at Fractal Central. The brisk north wind and temperature of only 54F 12C made things even worse. The fractal cats endured the discomfort with only minor complaints. The humans had no complaints at all -- we were too busy. The next FOTD will be posted in about 24 hours. Until then, take care, and let's avoid discussing religion, politics or philosophy for a few days. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= It's_Not_Quadratic { ; time=0:01:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.7796928496537461/-0.5595061592029913\ /3.314487e+008/1/112.5/0 params=1.5/0/33/0 float=y maxiter=2400 inside=0 logmap=162 periodicity=6 colors=000000SafRWfPQfOKgMEgLGgKKgPPpUUxWZvXcuYhtZ\ ms_or`qqctphwpmznrzjjzgdoddgadeZdUmdUmdUmdKmdKmdKm\ dKmdKzdKzdKzdKzZKzUKzPCzQKzRKzUKzWKzZKz`KzcQzePzfQ\ zgRzgRzhSzhSmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmz\ cmzcmmcmccmUcmKcmIcmLcjOcgRccTc_WcXZcTacPdcMfcIidE\ leBof7qg4kf8eeB_dEVdHTaKR_NPYPOWSMUUKRXIPZHNaFLdDJ\ fBGiAEk8Cn6Ap48s36u5At6Dt7Ht9KsAOsBRsDVsEYrFarHdrI\ hrJkqLoqMrqNuqe_ZwEHpHOiJUbL_WNeQPkTSjWVjYYi`_icbi\ eehhghkjhmmgppgsrguufxxfzzfzzazzWzzR4mMFmPQmS`mVjm\ YlmVnmTocQqcOscMtcJvcHwcFvcGucHtcHscIreJrkJllGflE`\ lCWlAZfC``EccGecIhcKjcMlcN8hxHhyKhhPcbUcXXcVZcTacR\ cePehNhjLjmJloHhoFdoE`oDYoC_nBanBczAezAizAjz9kz9lz\ 8mz8nz8oz7pz7qz7rz6sz6tz5uzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 22-04-14 (Broken Perfection [A-7,M-6])
by Jim Muth 22 Apr '14

22 Apr '14

FOTD -- April 22, 2014 (Rating A-7,M-6) Fractal visionaries and enthusiasts: Today's image is named "Broken Perfection". The reason for the name is readily apparent in the image, which shows an almost perfect ring around a minibrot. The ring resembles a donut- shaped planetary nebula puffed off from a dying star, but look closer. The ring is broken on its east side by a discontinuity that is caused by the fractional nature of the Z^(10.5) exponent and extends all the way to the central minibrot. The 9-1/2 bays of the minibrot point to an exponent of 10.5, while the 10-1/2 elements in the ring confirm the deduction. The location of the scene is at the edge of a larger but still order-10.5 minibrot on the main spike of the parent Mandelbrot set, just east of the prominent large quadratic minibrot. The art rates a 7, mostly due to the modicum of extra effort I put into the coloring. I could rate the math aspect no higher than a 6, especially after noting that we have been exploring this math trick for over a week. The calculation time of merely forty seconds makes up for any deficiencies however. This time will pass faster than Ali Baba's forty thieves. But there is no danger, since the web sites will keep the thieves at bay, at least for those who choose to take shelter there. The web sites are online at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Heavy clouds and light rain spoiled things here at Fractal Central today until the sun broke through in mid-afternoon. The temperature of 68F 20C was mild enough, but with the house heat turned down, the fractal cats would have preferred more sun. The humans had a thoughtful day. While I was out walking, I noticed that the trees in the town square are still as bare and bleak as in midwinter, and it's only one week until the month of May, when trees are usually in full leaf. The next FOTD will be posted in 24 hours or whenever. Until then, take care, and at this Easter time I hear of a decline in religious faith. The decline is nothing new, but could it be driven by the fact that among the over-educated, religious faith is widely seen as a vestige, which is now little more than a comforting diversion from reality clung to by the under-educated and easily disproved by scientific study and rational thought? Jim (both Theist and Atheist) Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Broken_Perfection { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip inside=0 center-mag=-1.741394475156175/+0.00000405269130397\ /2.773655e+012 params=10.5/1e+020/0/0 float=y maxiter=400 periodicity=6 mathtolerance=0.05/1 colors=000zdkzmsznlznezo_zoTzoNzoKzoHzfFzZDzRBzJ9z\ B7z35z4Ez5Mz6Uz7az8izA4z9Ez8Oz7Yz7fzEczKazRZzXXzcV\ ziSzpQzvOzqQzmRzhTzdUz`WzWXzSZzPYzO_zN`zMazLbz5xzD\ mzLczTUzcEz`KzPEzUKzZQzcWzhazmgzrmzwtzvszvrzvqzvpz\ vozvnzvmzzqzyozvlztjzrhzpfzzzzzzzzzzzzzzyzzxuzwrwv\ ouulsthqsbprZoqWlpTkoQjnNimKhlHgkIfjJeiKdhLcgMbeNa\ bO`_PZYQXVRUTSPQQLOLJLJGJGEGDAEB9CA79757725404NA4T\ F4YK4bP4gU4kb4ph4vo4zv4zzcztevtxjowZjwOfwVMbW1IU3K\ S5LQ7NP9ONBQLDRKFTIGUGIVFKXDMYBO_AQ`8Sb6Uc5Vd6Ue6T\ ezSezRezQezPezOezPdzQdzQdzRdzSdzUdzVdzObzSczWdz_ez\ cezgfzkgzohzshzdYzROzDEzJIz2EzOLzgEzhLziSzjYzkdzlk\ zouznszmqzlpzknzjlztnzolzjkzfizahzXfzTezOczKbzO_zR\ YzcFz`JzXNzURzRVzOZzPdzPjzQpzQvzOtzNrzMqzLozKmzJlz\ IazISzIIzFGzDEzBCzKKzTSzzzzX`zS`zN`zI`zD`z8`z4`z5U\ z6Oz7Hz8Bz85zCBzFGzIMzLRzOXzRazUgzXlz0mz7kzEizLhzS\ fzZdzdczSUzGLz4CzELzNUzWb } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 21-04-14 (A Split Opinion [A-8,M-5])
by Jim Muth 21 Apr '14

21 Apr '14

FOTD -- April 21, 2014 (Rating A-8,M-5) Fractal visionaries and enthusiasts: Today's brilliant image is a scene on the edge of the main spike of the Z^(2.0000001)+C Mandeloid. On the surface this parent fractal appears to be an everyday Mandelbrot set, and most of it is just that, but as today's image shows, strange things are happening along its main spike. The image is located on the northern edge of the spike, which is infinitely divided. The division of the spike is mirrored in the network of white filaments surrounding the central minibrot. And that central minibrot has its own problems. The minibrot is not a single minibrot. It lies on a discontinuity where it has been split into two separate minibrots, neither of which are fully there. The art rates an 8, even though I posted a very similar image about 5 years ago. The math rating of a 5 is held down by the over-familiarity of the divided-spike math trick. The name "A Split Opinion" refers to the divided spike. The calculation time of four minutes is slow, but at least in my humble opinion, is worth the wait. And the web sites are always there to make life easier. Regardless of my individual opinion, viewing the image on the web sites will be far more convenient than running the parameter file. The web sites may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> The glorious sunshine and temperature of 70F 21C here at Fractal Central today was just what the doctor ordered. I'm not sure what ailment it cured, but the fractal cats took full advantage of the sun, as they chased the shifting sunbeams. The fractal humans simply made it through the day with nothing happening that was worth reporting. The next FOTD will be posted in almost no time at all. Tomorrow is the best bet. Until this great fractal apparition, take care, and with all the misleading nonsense in the media, people probably know less than half as much as they think they do. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_Split_Opinion { ; time=0:04:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotN center-mag=-1.749737348005\ 255/+0.0000004927012753/3.447818e+011/1/32.5/0 params=2.0000001/0/0/0/0/0 float=y maxiter=32767 inside=0 periodicity=6 mathtolerance=0.05/1 colors=000pDzqCzm0zsCzyYzzstzzmzzhzzfzzczu_yqXwmUu\ hRsdOq_KpWFmRCkM7jH3hC0f50d00c00a00Y00W10S50PC0MH0\ JK0FP0CS07X03a10dA0hK0mU0pc0tm0zr0yz0wz0tw0qs0oo0n\ k0mh0le0kb0j_0iX0fU0cR0`O0YL0UI0PE0I80D30A00500300\ 000500900D00H01K03P05S07W09Y0Ca0Df0Fh0Hk0Jo0Kq0Pz0\ Ow0Mt0Kq0Jo0Jk0Hh3Ff7DcCD_DCXH9UK7RO5OR5KS3HW1DY09\ a00d03c05c57cD9aJDaOFaUH_YJ_cM_gO_mPYqRYuUYzWXzXXz\ YXz_X00N00Q00T10W20X30`43b59e6Bf7Bj8Ck9DkAElAFmAGn\ AHoAIpAJqALrAOsARtAUuBXvC_wGbxKeyPhzUmzZpzctzhzzmz\ zrzzzzzzzzamzahzaczaZzaUzaPzaMz_MzYOzXRzWSzUUzUXzS\ YzR_zPczOdyMfuMhtKjqJkpHomFpkDqhDtgCud9wc7z_5zY0zX\ 5zX9zXDyXHwXKuXPsXSqXWoXYmXakXfhXhgXkdXocXsXYqaXpd\ XogWojWmmUkpUjsSptXmuUjuSguPduOWHMaCJeAHh5FlCCoF9q\ J5sM3tP0tS0uW0wY0ya0zd0zg0zh0we0ta0qX0mS1hO5cJ9ZDF\ U7JP1MK7JFCH0HF0KC0P90S70W30_10c00g00j00m00j03g79d\ DFaKKYPPWWUSaYPfcMkgJpkFu } frm:MandelbrotN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 20-04-14 (Two Full Elevenths [A-7,M-7])
by Jim Muth 21 Apr '14

21 Apr '14

FOTD -- April 20, 2014 (Rating A-7,M-7) Fractal visionaries and enthusiasts: The parameters of today's fractal show that it is located on the west side of the north branch of Seahorse Valley of its parent Mandelbrot set. But this parent M-set is not just any old M-set, it is a set that has been corrupted in its depths by Z^(11) energies. The amazingly large imag(p1) parameter of 100000000000000000000 is necessary to keep the corruption down in the depths. I'm not sure how or why this works, but it does work, so why question such a useful thing. The corruption in today's image is of order 11, which is an odd number. When the M-set is corrupted with odd energies, the switch from the quadratic to the odd-order level is much more interesting, since an odd number of elements cannot be symmetrically melded into an even number of quadratic elements, and since the corrupting energies are not fractional, there are no discontinuities to make sudden 'quantum' leaps. The art and math values of today's image both rate a 7. The name "Two Full Elevenths" is based on the combination of Z^(2) and Z^(11) energies. The calculation time of 2-1/2 minutes will pass. How fast it will seem to pass depends on the patience of the individual fractalist. But everyone can have infinite patience by checking the finished image on the web sites, thereby eliminating the chore of calculation. The web sites are at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Total sun and a temperature of 68F 20C gave the fractal cats as well as the fractal humans the best Easter in several years here at Fractal Central today. The next FOTD will be posted in 24 hours. Until then, take care, and the more a person tries to figure out what's wrong with the world, the more confusing everything becomes. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Two_Full_Elevenths { ; time=0:02:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-1.768537043766396/+0.00289078841806103\ /1.482942e+012/1/45/0 params=11/1e+020/0/0 float=y maxiter=1800 inside=0 logmap=266 periodicity=6 mathtolerance=0.05/1 colors=000RUhQUgPUfOUeNUdMTcLSaKR_JQYIPWHOUGNTFMSE\ LRDKQCJPBIOAHN9GM8FL7EK6DJ5CF4BA3A028416704ASh7Um6\ Wr5Yv5_v4mx3mz3mz2wz2wz6wz9rvCmrFmoImlLniOpfSqcVr`\ YsY`tVcuSfvPiwMlrLhmKchJZcIUZHPUGKPFFKFBFF8AF78F76\ F64F63F6LFAaGDdGGfBTW6eL1rIAsFJsDSsNLzROuURpXTk_Wg\ cZbf`YicTlfPphKskFvnAyp6vm9skBpiDmfFjdHgbKd_MaYOZW\ QXUSWRQVPOUMNTKLSHKRFIQCGPAFO7DN5CQ7HT8MV9RYBW`C`b\ DeZCgWBhTAiQ9kN8lK7mH6nE5pB4q83r52sB5qG8pLBoQEnVGm\ `JleMkjPjocitchrccpc_wcWwcSwhOwcKwZGwUMwUSwWYwYbw_\ hwanwcswemwggwibrkXrmSmoMiqHhsGfuFevEdvEcvDawC`wB_\ wBZxAYx9Xx9WuFVrLUoQTmWSmaRmfQmlPmrOmwQmsRmoSmkTmh\ UpdVs`WwXXoUYfQZZM_PIw_jU9BP37wfjK66KA7PE8UIAUMBZL\ CZMEcNFcOGfOIjPJkPKlPMmPNnPOoPPpQcqQcrRcsSctUhuUhv\ UhwUhxZmyZmzZmzZmzcrzcrzcrzcrzhrzhrzhrzhrzmvzmvzmv\ zmvzrzzrzzrzzrzzvzzvzzvzzvzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 18-04-14 (Sandy Scenery [A-8,M-8])
by Jim Muth 18 Apr '14

18 Apr '14

FOTD -- April 18, 2014 (Rating A-8,M-8) Fractal visionaries and enthusiasts: Today's image lies in a parent Mandelbrot set corrupted by Z^(0.9) energies. In this case, the corruption extends all the way to the parent's surface, where it splits the main spike into fractal chaos. Today's scene is located very close to the X-axis in some of this chaos just west of the split-apart large minibrot. I named the image "Sandy Scenery" because of the well-defined area of near total chaos surrounding the minibrot lying at the center of the scene, well beyond the reach of Fractint . I have rated both the art and math aspects at an 8. I really did put extra effort into the coloring. And the math is kind of a mystery. It is far from obvious why corruption energies less than two have such a dramatic effect on even the surface of the parent M-set, and also why the minibrots of the corrupted parent remain quadratic and do not morph into lower-order ones. The calculation time of 1-2/3 minutes is fast enough to prevent impatience or boredom from arising, but life can still be made simpler by avoiding calculation completely and checking the finished image on the web sites. For maximum convenience, the image has already been calculated and posted to the FOTD web sites at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Clouds prevailed all day here at Fractal Central, but they were thin enough to let a trace of sunlight through. The fractal cats, who wanted more than just a trace, were spotted crouched in their cat sulk positions several times during the afternoon. The humans, who would have preferred a temperature higher than 54F 12C, took what they could get. The next FOTD will likely not be posted until April 20. Until the moment of bliss arrives, take care, and it's getting so confusing that a person can't tell the good aliens from the bad ones without a program. Jim (not an alien) Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Sandy_Scenery { ; time=0:01:40.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip logmap=-176 center-mag=-1.754416325421651/+0.000014838350617/\ 1.726933e+013/1/-15/0 params=0.9/100/0/0 float=y maxiter=1200 periodicity=6 mathtolerance=0.05/1 colors=00050A50B50C50D50E50F50H50J70L90NB0PD0RF0TH\ 0VJ0XL0ZN0`Q6cTCfWIiZOlaUocZqdcsfhuhmwjrzkvzzzzwlz\ wiqxgiwdbwcXvaVr`SmZPfYM_VLSLYJDKC6ABCAAIAANAATAAZ\ AAAAAAAAAAmRGjWGgaFcfF`lErqEpzCmuAhq8cm7ci6Ze5Ua4K\ X3EP49K4DF5HA5LA5PKFSKPVcZYch`gzVbzPczJczDcz7cz1cz\ 2cz2cz2cz2cz6cz9cMDcNGcOJcQNcRQcSTcT_UYeUbkUgqPlwQ\ pd`cNjRKkOIlMFmJDmHAnE8oC5p93p77mHAjQDgZBbWAcU9cS8\ cQ7cN6cL5cJ4cHCcMKcRScW_c`gceocjwcoaceGzWHtXHoYHjZ\ HeZH`_HW`HR`LQ_PQ_SQZWPZ_PYbPYcSVcUSdWPdYMe_JeaGec\ EaeQZf`wVYtWUrXQoYNmZJk_Fh`Cfa8db5cpbdtbgegjRkmDom\ GpmIpmKqmNqmPrmRrmUsmWsmYtm`tmbumdumgvmivmkvljrkio\ jikihhhgdggaffZeeVdeScdObcLacH`bE_cBScILcPEcW7cb0c\ i3cf6cd8cbBc`EcYGcWJcUMcSOcPRcNUcLWcJXcLYcMZcN_cO`\ cPacQbcRbcSccUdcVecWfcXgcYhcZic_ic`hcagcbfcceccdcd\ dceccfbcfacg`ch`ci_ciZcjYckXclXcldc_lcNtcBqc9oc8lc\ 6jc5hc4dcA`cFXcLTcQQcVMc` } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 17-04-14 (Antibifurcation [A-7,M-9])
by Jim Muth 17 Apr '14

17 Apr '14

FOTD -- April 17, 2014 (Rating A-7,M-9) Fractal visionaries and enthusiasts: Today's image lies at the western edge of yesterday's morphing minibrot. It is the most striking example of an area of antibifurcation that I have yet found, and this is exactly what I have named it. My definition of an area of antibifurcation is the exact opposite of the area surrounding a minibrot. Instead of the maxiter increasing toward the center, it decreases, while the number of elements is cut in half instead of doubling. When we zoom into a minibrot that lies in the basin of attraction of a larger minibrot, the doubling of the surrounding elements often reaches a maximum, then resets itself to a smaller power of two and resumes doubling from there. This resetting is sometimes referred to as antibifurcation, though I prefer the term resetting. In today's image the art rates a 7, since I see nothing unusually striking in the picture. The math however rates a superior 9, since the entire scene appears to be inside out, with even the colors cycling in the wrong direction. It takes 6-1/4 dragging minutes for the image to finish, a time that could lead some to become impatient and miss the incredible antibifurcation. So if impatience strikes, don't forget the web sites. Find anti-impatience by viewing the finished image on the FOTD web sites at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Glorious sunshine poured down on Fractal Central today, while the temperature of 55F 13C made the outdoors at least a little better than yesterday, though well below the normal high of 66F 19C. The fractal cats wished for further improvement, but the humans made it through the day with no major problems. The next FOTD will be posted in a certain period of time. Until the certainty becomes more specific, take care, and let's live life to the fullest while we're here. After all, we only go around a couple hundred times. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Antibifurcation { ; time=0:06:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip center-mag=-1.777252088172983/+0.00042575899897272\ /1.721917e+012/1/-85/0 params=13/1e+055/0/0 float=y maxiter=12000 periodicity=6 mathtolerance=0.05/1 colors=000koplqrlsumuwmvzmuzlszkqwipthoqgnmfmidkhc\ ihbggaff_eeZddYcdXbcVabU`aT_aSZ`QY_PXZOWYNVYLUXKTW\ JSVIRVJQUKPTLOSMNRNMROLQOKPPKOQKORLNSMMTNLTOLUPKVQ\ JWRIXRIYRHYRGZRF_RF`REaRDbRC`PAbRCcTEdUGeWIfXKgZMi\ _OkaQmbSodUqeWsgYth_ujavkcwmeunftlfskftifthfuffuef\ udfvbfvafw_fwZfxXfxWfxVfyTfySfzQfzPfzLczOfzRhzUjzX\ lz_nzbpzerxfpvfnufmsfkrfipfhngfmgekgcjgahg`ggZegYc\ gXagW_gUYgTWfUUfWSfXQfZOf`MfbKfcIfeHfgGfiGfkFelEdn\ EcpDcrCcsCcuBcwAcyAczEcyHcxKcxOcwRcwUcvYbu`auc`tf_\ tdZrbYqaXp_WoYVmXUlVTkTSjSRhQQgOPfNOeLNcJNbIMaGM`E\ LZDLYBKX9KW9JX8IY8HZ8G_7E`7Ca7Bb7Ac69b68a67`66_55Z\ 54Y53X52W41U40Q40M40I30F30C30930630540430321232343\ 4545656767878A89C9AEABGACIACKADMAEOAFQAGSAHUAIWAJY\ AK_ALaBLcCMeDNgEOiGPkIQmKRoLSqMTsNUzPNwNUuL_sKeqIk\ oHqmIrkJriKsgLseMscNtbOtbPucQucRudSvdTvcSwdUveWueY\ uf_tgatgcsheshgriiqjkqjmp } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 16-04-14 (Metamorphosis [A-7,M-7])
by Jim Muth 16 Apr '14

16 Apr '14

FOTD -- April 16, 2014 (Rating A-7,M-7) Fractal visionaries and enthusiasts: Today's image shows an order-13 minibrot just beginning to feel the effects of the quadratic aspect of the parent fractal, which on the surface is an everyday Mandelbrot set. Today's scene is located in the northern branch of Scepter Valley of the large minibrot on the main spike of the parent M-set. The name "Metamorphosis" simply points out that the central minibrot is starting to change from an order-13 minibrot into a quadratic one. The image is filled with hills of 'antibifurcation' one of which will appear as tomorrow's fractal image. Neither the art nor the math aspects of the image are overwhelmingly exciting, which prevents me from rating either of them any higher than a 7. And the calculation time of 4 minutes is definitely on the slow side. Considering all this, checking the finished image on the web sites could be the best choice. So enjoy calculation freedom. Check the web sites at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> After a morning low of 25F -4C, the temperature rose to an afternoon high of only 46F +8C. The fractal cats were unhappy about the chill and even more unhappy about the angle of the sun, which now merely skims the edge of their shelf. The humans kept busy doing the usual boring stuff. The next FOTD will be posted in about 24 hours. Until then, take care, and wonder what comes next. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Metamorphosis { ; time=0:04:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip float=y center-mag=-1.777252088186267/+0.00042575900154386\ /1.608245e+010/1/-167.5/0 params=13/1e+055/0/0 maxiter=2250 inside=0 logmap=748 periodicity=6 colors=000ARcARcARcARcAQdAQeARfARf6Qf0Qg0Pe1Pc2Oa3\ N_4MY5LV6KT7JR8IP9HNAGKAFKAEKADKACKABKAAKzzzxgphYd\ TOTEFHDJTCNcBRoBUzGXrK_kObdSdYZGfdML0L5AFLJ9`S4pQ9\ cODSNHGJFWGEkLRZQcNUoBSlCRjDPgEOeELc9Ia4G`0F5Nb8Qy\ ASt8Qo6Pj4Oe2Nf3Kf3If4Gf4ELcTTSZ_Hcf6h63FW4XL3MA1B\ Oj7BX_6wK4cD2K62gjh5wX3hM2UB1FfVLSKEEA7OMPCBC4Ci39\ Y26N13BG7EC5A837413sBreJskzZ_jQOVHCF8SQgfJwL9UQDtJ\ 9eD6S63ETNCLH9EB6753sylei_SVOEFCT19SP0IG0980FWBAL7\ 5A3j80YjEPZAHN78B3PuXIfOCTG6E8EIp9OK6GD386WzTOjLGV\ E8F7yRv59kWIZG9HcO5UI3KC2A61P6BG28A15502xKgcDTK6EB\ Nc8HU5BK25AmTATCBflKW_FLOAAC5rFHdBCR78D34VI0KC0A60\ x6PIdxCRc6DKmmmVVW2L61F41A3051ETXALO7EG378hjGlvTOT\ EJPfEIW9CL46A8BZ45HediLKNhO3UG2zcUm052m0AUg7hLOMFk\ CpVa6NS4FJ3791QCED674w92cz1K3Uz8Uz6Uz4Uz2UzeUzYUzP\ UzHcz8czNczHczBcz5czVczZczgmzXmzMmzBmzRmzKmzDmz6mz\ UwzVwzFwzjwzNwz6wz3wz2wz1 } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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