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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Because the higher order Mandelbrot sets tend to be monotonous, I usually do little exploring in them. But today, while idly wandering through the Z^7+C fractal, doing a speed check of a test formula, I zoomed deep into a spiral and found a midget. As the exponent of Z increases, the size of the midgets it contains also increases. In fractals of Z^16 and up, midgets become so large that they shift from hard to find to hard to escape. But as the midgets themselves grow ever larger, the patterns around them, which make the midgets so interesting, become ever smaller and more condensed toward the midget. To make things worse, the patterns all start to look the same, but despite this bleak outlook, an interesting midget still occasionally pops up, today's image being a prime example. With its seven tightly wound spiral arms, there is no doubt that the midget in today's image lies in a spiral. These arms surround the midget so tightly and so completely that I decided to name the image "All Enclosed". Considering the near one-hour render time of the parameter file, the rating of 6 might be a bit liberal. I recommend letting Paul and Scott do the rendering work and then downloading the image from their web sites at: The fractal weather today here at Fractal Central was sunny but brisk and breezy. The fractal cats enjoyed the sun, but they complained about the brisk temperature of 54F 12C and fresh breezes. And if I don't get some work done, I'll have customers complaining. Until next time, take care, and what size shoe does a bigfoot wear? Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
All_Enclosed { ; time=0:41:59.16--SF5 on a P200
reset=2002 type=formula formulafile=slices.frm
formulaname=MandelbrotN7 passes=1
center-mag=-0.81581942134366960/+0.560929165960617\
90/2.546927e+013/1.0508/82.1226980580561445/0.8125\
65191541250176 params=0/0/0/0 float=yes
maxiter=24000 inside=0 logmap=2730 mathtolerance=/1
colors=000mUsmUumUwmUxmUzmUzmUwmUtmUqmUnmUkmUhmUem\
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_mU_mU_mU_mU_mU_mU_mUamUcmUemPfmKhmFhmAjm3lm0nm0om\
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sWwsPzqJzqDzq6zq0zq0zq0zs0zw0zx0zz0zz0zz3zzBzzJzzP\
zzDzz1zz0zz0zz8zzDzzDzzDzzDzzDzzDaza0zw1zjJzY_zNoz\
9zz0zz0zz0zz1xz96zn8zoBzq
}
frm:MandelbrotN7 {; Jim Muth
z=p1, c=p2+pixel:
z=z*z*z*z*z*z*z+c,
|z| <= 16
}
END 20.0 PAR-FORMULA FILE==================================
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