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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's half-hour fractal is named "Mandelbrot Garden". I gave it that name after 10 minutes or so of staring at it, trying to make something of it. The name isn't too appropriate, but it's adequate. The formula behind the image is a very simple Z^(sqrt2)+C. When I go exploring in the area between Z+C and Z^2+C, I often choose the Z^(1.414...)+C fractal to explore. The reason I choose this fractal is because the midgets in it are often surrounded by the same 2-way symmetrical pattern that makes quadratic midgets so easy to find. Today's distorted midget, for example, lies in a feature that resembles one of the higher order scepters of the classic Mandelbrot set. And today's midget is located just where one of the Z^2 midgets would be expected. After a brief consideration, I decided to rate today's image at a 7, which might be a bit optimistic. The features are actually a bit more fractured than I would like to have seen, but the colors are pretty good. Actually, a 6-1/2 may have been a more accurate rating. As I remarked yesterday, I will not be posting the FOTD to ABPF until I get the current computer-ISP confusion straightened out. I'll probably end up with a DSL connection, though that has not yet been arranged. Regardless, the GIF image will appear on the Web at: The fractal weather today was totally miserable, with a raw mixture of rain and snow that kept the cats pinned indoors. The temperature of 36F (2C) did not help matters. I see it's time to shutter the shoppe and call it a night. Until next time, take care, and be sure to de-ice your fractals. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Mandelbrot_Garden { ; time=0:29:01.69 -- SF5 on a P200
reset=2001 type=formula formulafile=branchct.frm
formulaname=MandelbrotBC passes=1
center-mag=-0.1694281645165105/+1.5429071620987/6.34\
9252e+007/1/-87.5 params=1.414213562373/0/0/0 float=y
maxiter=15000 inside=0 logmap=707 periodicity=10
colors=0001zi3zp4zv7zs<2>CyjDxgFvdGuaIu_JsXLrVMpSOpP\
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lzsjzsjzuizvizvizxgzy<2>fzz0zP0zV0za
}
frm:MandelbrotBC = { ; Z = Z^E + C
e=p1
p=real(p2)+PI
q=2*PI*trunc(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| < 100
}
END 20.0 PAR-FORMULA FILE==================================
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times.
