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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal has been named "Halfway Midget". I gave it this name not because of its behavior, but because the generating formula of its parent fractal is Z^(2.5)+C, and 2.5 of course is halfway between 2 and 3. Midgets in this range come in all shapes. The shape of the midget in today's picture, with the midget splitting along its East Valley, is one of the most frequently seen. I originally found today's midget by using the MandelbrotBC formula. But when the image was completed, I realized that the second parameter was set to pi, and the formula was therefore drawing the same image as Fractint's built-in manzpower formula would draw. I then rendered the image with the manzpower formula, but found it too slow. I finally turned to my own MandelbrotN formula, and found that this formula draws the identical image in 2/3 the time of the manzpower formula. In my opinion, the most notable thing about the image is the inconspicuousness of the branch cut discontinuities. The breaks are there, but they are so well hidden that unless looked for, they would never be noticed. All in all, it's a slightly-above-average image, well worth the rating of 6. Rendering the image with the fastest formula, MandelbrotN, takes 4-1/2 minutes. Downloading the GIF image file is even faster, but before going for the download, give Paul and Scott a chance to post the image file to their web sites. The GIF image will be available for download at: The fractal weather today was perfect. The sunny skies, low humidity, and temperature of 81F 27C made the cats as well as myself happy. Until next time, take care. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Midget_and_a_Half { ; time=0:04:34.35--SF5 on a p200
reset=2001 type=formula formulafile=slices.frm
formulaname=MandelbrotN passes=1 center-mag=-0.923\
23411769327450/-0.00079409795476115/2.610506e+008/\
1/-14.999 params=2.5/0/0/0/0/0 float=y maxiter=3500
inside=0 logmap=106 periodicity=10
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}
frm:MandelbrotN {; Jim Muth
b=p1, z=p2, c=p3+pixel:
z=z^(b)+c,
|z| <= 16
}
END 20.0 PAR-FORMULA FILE==================================
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times.
