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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image could be considered the halfway point on the quest for a great fractal. I stopped halfway because of the very busy day on Friday, which left little time for fractals. The image is a scene in the southern branch of Seahorse Valley of the parent Mandelbrot set that results when 0.6 parts of Z^(-1.5) are combined with 0.6 parts of Z^(+1.5) and straight C is added. Perhaps I should not say the image is a scene in Seahorse Valley. The image is a cross section of the center part of the entire valley. There is no midget M-set lurking boldly at the center, (though plenty midgets are likely lurking in the purple chaos along the upper and lower edges of the frame). In keeping with the trend lately, I gave the image no name or rating. The reason is that I had no time to do a proper search, and had to settle for a picture of the valley itself. The chief attraction in the picture is the curious features scattered through the center of the valley. Midgets might lie deep in these features, but I rather suspect that the features, in typical fractal style, go on forever with little or no change. One might call such features Cantor dust. The render time of 14-3/4 minutes is slow for an image of such mediocre worth. But relief for fractal indigestion is at hand on the FOTD web site at: Partly cloudy, cold and blustery weather here at Fractal Central on Friday, with occasional squalls of snow and a temperature of 32F 0C, did not worry the fractal cats, who passed the day playing and keeping warm. When the time for their treat arrived, they were worn out and ready to enjoy their food. As expected, my day was very busy, and the next week or so will be the same. The next FOTD will most likely appear in 24 hours. If it doesn't make it, you'll know the rush has turned out to be worse than anticipated. Until then, take care, and keep alert for new fractals. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
FOTD_for_Jan_20_07 { ; time=0:14:47.60--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=ident inside=0
center-mag=-0.54236448905823150/-0.006164703739392\
35/9755.016/1/-87.5/3.39722000530784385e-012
params=0.6/-1.5/0.6/1.5/0/0 float=y maxiter=72000
periodicity=10
colors=000RazQczPdzQ`zRYzSVzTSzUPzVLzWIzXFzYCzZ9z_\
6za9zcBzdDzfFzgHziJzkLzlOznQzoSzqUzsWztYzv_zwazrdz\
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zS7zR6zQ5zP4zN3zM2zL1zK0z }
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 PARAMETER FILE=========================================
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times.
