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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: There must be a name for someone as obsessed with fractal midgets as I am, but if there is, I have yet to find it. Today's image features yet another midget. The little thing might be too small to be visible, but be assured, it is there at the center, waiting for revelation, though looking little better when seen in person than it does at this distance. The formula behind the image combines portions of Z^(-0.414213562373) and Z^(-2.414213562373). These two numbers are reciprocal to each other, and even more curious, the decimal parts of these numbers are equal to the decimal part of the square root of 2. This curious coincidence might have a deeper mathematical meaning, or it might not. In any case, the coincidence has little effect on the appearance of the fractal the numbers generate. The parent fractal resembles a first-quarter moon, (last-quarter in the southern hemisphere), with today's scene lying in some rather unique appearing material on the northern terminator of the moon. For unknown reasons I named the image "Eight-or-Sixteen". Because it is only a bit above average, I rated it a 6. Because the 7-minute render time is a bit slow, it might be more convenient to download the pre-rendered GIF image from Paul's web site at: The fractal weather Wednesday featured increasingly thick clouds as the moisture from a tropical storm drifted this way. But the temperature was a comfortable 75F 24C, and all else was under control, giving the fractal cats a pleasant day, actually romping in the yard. When their fun was done, the dynamic duo had an enjoyable treat of tuna. All-in-all they had one of their all-time best days. I hope their mood is just as congenial this week-end when I try to take up-to-date photographs of them for the soon-to-appear FOTD CD. As for me, my day will be the best only when I get the work done. And if I hope to do that, I've got to get started. So until next FOTD, which will appear on schedule on Saturday the 28th, take care, and solve the mysteries. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Eight_or_Sixteen { ; time=0:07:13.37--SF5 on a p200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+0.73830742505459010/+4.543148571881168\
00/7.456448e+008/1/-60/-8.19321895876440331e-005
params=1/-0.414213562373/3/-2.414213562373/0/525
float=y maxiter=1000 inside=0 logmap=134
colors=0000QS0Qh1Qx3Qm1QzLQzLQzLQzFUzLQzPUzLQzVUzV\
QzbRzaFzeBzfFzfBza8z`3xY0sZ0nL0nY0aD1fD6QDBLDFF3J9\
0M30N33P3BQ3RS3VS3ZU3aW3iY3l_3sa3xa3ve3ze3zf3zh8zj\
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zDDzDFzDHzBJz9Lz8Nx6Pw3Qw8QwBQwFPwJPxNPxQNxSNxWNx_\
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z90sD0lF0fJ0_L0UP0NQ0HU09W03_00a00c00h90nN6sY9wjFz\
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0cH0cW9ahQ_wfYzwWzzUzzSzzQzzPzzNzzLzzJzzHzzFxzDwzB\
sz9qz8oz6lz3jz1hz0ez0az0_z0Wz0Uz0Qz0Nz0Lz0Hz0Fz0Bz\
08z06z01z00z03z06z19z3Bz6Fz8Hz9JzBNzFPzHSzJUzLYzN_\
zPazQ_zSYzUWzWUzYSz_QzaPzcNzeLzfJzhHzjFzlDznPzaSzQ\
WzWWzWak8ak9clDcmFelJejLfgPfeQfcSjrjliznez7mShnnRh\
_coL_f6Yh0We0Jl06g00p00hg }
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 20.0 PAR-FORMULA FILE==================================
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