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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: What kind of fractal does the formula Z^0+C or 1+C create? It creates no fractal at all, just an empty circle. What type of fractal then does Z^(0.05)+C create? In this case the empty circle is lopsided, with no evidence of the typical fractal chaos. But take Z^2, subtract Z^0.05 from it, and then add C, and an interesting fractal does appear. I'll not try to describe the indescribable figure, but the oversized thing can be seen by entering the parameters -1, 0.05, 1, 2, 0, 0 into the M-Mix4 formula and letting it iterate. Today's midget lies in a prominent valley on the north side of this fractal. I named the image "Windmills of Chaos" when I noticed that the four open spirals toward the corners vaguely resemble windmill blades. And of course the chaos is there as always, lying in vaguely organized form all through the picture. With a render time of just under 5 minutes, running the parameter file is a bit annoying. A better choice is to give Paul and Scott a chance to post the GIF file of the image to their web sites at: The fractal weather today was very summer-like. In fact the temperature of 90F (32C) felt a bit too warm. The fractal cats enjoyed the warmth however, as they stretched to their full cat-lengths on the porch most of the afternoon. As for me, I'm about finished for the day. It's been another busy one, but I'll be here again tomorrow, with more fractal goodies. Until then, take care, and be at ease. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Windmills_of_Chaos { ; time=0:04:45.45--SF5 on a P200
reset=2001 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+0.64915135165492830/-0.619948053295606\
6/1320520/1/-134.999 params=-1/0.05/1/2/0/0 float=y
maxiter=500 inside=0 logmap=78 periodicity=10
colors=000d1gd1ge2hf3ig4jh5ki6li7lh8if8dd8`b9W`9SZ\
ANXAJVAETBARB5PB1V9F_7Td9fi6tjNokSklXgk_`hZZdXV`UR\
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TezPgzLizIdzG_zFqzKpzKpzK
}
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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