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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's discussion will be short because even though it is a Sunday, I was busy most of the day finishing a job which must be at the printer's tomorrow morning. But despite the rush, I found time to find a fractal. Don't ask how I find the time to locate all these fractals -- it's as much a mystery to me as it is to anyone. Today's FOTD resembles a midget under a shallow layer of water. I named it "Undersea World". The formula that I used to draw the image is the MandelbrotMix4, which calculated the expression Z^(-0.95)+Z^(-2.95)+(1/C). I have decided to give this overworked formula a rest for the month of August, and concentrate on things such as new and unfamiliar slices through the four-dimensional Julibrot figure, which is the sum of all Julia sets and all warped Mandelbrot sets. The parent fractal is a multi-lobed Mandeloid consisting of the typical fragmented debris that results when negative exponents of Z are calculated. But toward the center top lies a strangely different area. It is in this area where I found my midget. The image rates an average 5 on my scale, since I can't imagine something found in such haste having above-average value. The parameter file is another slow one, so the trip to: The fractal weather today was partly cloudy and oppressively humid with a heavy thunder-shower in the afternoon that caused local flash-flooding. Luckily, the rain fell just short of again flooding the fractal basement. The temperature of 84F (29C) was ideal for cats, but cats don't like wet grass, so the fractal cats spent the day indoors. Needless to say, with all the work and the rain that threatened to flood the basement, I found no time to philosophize today, and probably will find no time again tomorrow. But sooner or later the philosophy will come, and when I philosophize, I philosophize with no holds barred. So until tomorrow, take care, and be at peace. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Undersea_World { ; time=0:30:39.40 -- SF5 on a P200
; Version 2000 Patchlevel 9
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-0.05943680542175839/+1.33301484757948400\
/2.015923e+008/1/-125 params=1/-0.95/1/-2.95/0/0
float=y maxiter=3000 inside=0 logmap=656 periodicity=9
colors=000oidpmfppgdqZUqQWYcJqHKUwmwr<3>RStLKtGCt`Gn\
uKi<7>bRh`ShZTh<3>QWhXeVbnH<3>RWTORWMNZ<3>A4jwwm80lZ\
SVyrD<2>_Za<8>WZXWZWVZW<3>UZUJTL9ND<3>HDTJAXL8`N5dO3\
h<3>kFfyGi<3>XLYQMVDM`JNTOOMUPE`R1<3>TQMSQSQQX<2>LQk\
<3>0Hd<3>bUFlX9u_3SDCQYBMsA<5>WlGYjHZiI<3>edN<6>afB`\
fA`f8<3>Zf2<3>jPMmKRpGWsB`v7e<3>lDljFngGpeIrcJs<9>`Q\
l`Rk`Sj<3>_UhUYdO`aIok<2>IH9abWuwqsGF<2>C7M<3>PPFSUD\
VYC<3>fo5mv0<3>`jGYgKUdO<2>LW_PfvITc8J6<2>G7p<7>PSXQ\
VURXS<2>UdKVgIVlB<3>WcSX`XXZ`XXdZXg<8>LHpKGqIEr<2>E9\
uC7vA5y<3>D7sD7rG6p<2>P6j
}
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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