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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: We're in the middle of another rush today here at Fractal Central, so I'll have to keep the words to a minimum. Today's image has been rotated until it lies only 10 degrees from the Julia plane. When sliced at this angle, the bridges, which are made of Mandelbrot stuff and are actually plates, appear to have expanded to almost 6 times the width they have when sliced perpendicularly. In today's image, we see the entire lower half of the screen filled with the Mandel stuff that makes up the bridge. The straight edges of the bridge remain clearly visible. The banded Julia material in the lower half of the image has taken on a tortured, stretched, twisted look, which is not very attractive to look at. Also, the four arms in the upper right, which in yesterday's image converged in a vague spiral, have taken on a decidedly more spiral-like appearance. In the next FOTD, we'll rotate the view still closer to the Julia plane, and see what happens to the ever-broadening bridge of Mandel-stuff. Today's image renders in a quick 46 seconds, fast enough to make the download unnecessary. But for those who would still wish to download the finished GIF image file, the file is available at: The fractal weather today was partly sunny with occasional flurries of snow. With a temperature of 32F (0C), the fractal cats didn't even think of going outdoors. But I'm thinking of getting busy and finishing that job that's been fighting me most of the evening. I'll reappear tomorrow at about this same time, with the next in the series of rotation images. Until then, take care, and when working with fractals, don't get cold feet. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
FourPerfectSpirals { ; time=0:29:18.22, SF5 on a P200
; Version 2000 Patchlevel 9
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+0.09743271960894634/-1.19914809623739200\
/1.109749e+009/1/-139.999 params=1/-2/1/-15/1/0
float=y maxiter=7200 bailout=25 inside=0 logmap=466
symmetry=none periodicity=10
colors=000IH4IH4KJ8NMD<2>VUOYXS_ZX<3>jikmkoonsiqvbrw\
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0fX0fX0fV0fU0fU
}
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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times.
