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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal is filled with those goofy looking, cross-eyed, double spirals that characterize the East Valley areas of midgets. The eyes are everywhere. There are so many of them that I had no choice but to name today's image "The Goofiest Fractal". Well, I guess I did have a choice, but I decided on the name because I like it. The iterated formula subtracts Z^20 from Z^7 and adds C. The resulting fractal is an unassuming affair with X-axis symmetry and a curious dimple on the eastern border of the main bay. Within this dimple lies a fragment of an east valley. Unlike the East Valley of the classic Mandelbrot set, this valley has a row of midgets along its center line. These midgets are surrounded by the typical goofy-eyed Julia features of East Valley. Today's midget lies buried deep in one of the goofy-eyed spirals in the pattern around one of these larger midgets. This explains why today's image swarms with double spirals. I rated the picture at a slightly above average 6. At one time I briefly considered a rating of 7, but a second look convinced me that a rating of 6 would be the most honest. With its render time of 14 minutes or less, the parameter file is a bit on the slow side. With a download time of one minute or less, downloading the GIF files from the W.W.W. is the more efficient way to see the image. The GIF image files will be available in a few minutes on the W.W.Web at: A perfect sunny midsummer-like day in early Autumn today here at Fractal Central made the cats happy. The temperature, which should be around 70F 21C, actually reached 84F 29C. The cats showed their happiness by sleeping most of the afternoon. I have little philosophy today, since I'm still reading the Sep-Oct issue of "Skeptical Inquirer" magazine -- the official publication of CSICOP -- the Committee for the Scientific Investigation of Claims of the Paranormal. The topic of the magazine is the conflict between science and religion. As would be expected from articles written by rationalists, the opinions are biased heavily toward the side of science, but despite the bias, the articles are still quite informative. I'll hold off comment for a few days until I've finished reading the magazine, and the current activity on the Philofractal list dies down a bit. I'm considering the direction the FOTD is taking. Perhaps it's time to leave the world of Minibrots for a while, and get back to that four-dimensional (five-dimensional when time is included) stuff I was doing a while back with the Julibrot figure. We'll see how I feel in the days to come. I'll be more relaxed when I get the day's work finished, and the way to get finished is to get started. So until tomorrow, take care, and finish what you're doing, so you can enjoy the fractals without distraction. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
TheGoofiestFractal { ; time=0:14:06.51--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=ident passes=1
center-mag=+0.62576838904586850/+0.000016702092589\
72/8.099607e+009 params=1/7/-1/20/0/0 float=y
maxiter=1500 inside=0 logmap=-274 periodicity=0
colors=000_UISOELI9ED5IF6LG6OH6RI6UJ7XK7_L7bM7ZLCV\
LGRLKNKPJKTFKXBK`9Oc7Rf5Ui3Xl2_n4Vh6Qc8LZAGUCBPD7K\
MIJUOIaWHicGqkFpkEokDnkCmlBllAklAilAhmAgmAfmCenFdn\
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K_7QZBWXEZWHaULdTPeRTcQXZk`UldPmeKnhMokPolTlmWim_g\
nbdocaoc_pcXpcVhcWacWUdWNaWGZWJVVLSVNOVQLVSHVUEVQF\
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ziQzfJzcCz`6zZ5zX4zW3zU2zT2zS9zTFzULzVRzWXzXbzYhzZ\
nz_tz`zz`izOTzCCz0HzCLzOPz_TzkSzlRzlRzmQzmQznPznPz\
oOzoNzpNzpMzqMzqLzrmzRfzN
}
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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