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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal pictures a quadratic midget. There is nothing unusual in having a quadratic midget at the center of the screen. Most of my images have them. But this midget is strange indeed. By their nature, quadratic midgets are surrounded by symmetrically spaced elements that continually split in two as they approach the midget. The first indicator of a midget is the presence of two symmetrical elements that split into four similar but smaller elements. This splitting continues in the series 2,4,8,16,32... as the elements approach the midget. We now can see what is wrong with today's midget, which I have named "Somber Snowflake". I gave the image this name because the pattern surrounding the midget is shaped quite like a dark snowflake with a green aura. But snowflakes have six sides, and the number 6 is not part of the 2,4,8,16... series. Something has gone wrong. Some other series has infected the quadratic series, and this infection will become only worse as the exploration of the Z^3+x(Z^4) fractals continues in the days to come. Though it is on the dreary side, today's image rates a 6, which is just a little above average. The render time is a speedy 2-1/2 minutes, which results in an overall value of 233. The pre-rendered GIF image is available on the FOTD web site at: With sun and a temperature of 61F 16C, Wednesday was a rather pleasant day here at Fractal Central. Thomas, the oversized orange, spent several hours in the yard. Tippy, the lean wiry tabby, passed the day sleeping on his window shelf. Since 14-year-old cats do little but sleep, it was hard to tell if Tippy did not feel good. In the evening all appeared well when the tuna treat vanished as it should. This morning is starting with clearing skies and warmer temperatures. I expect a good day for the duo. As for me, being not quite as old on the human scale as the cats are on the cat scale, I still enjoy an occasional bit of the unusual, but when it appears it will be another in a seemingly unending stream of normal days, with the exception of a new fractal at the end. Until tomorrow, take care, and fractals are never boring. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Somber_Snowflake { ; time=0:02:34.39--SF5 on a P200
reset=2003 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=ident passes=1
center-mag=-0.54195976260355410/+0.002250716455883\
61/127978.5/1/-52/1.42828571886299827e-009
params=1/3/0.357/4/0/0 float=y maxiter=1000
inside=0 logmap=37 periodicity=10
colors=000NMfONgPOhQPiRQjSRkTSlSTmRUnRVmQWlPYkP_j`\
kf_mcZr`YvXWyUUzRTyOQtQNoSLjTIeVG`WCXT9TR6PP3LN0IL\
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zfXzeazdazeazfazgazgazhaziazjazjazkazlazl`zp_zsZzv\
YzyXztXzoXzkXzfXzaXzYXzTXzOXzKVzIUzHTzGSzFQzDPzCOz\
BNzALz8Kz7Jz6Iz5Hz4Iz9JzD }
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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