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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image reminds me of Haidinger's brush, and that is what I named it. Haidinger's brush is not a cleaning device or scrubbing device; it is almost like a fractal. The brush is not a real brush at all; it is a figure seen at the center of the field of vision when gazing at a smooth and polarized source of light, such as the clear blue sky at 90 degrees from the sun. This ability of the unaided human eye to detect polarized light is little known, but most certainly does exist and can be scientifically demonstrated. Though it is not actually a sixth sense, it comes rather close. A far more complete discussion can be found on the internet at: As a fractal, today's image rates a 6. It was created by subtracting 1.2 parts of Z^(-0.93) from 1.2 parts of Z^(0.93) and adding (1/C) instead of plain C. The resulting parent fractal has a large bay with a very extended, drawn-out shoreline dotted with tiny bays. Today's scene is located on one of the arms of a 'star' at the tip of the filament extending from one of these bays. The image is not all that different from what would be found in the classic Mandelbrot set at a similar location. Therefore, I could rate it no higher than an average 5. But this is the *FOTD* average. And the FOTD average is well above the average of all fractals  so the image is worth a quick look, if not the 23-minute render time.That quick look may be found at Paul's web site: Scattered thunder-showers started popping up in the local area around 4pm on Saturday, finally joining together into one monster storm at 7pm, which flooded many sections on the east side of town. Fractal Central, which is on the east side, escaped with only a puddle of water in the basement; others were not so lucky. Before the rain arrived, the temperature reached 73F 23C, and there was enough sun to give the cats a satisfactory day in the grass. The forecast for today is for improved conditions. We'll see what happens . . . Today I find myself going on another of those trips to examine the old junque that others have discarded. Departure time is in an hour, so until next FOTD, take care, and the best is yet to come. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Haidingers_Brush { ; time=0:23:23.32--SF5 on a p200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix2 function=recip passes=1
center-mag=-1.97873106110103800/+1.880302311215394\
00/486402.7/1/-30/1.06422635703928847e-008
params=1/0.93/-1/-0.93/0.2/-30/0/0 float=y
maxiter=3200 inside=0 logmap=347 periodicity=10
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NyzNzzNzzNzzNzzQzzSzzUzzW }
frm:MandelbrotMix2 {; 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)+(p4)),
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.
