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Fractal of the Day
by Jim Muth
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FOTD -- January 29, 2009 (No Rating) Fractal visionaries and enthusiasts: Since today's image is more of an experiment than an effort at fractal art, I decided to give it no rating. The parent fractal is a grotesquely bloated Mandelbrot set with order-1000001 undertones. Today's image lies in one of the elephant trunks in East Valley. I named the image "Crouching Minibrot" because part of it is occupied by a hidden minibrot. The black area at the right side of the image is the edge of a minibrot of order 1,000,001. This means it has exactly one-million similar bays around its perimeter, which caused me to open my desktop calculator. Since only four bays appear in the image, this means that only 1/250,000 of the total circumference of the minibrot appears on the screen. On my screen the four bays extend over a distance of 30cm or one foot, which means that the total circumference of the minibrot must be 250,000 feet or 7,500,000cm. Dividing this distance by 3.14159265 we determine that, at the same scale, the diameter of the minibrot whose edge appears at the right side of today's image must be near 2,400,000cm or 24km, which is near 15 miles. It's quite a minibrot. To see the entire circular minibrot, turn off the logmap and reduce the magnitude of the image to 1,000,000. Perhaps the most curious thing in the image lies in the peninsulas that separate the bays, where the same pattern repeats, only very slowly changing from one peninsula to the next. I see much stuff for investigation here. Despite all the weirdness, the image calculates in only 1-3/4 minutes, about the time required to visit the FOTD web site at:and appreciate the finished experiment there. Snow, sleet and freezing rain made for a most unpleasant day here at Fractal Central on Wednesday. The temperature of 30F -1C only added to the unpleasantness. But strangely, the fractal cats seemed to enjoy the day, watching the neighborhood snow removal activities from their window shelf, with obvious fascination. My day would have been pleasant had it not been for the task of clearing the fractal sidewalks. Five inches of sleet is quite heavy to move around. If nothing worse happens, the next FOTD will be posted in 24 hours. Until then, take care, and I wonder what the world is really made of. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Crouching_Minibrot { ; time=0:01:43.64-SF5 on P4-2000
reset=2004 type=formula formulafile=basic.frm
formulaname=DivideBrot5 passes=t float=y logmap=126
center-mag=+26.0517371691385/-0.177380788769248/1.\
700493e+011/1/80.7/0 inside=0 mathtolerance=0.05/1
params=1000001/100 maxiter=1500 periodicity=10
colors=000hgsghofikdkgclcbwVbrYbm_biabdcb`ecWgeRig\
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ADvBEpCFjDGdDGZN9BSQbfMguJkfLbSNUEPLM9fTOT_bFfp1RF\
3uHBsLHqPNoTTmXZk`didjjew }
frm:DivideBrot5 { ; Jim Muth
z=(0,0), c=pixel, a=real(p1)-2,
b=imag(p1)+0.00000000000000000001:
z=sqr(z)/(z^(-a)+b)+c
|z| < 1000000 }
END PARAMETER FILE=========================================
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times.
