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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Unless I have an operational time machine hidden in the garage, the year it was 24 hours ago is, always was, and always will be 2008. But old habits are like old fractals. They die hard. Today's image takes us to a bud on the north shore of HyperEast Valley. I named the image "Deep HyperRadical" because it sits deep in the interior of the bud, and buds, along with their associated elements, are sometimes called radicals. This particular bud is a very tiny one with a very high periodicity, which lies comfortably between much larger buds of much lesser periodicity. I have no idea why today's image, which lies inside this tiny bud, should appear to have a cycle of 6. Yes, there are more unusual scenes of varying cycles lying as deep as it is possible to go into the center of today's image, and likely extending to infinitesimal infinity. These scenes are not mere boring fractalish repeats of the top scene. Each level has a character of its own. The maxiter of today's image is an arbitrary choice. As the maxiter is increased, the open areas with the twisting greenish arms gradually fill in, until ultimately they are filled solid with fractal debris. In my opinion, the image rates an honest 9. It is worthwhile artistically and interesting mathematically. And its calculation time of 3 minutes is not bad either. Of course, for extra convenience, the finished image is posted on the FOTD web site at: Absolutely miserable weather prevailed here at Fractal Central on Friday. The day began with one inch, or 2.5cm, of sleet on the ground. The sleet changed to freezing rain by 9am, and it rained steadily for the rest of the day, while the temperature slowly rose to above freezing by afternoon, leaving an inch of heavy wet slush everywhere. The fractal cats watched from the front window shelf as I squeegeed away the sloppy mess by hand. The rest of my day was easy enough, though a small but hurried design job is expected tomorrow. The next FOTD will appear in about 24 hours. Until then, take care, and is the Mandelbrot set infinite or half infinite? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Deep_HyperRadical { ; time=0:03:13.47-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=HyperMandelbrot2 passes=1 periodicity=0
center-mag=+0.2689640429736179/+0.0054866527972904\
72/5.9811e+007/1/105/0 params=0/0/0/0/1/0/1e-100/0
float=y maxiter=1900 inside=0
colors=000hzRizQizPizPjzOjzOjzNkzNkzMkzMlzLlzKmzKm\
zJmzJnzInzInzHozHozGozFpzFpzEpzEqzDqzDqzCrzCrzBszA\
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`k_ak_ak`bj`bjabjacjbcjbcjcdicdideideieeiefiffhfgh\
gghgghhhhhhhiigiigjigjjgkjgkjglkflkfmlfmlfnlfnmfom\
eonepnepneqoeqoerpfsoernernermdrmdrldqkcqkcqjcqjbq\
ibphbphapgapQEzZQugapnpgooipnkpmlqlnrkprjqsisthuuh\
ythwthvthtshsshqshprgoqgo }
frm:HyperMandelbrot2 {; periodicity must be turned off
a=(p1),b=(p2):
q=sqr(a)-sqr(b)+pixel,
b=(p3+2)*a*b+p4,
a=q,
|a|+|b| <= 100 }
END PARAMETER FILE=========================================
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times.
