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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image of a Julia set shows a Siegel disk fractal. My math encyclopedia implies it is the only Siegel disk fractal, though it is obvious that a mirror image fractal exists at C=-0.390541+0.586788i. The Siegel disks are the flat but irregular concentric rings filling the 'inside' part of the Julia set. They were made visible by the 'bof60' inside fill. These rings are actually the limiting case of spiral arms that have tightened to infinity, where they will take an infinity of revolutions to converge an infinitesimal bit closer to the central point. The spiral arms have become true closed curves, just as the circumference of a circle of infinite radius on a flat plane becomes a true straight line. I know of no special significance in fractals that contain Siegel disks, though I feel that there must be something of value in them. Why else would they have earned an entry in the math encyclopedia? One thing certain is that today's fractal contains some interesting sub-images. If I find anything of unusual worth, I'll post it as tomorrow's FOTD. I rated today's image at a 7 for its mathematical interest. The name I gave it -- "Siegel Disk Fractal" -- is its description. The calculation time of 37 seconds is true on the P2000 machine. On the P200 it would take about 2 minutes. On the FOTD web site, however, the image has already been rendered, and is posted for instant viewing. To see today's image as well as many past images, direct your browser to: With a high temperature of 88F 31C here at Fractal Central, and with the sunshine dimmed by haze, Sunday was too summery to be considered perfect. But it was good enough to satisfy those who had planned Father's Day outings. At the same time, the indoor climate was good enough to please the fractal cats. And the work was slow enough to give me a restful day, which is all I can ask for on a Sunday. The next FOTD will appear in 24 hours on the same mailing lists and on the FOTD web site. Until then, take care, and be alert for flying Siegel-disc saucers. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
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END PARAMETER FILE=========================================
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