Fractal visionaries and enthusiasts:

In yesterday's discussion I mentioned Siegel Disks.   Actually, I'm not sure of the significance of Siegel Disks.   The math encyclopedia defines the Siegel Disk Fractal as a Julia set (of the Mandelbrot set) with c=-0.390541,-0.586788i.   But why this particular fractal is special is a mystery.   I can see nothing unusual or unique about it.   The corresponding point of the Mandelbrot set lies exactly on the boundary of the main bay, but other points on the boundary give similar fractals.   The answer must lie somewhere in one of the fractal books I have not yet come upon.

Today's image is an extension of the Siegel Disk idea, a Julia set of a point on the boundary of the Z⁶+C Mandeloid.   It is filled with things that closely resemble Z²+C Siegel Disks, with six large disks and an infinity of smaller ones, their position made obvious by the coloring.   The fractal is rather attractive, though its familiarity prevents it from earning a rating above a 6.

I named the image "Siegels on Parade", and why not?   After all, a parade with an infinity of marching Siegel Disks would take forever to pass the reviewing stand.   Luckily, the march is only symbolic, and the fractal takes only 3-3/4 minutes to calculate.   And even better, the already-calculated image is or soon will be posted on the FOTD web site for immediate and intense gratification.   The web site may be accessed at:
Sunday brought a prelude of spring to Fractal Central, with total sun and a temperature of 55F 13C.   The wind was a bit higher than ideal, but the fractal cats didn't mind a bit.

My day was uneventful, though I heard that a rather sizable job will be coming in sometime Monday.   The next FOTD will be posted in 24 hours.   Until then, take care, and is skepticism always the most rational approach?


Jim Muth
jamth@mindspring.com
jimmuth@aol.com

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