;     Date: Sun, 17 Jun 2007 19:49:08 -0400
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 18-06-07 (Siegel-Disk Fractal [7])
;       Id: <1.5.4.16.20070617195403.2a7f5ec0@pop.mindspring.com>
; ---------
; 
; FOTD -- June 18, 2007 (Rating 7)
; 
; 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:
; 
;        <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
; 
; and enjoy the enigmatic Siegel disks.
; 
; 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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  center-mag=0/0/0.9363296 params=-0.390541/-0.586788
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  logmap=yes symmetry=origin periodicity=no
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; END PARAMETER FILE=========================================
; 
;