September 13, 2011: A Siegel Connection | Sept. 12 | Sept. 14 | 2011 | FOTD Home |
Fractal
visionaries
and enthusiasts:
Today's image in the Mandelbrot set lies within the range of
conventional math, yet it rates an 8.5. This shows that the
more
accessible shallow parts of the M-set are not quite as thoroughly
explored as some might assume. The image is located in the
debris-filled radical of a remote bud on the northwest shore line of
the main bay of the M-set.
The name "A Siegel Connection" refers to the resemblance of the basins
in the image to the so-called Siegel Disks of the siegel-disk fractals,
the Julia sets with a C-value of -0.390541,+-0.586788i.
Actually,
I am not sure what is so special about Siegel Disk fractals.
I
assume the corresponding Mandelbrot points of the official Siegel Disks
are on the exact edge of the M-set, yet an infinity of other points are
also on the edge. Why then should these particular points be
so
special?
As is usually the case with fractional ratings, the extra half-point is
a reward for my coloring, which is the greater part of the image.
The extremely brief calculation time of 45 seconds can be attributed to
the relatively shallow magnitude of 3*(10^11), which is within the
range of the high-speed conventional math routine.
A near perfect day prevailed here at Fractal Central on Tuesday. The
blue skies, puffy clouds, gentle breezes and temperature of 84F 29C
were just what the fractal cats ordered. They spent the day
in
their window, wishing they could go out and be a part of the world.
The humans passed the day just being human, which is sometimes not as
easy as it appears. The next FOTD will be posted in 24
hours. For all I know, it might make it. Until
then, take
care, and are fractals animal, vegetable or mineral?
Jim Muth
jimmuth@earthlink.net
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