Aug. 28, 2012: The Edge of Infinity | Aug. 27 | Aug. 30 | 2012 | FOTD Home |
Fractal visionaries and enthusiasts:
For
today's FOTD we
dived deep into the Mandelbrot image of August 25, to a depth of over
10^24 to find today's striking infinitesimal minibrot. The
magnitude is so great that if the entire Mandelbrot set were included
at the same scale, it would be larger than the galaxy.
I kept the same color palette, which I kind of like. Greens
and
oranges remind me of a bed of marigolds. But reusing the same
colors holds down the rating, which might have been higher if I had
found new colors.
The name "The Edge of Infinity" is true of all fractals, especially at
the depth of today's image.
The image is a good example of anti-bifurcation. The
outermost
ring consists of 16 elements arranged in a circle around the tiny
central minibrot, and the next ring inward has the expected 32
elements. But in the following ring we find the count has
reset
itself to 8, from where it again begins doubling. This
resetting
indicates that the scene lies in the basin of a larger minibrot rather
in the basin of the parent M-set.
The image lies deep in the Seahorse Valley of the large minibrot on the
main spike of the M-set, where the iteration count is already quite
high. In addition, the magnitude is great enough to require
arbitrary precision math. As a result, the image takes almost
three hours to complete, making a trip to the web sites a necessity.
A virtually perfect day prevailed here at Fractal Central today. The
temperature of 86F 30C and photoshop (aka Kodachrome) blue skies made a
scene the Chamber of Commerce could only wish for. The
fractal
cats, being non-commercial, spent the day watching for a pet ferret
that escaped and is running loose somewhere in the area. The
humans, who have enough trouble with the fractal cats, do not need
ferrets to keep them occupied.
The next FOTD will be posted on August 30. Due to a prior
commitment, there will be no FOTD for August 29. Until then,
take
care, and don't wish for something until you are absolutely sure you
want it.
Jim Muth
jimmuth@earthlink.net
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