August 15, 2011: Antibifurcation | Aug. 14 | Aug. 16 | 2011 | FOTD Home |
Fractal
visionaries
and enthusiasts:
Today's image is named "Antibifurcation" because it shows the scene of
the horrendous crime of antibifurcation, where, in total violation of
the laws of fractal math, the number of elements around the center
shrinks to a tiny fraction of its value instead of steadily doubling as
the laws of fractal math state it must do.
But actually, there is no crime at all. The image shows a
minibrot in the basin of attraction of a larger but still infinitesimal
minibrot lying near the limit of the main spike of the Mandelbrot set,
which is (-2). When a minibrot lies in the basin of a larger
minibrot, this antibifurcation always happens. By contrast,
minibrots in the basin of the M-set itself continue bifurcating in the
normal manner, with no setbacks, until reaching the limit of infinity
at the edge of the M-set.
The curving tentacles in the image are caused by the closeness of the
scene to the cutoff point of 2. Why the tentacles curve and
twist
in such an unlikely manner is known only to the gods of mathematics,
and since I am not one of that exalted group, I have no idea why the
image appears as it does. All I can do is apply colors to the
forms that were already there.
The rating of an 8-1/2 is held down because such scenes are quite
common in the world of fractals. I added a half-point bonus
for
the coloring work I put into the image, but even this seems a bit
liberal.
The calculation time of 23-1/3 minutes is slow, but still reasonable
for an image with a magnitude of almost 10^58.
Heavy clouds and light rain spoiled the day here at Fractal
Central. The fractal cats approved of the temperature of 73F
23C
even though to the humans it felt unusually chilly for mid-August.
The next FOTD will be posted in 24 hours. Until then, take
care,
and I once had faith in science, but now I'm not so sure.
Jim Muth
jimmuth@earthlink.net
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