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Aug. 28, 2012: The Edge of Infinity Aug. 27 Aug. 30 2012 FOTD Home
 Rating 8

edge of infinity

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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