[NetBehaviour] homage to leavitt #3

James Morris jwm.art.net at gmail.com
Thu Nov 25 08:32:32 CET 2010


http://jwm-art.net/mdz/gallery/oldwooddish.png

Jonathon Leavitt, a Mandelbrot explorer, the discoverer* of
'de-bifurcation' or 'reverse-bifurcation' within the Mandelbrot Set.

This is what you're looking at: oldwooddish - homage to leavitt #3 -
'reverse-bifurcation'.

to find such images, you must be aware of a rule, as in the ancient
drawing language LOGO

but you follow the paths of the twists and the turns and distances
along the infinitely twisted border of the Mandelbrot Set.

as you are no doubt aware, you can zoom in and zoom in for ever within
the mandelbrot set and still see self-similarity.

this reverse bifurcation is a little different however, it only
appears to possess fractal bifurcation - in theory?

now, take the image i am showing you, divide it in half along the line
of symmetry and count the branches - 128.

128 64 32 16 8 4 2 1

after making 4 branches off a single main branch, to get to 8
branches, zooming further deeper takes one back through two branches,
4 branches, before 8 branches are found. one must remember the correct
place to make the branching magnification instead of heading straight
to the center all the time.

the location of the oldwooddish image within the mandelbrot set (which
itself is located within the complex (2D) plain bound by a radius of
2.0 (centered on 0,0)) is:

-7.621179376797638683152412470302754234697554266277384201803182452707988048871166668157739268919140091423417335237629214081127371665327888360528335010378835950994472786588199757e-1

9.573175593807915218110127195876981729185284295753173780078525497988166932168660068170631431015884613850090347745780605812248444859260422571076360932193737688403082995582081506e-2

and the numerical range from the left of the image to the right of the
image  is:
1.796668676625665441038967911552250775193750305575687707926958355510177201240113669896258768588917386783877219879474166891511967516410809575490262066086562660939534951057637354e-152

128 branches is the limit of the fractal bifurcation of the emblem in
this image. i feel like i constructed it, but i did not, it exists
whether anyone discovers it or not. somewhere, is the same image with
256 branches, somewhere else, there is 512, 1024, 2048, 4096, 8192,
16384, 32768, 65536... it's hard to believe that these things exist
without someone constructing them by carefully selecting magnification
sequences.

they exist!




* see http://mrob.com/pub/muency/reversebifurcation.html
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