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Welcome to Fractal Forums > Fractal Art > Images Showcase (Rate My Fractal) > Mandelbrot Foam Ib-III
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Author Topic: Mandelbrot Foam Ib-III  (Read 1304 times)
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Pauldelbrot
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pderbyshire2
« on: January 08, 2013, 10:42:26 PM »
Mandelbrot Foam Ib-III



http://www.fractalforums.com/index.php?action=gallery;sa=view;id=13140

A zoom of some of the structures at the right side of the "curlicue hole" in Ib-II. Scaly patterns, spirals, and the ghosts of Mandelbrot buds all put in appearances.
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Alef
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« Reply #1 on: January 09, 2013, 08:43:38 AM »
At first it looked like some broken mandelbrot with perturbations, but now I see interesting structures inside, a mix between seahorse and kleinian nereis + sea anemones.
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cKleinhuis
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« Reply #2 on: January 09, 2013, 10:40:33 AM »
nice pics pauldel, have you the formula described somewhere ?!?!?
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Pauldelbrot
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pderbyshire2
« Reply #3 on: January 09, 2013, 09:43:14 PM »
Quote from: cKleinhuis on January 09, 2013, 10:40:33 AM
nice pics pauldel, have you the formula described somewhere ?!?!?

Thanks. There's a UF formula at http://www.fractalforums.com/index.php?topic=14541.0 -- it's an iteration with two complex variables and two complex parameters:

z_{n + 1} = z_n^2 + w_n^2 + c

w_{n + 1} = d\frac{w_n}{z_n}

The Julia images have been z-plane images with initial w specified along with c and d. The Mandelbrot images (including this one) have been c-plane images with initial w and z specified along with d.
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Alef
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« Reply #4 on: January 11, 2013, 10:36:44 AM »
Now you need nice name for formula, and then to UF database;)
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