Print Page - Mandelbrot Foam Ib-III

Title: Mandelbrot Foam Ib-III
Post by: Pauldelbrot on January 08, 2013, 10:42:26 PM

Mandelbrot Foam Ib-III

(http://nocache-nocookies.digitalgott.com/gallery/13/511_08_01_13_10_42_26.jpeg)

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.

Title: Re: Mandelbrot Foam Ib-III
Post by: Alef 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.

Title: Re: Mandelbrot Foam Ib-III
Post by: cKleinhuis on January 09, 2013, 10:40:33 AM

nice pics pauldel, have you the formula described somewhere ?!?!?

Title: Re: Mandelbrot Foam Ib-III
Post by: Pauldelbrot 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.

Title: Re: Mandelbrot Foam Ib-III
Post by: Alef on January 11, 2013, 10:36:44 AM

Now you need nice name for formula, and then to UF database;)

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Fractal Art => Images Showcase (Rate My Fractal) => Topic started by: Pauldelbrot on January 08, 2013, 10:42:26 PM