Print Page - Spacefilling Seahorse Valley

Title: Spacefilling Seahorse Valley
Post by: Pauldelbrot on June 24, 2014, 11:25:48 PM

Spacefilling Seahorse Valley

(http://nocache-nocookies.digitalgott.com/gallery/16/511_24_06_14_11_25_47.jpeg)

http://www.fractalforums.com/index.php?action=gallery;sa=view;id=16336

A Triple Matchmaker parameter slice near a looking glass. Outside the regions with a stable attractor (black Mandelbroid structures and minibrots) space is filled with details. Seahorse Valley details, in the form of the dendrites clinging to the valley walls. But the seahorse centers have expanded cores reminiscent of Supernova's, and the valley space is filled with an infinite regress of seahorsey stuff and dark, five-armed Julia matter from a parallel dimension.

Title: Re: Spacefilling Seahorse Valley
Post by: Dinkydau on June 24, 2014, 11:29:52 PM

Well-done

Title: Re: Spacefilling Seahorse Valley
Post by: Roquen on June 25, 2014, 11:52:22 AM

My search-foo is failing me. Can you translate the description?

Title: Re: Spacefilling Seahorse Valley
Post by: Pauldelbrot on June 26, 2014, 12:33:46 AM

Quote from: Dinkydau on June 24, 2014, 11:29:52 PM

Well-done

Thanks!

Title: Re: Spacefilling Seahorse Valley
Post by: Pauldelbrot on June 26, 2014, 12:38:27 AM

Quote from: Roquen on June 25, 2014, 11:52:22 AM

My search-foo is failing me. Can you translate the description?

What part didn't you understand?

Title: Re: Spacefilling Seahorse Valley
Post by: Roquen on June 26, 2014, 01:31:15 PM

This part: A Triple Matchmaker parameter slice

Title: Re: Spacefilling Seahorse Valley
Post by: Pauldelbrot on June 27, 2014, 02:29:57 AM

Quote from: Roquen on June 26, 2014, 01:31:15 PM

This part: A Triple Matchmaker parameter slice

"Parameter slice" = 2D slice through the parameter space (in this instance eight-dimensional). Basically, "Mandelbrot rather than Julia".

"Triple Matchmaker" = $z_{n+1} = \frac{z_n + \frac{a}{\sqrt{3}}}{b(z_n^3 - \sqrt{3}az_n^2 + cz_n + \frac{ac}{\sqrt{3}}} + d$ (note the four complex parameters a, b, c, and d, hence eight dimensional parameter space.

Title: Re: Spacefilling Seahorse Valley
Post by: Roquen on June 27, 2014, 07:42:45 AM

Thanks. Now all is clear.

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Fractal Art => Images Showcase (Rate My Fractal) => Topic started by: Pauldelbrot on June 24, 2014, 11:25:48 PM