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Welcome to Fractal Forums > Fractal Art > Images Showcase (Rate My Fractal) > Spacefilling Seahorse Valley
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Author Topic: Spacefilling Seahorse Valley  (Read 1067 times)
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Pauldelbrot
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pderbyshire2
« on: June 24, 2014, 11:25:48 PM »
Spacefilling Seahorse Valley



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.
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Dinkydau
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« Reply #1 on: June 24, 2014, 11:29:52 PM »
Well-done
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Roquen
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« Reply #2 on: June 25, 2014, 11:52:22 AM »
My search-foo is failing me.  Can you translate the description?
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Pauldelbrot
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pderbyshire2
« Reply #3 on: June 26, 2014, 12:33:46 AM »
Quote from: Dinkydau on June 24, 2014, 11:29:52 PM
Well-done

Thanks!
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Pauldelbrot
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pderbyshire2
« Reply #4 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?
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Roquen
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« Reply #5 on: June 26, 2014, 01:31:15 PM »
This part: A Triple Matchmaker parameter slice
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Pauldelbrot
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pderbyshire2
« Reply #6 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.
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Roquen
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« Reply #7 on: June 27, 2014, 07:42:45 AM »
Thanks.  Now all is clear.
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