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Author Topic: The Blob  (Read 726 times)
Description: Triple Matchmaker Mandelbrot slice
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Fractal Senior
Posts: 2592

« on: July 05, 2009, 08:54:28 AM »

A slice of the Triple Matchmaker Mandelbrot set. The three layers correspond to the three critical points a, 0, and -a. (There is a critical value at d when d is not zero, but for this slice d is identically zero.)

The green component of pixel color comes from smoothed iterations of zero, the red component smoothed iterations of a, and the blue component smoothed iterations of -a. So the bright red areas are where a takes a lot more iterations than -a or 0 to converge, cyan areas had -a and 0 both take many iterations, yellow both a and 0, etc.

Many features are apparent. The first impression is of lava lamp blobs on a black background, and the blobs fairly densely filling space. The background points have no attractors, so the Julia set is the whole Riemann sphere for those parameter values. For almost all other points, all three critical points converge, but not always to the same attractor. There can be up to three separate ones, but it's hard to find anywhere where there are. It's easy to find places with two: look for places where two blobs overlap.

Also notable are cusps, the interesting blob structure at lower left, and some chains of blobby components that hint at the potential for Herman rings in some of the Julia sets.

Freely redistributable and usable subject to the Creative Commons Attribution license, version 3.0.

Detailed statistics:
Name: The Blob
Date: April 11, 2009
Fractal: Triple Matchmaker Mandelbrot set
Location: a-plane, b = 0.1033577 + 0.0109489i, c = -1.42628 + 2.70015i, d = 0
Depth: Very Shallow
Min Iterations: 8
Max Iterations: 1,000,000
Layers: 3
Anti-aliasing: 3x3, threshold 0, depth 1
Preparation time: 15 minutes
Calculation time: 79 hours (2.5GHz dual-core Intel E5200)
« Last Edit: July 16, 2009, 02:30:09 AM by Pauldelbrot, Reason: pic url changed » Logged

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