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Author Topic: Fractured Mirror and Fractured Mirror II  (Read 957 times)
Description: Herman Ring c-plane M-Set images
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Fractal Senior
Posts: 2592

« on: February 14, 2009, 12:43:32 AM »

The "standard" parameter Antimatter Mandelbrot, zoomed on the terminus of the linear Mandelbrot feature to the north. There is a small curved version of this feature crossing it before its terminus and numerous other interesting features.

The "fractured mirror" name has double meaning: first, the stuff at lower right looks a bit like shattered reflective stuff; second, the image is quasi-symmetric in the Y-axis, but with intact Mandelbrot buds on the left reflected on the right as "damaged" versions.

In fact, the buds are intact on both sides, in that there is an extra finite attractor in corresponding regions on both sides. But the selected critical point does the "Mandelbrot thing" on the left side only, and on the right side, it does not seem to "own" the attractor and one gets pieces of connected Julia set and complicated geometry where the attracting basins of zero, infinity, and the "extra" attractor compete for the critical point as the parameter varies.

A red to orange to yellow to white smoothed-iterations gradient is used for the points convergent to zero and a blue to pink to white one for the divergent points.

Three more layers get the Mandelbrot interior pixels. One is maroon to black, by smoothed iterations, and applied only to points where both critical points go to the same attractor and that attractor is neither zero nor infinity. The second is pink to yellow to pink again, applied to the same regions with HSL addition, and is based on phi rather than smoothed iterations. It creates the shimmery color shifts, "dings" and "cones", and other features, particularly in the "fracture zone" at right. Lastly, a barely noticeable layer with an aqua to dark blue to black smoothed-iteration gradient colors points where the critical points go to separate attractors, neither of which is zero or infinity. That is, points for which the dynamics has /four/ attractors.

A small blue mini-Mandelbrot is visible in the fracture "zone" at lower right, surrounded by repeatedly-doubling patterns of the three other basins.

For extra added bonus fun, the image is full of seahorse tails and other nifty and often quite-complicated geometric forms.

Fractured Mirror II is zoomed modestly about the blue mini Mandelbrot at lower right in Fractured Mirror. The gradients have been tweaked somewhat in hue and distribution to better fit the image.

The tripled calculation time for this zoom is a result of the diagonal band of brownish at the edge of the largest "ghost bud" (the one containing the minibrot). The "Julia interior" points within this region are very high iteration -- tens or even hundreds of thousands of iterations.

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

Detailed statistics:
Fractal: Herman Ring Mandelbrot, c-plane
Location: angle parameter ~= phi (0.61803398), north-central area

Name:Fractured MirrorFractured Mirror II
Date:February 11, 2009February 12, 2009
Min Iterations:100100
Max Iterations:1,000,0001,000,000
Anti-aliasing:3x3, threshold 0.10, depth 13x3, threshold 0.10, depth 1
Preparation time:1 hour1 hour
Calculation time:5 hours15 hours (2GHz dual-core Athlon XP)

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