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Author Topic: Twofold Seahorse Valley  (Read 1049 times)
Description: Matchmaker Mandelbrot image
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Pauldelbrot
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pderbyshire2
« on: April 10, 2009, 08:01:52 AM »



The Mandelbrot zoom generated on the way to producing the Trinity Campus Julia set image.

A seahorse valley (leftmost and rightmost valley walls) intersects a period-3 bud (edge at left, intersecting left wall of valley).

Triple seahorse spirals can be seen at far left, attached to the sprouts of the period-3 bud and in the period-2 bud of the seahorse valley.

At lower left is a green area where there are no attractors at all. The gradient is from iterating both critical points one million times in tandem, measuring their separation each iteration, and averaging.

The broad central band of blues and purples is in the period-3 bud in the seahorse valley (so no second attractor). The triple spirals are due to the period-3 nature of the attractor there.

Seahorses are attached at right. This and the triple-seahorse area at far left have separate gradients and separate layers. Both critical points' smoothed iterations are averaged to determine color in these layers.

The final layer gives a simple gold gradient to points with two attractors. Again, both critical points' smoothed iterations are averaged to determine color in these layers.

The Trinity Campus Julia set corresponds to a point near the center of one of the buds in the column adjoining the far-right gold region.

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

Detailed statistics:

Name: Twofold Seahorse Valley
Date: February 19, 2009
Fractal: Matchmaker Mandelbrot set
Location: b-plane; a = -0.854015 - 0.330706i
Depth: Very Shallow
Min Iterations: 1
Max Iterations: 1,000,000
Layers: 4
Anti-aliasing: 3x3, threshold 0.1, depth 1
Preparation time: 2 hours
Calculation time: 23 hours (2GHz dual-core Athlon XP)
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bib
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« Reply #1 on: April 10, 2009, 09:17:25 PM »

Your fractals are great, Pauldelbrot, and your explanations very interesting. Thanks  cheesy
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Between order and disorder reigns a delicious moment. (Paul ValÚry)
Pauldelbrot
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pderbyshire2
« Reply #2 on: April 10, 2009, 09:51:10 PM »

You're welcome.
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Nahee_Enterprises
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« Reply #3 on: April 18, 2009, 01:40:10 AM »

I really like this image very much!!!

And I agree with Jeremie Brunet (BIB) concerning your detailed explanations.  I appreciate the time you take for entering such information for each of your fractal postings.

Thank you for sharing with us!!!     smiley

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