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Author Topic: Twisted Nebula  (Read 1944 times)
Description: Matchmaker Julia set
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Pauldelbrot
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pderbyshire2
« on: August 03, 2009, 03:05:23 AM »



A Matchmaker Julia set with two attractors, one fixed point and one 3-cycle. The fixed point is barely stable, close to becoming a 2-cycle, resulting in high iterations and via the spirals a need for aggressive AA; combined these make the image calculations quite slow.

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

Detailed statistics:
Name: Twisted Nebula
Date: February 9, 2009
Fractal: Matchmaker Julia set
Location: a = -0.854015 - 0.330706i; b = 0.1594267693808 + 0.05594006158511i
Depth: Very Shallow
Min Iterations: 83
Max Iterations: 10538
Layers: 2
Anti-aliasing: 3x3, threshold 0, depth 2
Preparation time: 10 minutes
Calculation time: 32 hours (2GHz dual-core Athlon XP)
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Duncan C
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« Reply #1 on: August 09, 2009, 03:31:23 PM »

Very pretty. I like the choice of colors and the pearly looking texture. Well done.
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Regards,

Duncan C
Pauldelbrot
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pderbyshire2
« Reply #2 on: August 10, 2009, 03:17:16 AM »

Very pretty. I like the choice of colors and the pearly looking texture. Well done.

Thank you.
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Nahee_Enterprises
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« Reply #3 on: January 08, 2010, 11:45:02 PM »

    A Matchmaker Julia set with two attractors, one fixed point and one 3-cycle.
    ....   Calculation time: 32 hours (2GHz dual-core Athlon XP)

    I like the choice of colors and the pearly looking texture.  Well done.

I missed this image before.  Glad I came back and started looking over some of the past few postings.  I agree with Duncan, very nice indeed!!!     smiley

If it were not for the rendering time, I believe this would make a fantastic zoom sequence.
 
« Last Edit: September 11, 2013, 08:09:32 AM by Nahee_Enterprises » Logged

Pauldelbrot
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pderbyshire2
« Reply #4 on: January 09, 2010, 02:49:12 PM »

If it were not for the rendering time, I believe this would make a fantastic zoom sequence.

Thanks. But I doubt it -- it's a Julia set image, so you wouldn't find minibrots or anything else much in there, just more views similar to this one. Mostly, with Matchmaker Julias I don't even bother to change the zoom rect; for all interesting parameters, the Julia set has all its representative structures occur inside the default zoom rect of my program. When a = 0 zero is a usually-repelling fixed point and this point does not seem to move much when a is perturbed. (The fixed points are the roots of bz3 + (b - 1)z - a. If you had a = 0 and b negative and large, you'd have a big sideways S shaped curve dropping steeply through the x axis left of the origin, rising steeply through the origin, and then dropping negative again to the right. Changing a away from zero a small amount moves the whole graph up or down a bit, but the steep part near zero means the root there doesn't move much. This doesn't change much, though becomes more difficult to visualize, if b is positive (or complex) and some of the roots are complex, except if b gets quite close to zero. Even then, the Julia set seems to always pass close to zero, though I'm not sure why. The only time it doesn't is when b is so large that zero attracts, and those Julia sets generally aren't very interesting.
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Nahee_Enterprises
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« Reply #5 on: January 11, 2010, 01:46:42 PM »


   
        If it were not for the rendering time, I believe this would make a fantastic zoom sequence.

    Thanks.  But I doubt it -- it's a Julia set image, so you wouldn't find minibrots
    or anything else much in there, just more views similar to this one.

Probably so, but it would make a mesmerizing and hypnotic video loop.    wink
 
« Last Edit: September 11, 2013, 08:11:18 AM by Nahee_Enterprises » Logged

kram1032
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« Reply #6 on: January 11, 2010, 09:52:45 PM »

looks like pure magic cheesy
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Pauldelbrot
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pderbyshire2
« Reply #7 on: January 12, 2010, 05:49:40 AM »

Thanks.
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