Twisted Nebula

[Pauldelbrot]

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)

[Duncan C]

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

[Pauldelbrot]

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

Thank you.

[Nahee_Enterprises]

    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!!!    

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

[Pauldelbrot]

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.

[Nahee_Enterprises]

   

        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.    
 

[kram1032]

looks like pure magic

[Pauldelbrot]

Thanks.