Petals

[Pauldelbrot]

There is only one attractor, with period 6, for this Matchmaker Julia set, but there are parameter values close by for which there is a second. As a result, the basin is broken up by large regions of chaos that contain areas of higher iteration that resemble a disconnected classic Julia set. Essentially, the Julia set is that classic one, except extended to also bound the six-petaled structure of the attractor's basin, where the classic one has only one petal to bound as the sole attractor there is a fixed point.

The single basin is colored with a gradient, from white to purple to yellow, orange, red, and black, by smoothed iterations (computed as described for Dragon II).

As with all of these images, the actual maximum iterations setting was higher than the reported number; here I used 10,000 but the highest iteration to actually appear in the image was 100.

The slow calculation is a consequence of the very aggressive antialiasing, unfortunately a frequent requirement to do justice to Matchmaker Julia set images.

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

Detailed statistics:
Name: Petals
Date: February 21, 2009
Fractal: Matchmaker Julia set
Location: a = 0.53256 + 0.31163i; b = -0.942843205506 - 0.343975614912i
Depth: Very Shallow
Min Iterations: 7
Max Iterations: 100
Layers: 1
Anti-aliasing: 3x3, threshold 0, depth 3
Preparation time: 10 minutes
Calculation time: 6 hours (2GHz dual-core Athlon XP)