Three and Seven

[Pauldelbrot]

This one has two attractors, one of period six (from the trifurcation of a period 2 attractor) (blue gradient) and one of period seven (purple gradient). The shapes of the familiar "classic Julia" fractals for these periods occur, but they are forced to intertwine. Petals of the period-6 basin have to fill the narrow gaps between the petals of the period-7 basin and vice versa, resulting in an infinitely complex filigreed boundary with spiral extensions.

Both basins are colored by smoothed iterations.

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

As always, the picture above is a link and a 2048x1536 jpeg version is available there, with a png available upon request.

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

Detailed statistics:

Name: Three and Seven
Date: February 5, 2009
Fractal: Matchmaker Julia set
Location: a = -1.316107i; b = -0.12517076664 + 0.22518318594i
Depth: Very Shallow
Min Iterations: 20
Max Iterations: 100
Layers: 2
Anti-aliasing: 3x3, threshold 0, depth 2
Preparation time: 10 minutes
Calculation time: 6 hours (2GHz dual-core Athlon XP)