Puddles

[Pauldelbrot]

A Matchmaker Julia set with two attractors, both of period 35. The same "splitting" of one attractor into two interleaved ones of the same period that occurs in the Christmas Balls subspace (a = 0) affects all of Matchmaker, only when a moves off zero the interleaved attractors can cease to behave identically and start changing. In Puddles a dynamic similar to that in Vergence is perturbed so that one basin's petals (blue) is shrunken and twisted (the point in parameter space close to the cusp of the cardioid of some minibrot, but near the center of an overlapping one associated with the other critical point).

Both basins are colored by smoothed iterations. The full-size version has a bit of fuzzy aliasing in the core, but using a depth-3 antialias would have taken forever and a day on even this hardware with this high-iteration fractal.

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

Detailed statistics:

Name: Puddles
Date: February 19, 2009
Fractal: Matchmaker Julia set
Location: a = 0.53256 + 0.31163i; b = -1.0409127952309 - 0.12446653010663i
Depth: Very Shallow
Min Iterations: 2031
Max Iterations: 63,222
Layers: 2
Anti-aliasing: 3x3, threshold 0, depth 2
Preparation time: 10 minutes
Calculation time: 36 hours (2GHz dual-core Athlon XP)