Sevenfold

[Pauldelbrot]

A Supernova Julia set. One layer colors the basin of infinity grey. A second gives all finite attractors a color gradient by convergent smooth iterations. A third alters the hue of finite attractor points based on "attractor angle", the argument of the attractor's barycenter, thus giving each basin a distinct color. In theory, just three layers like this can be used on e.g. any Newton fractal to give every basin a distinct gradient. Attractor angle could also be interesting in Mandelbrot images in set components. And was was mentioned previously it may be useful when rendering parameter-morph animations to make basins' colors change smoothly as the parameters change (except where actual bifurcations occur, and sometimes even then).

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

Detailed statistics:

Name: Sevenfold
Date: February 19, 2009
Fractal: Supernova Julia set
Location: a = 0.87307, b = -0.052555 - 0.035036i, c = -0.103653 + 5.384821i
Depth: Very Shallow
Min Iterations: 4
Max Iterations: 1048
Layers: 3
Anti-aliasing: 3x3, threshold 0.1, depth 1
Preparation time: 5 minutes
Calculation time: 3 minutes (2GHz dual-core Athlon XP)

[Nahee_Enterprises]

A Supernova Julia set.  One layer colors the basin of infinity grey.
A second gives all finite attractors a color gradient by convergent smooth iterations.
Name: Sevenfold
Location: a = 0.87307, b = -0.052555 - 0.035036i, c = -0.103653 + 5.384821i
Max Iterations: 1048
Calculation time: 3 minutes (2GHz dual-core Athlon XP) 

I really like the way this image came out.  The coloring is very good.   

[Pauldelbrot]

Thanks.

One of the nifty things with Supernova is you can find quadratic Julia shapes, as in this one, with added "bubbles" in the interior that can form spirals and other shapes. Antimatter does this too, but with Supernova it can be taken further; the central hook-like spirals in the green zones are not possible in Antimatter.