END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

A Julia set of the discrete Volterra-Lotka map-family found in The Beauty of Fractals. Aggressive antialiasing but no ergodic or limit circle attractor so not too slow. This is from the VL equivalent of a minibrot: one of the long, narrow "horns" that protrude from the bulk of the Mandelbrot, tapering off exponentially as it goes. The horn comes from a component of period 11. In the body of that component the Julia sets look more like Vortex, though with 11 rather than 7 "petals" to the interior basin. Move along the horn until it exits the body of the M-set, though, and the Julia set will shatter into these X-shaped basin fragments, boiling with bubbles of divergent points and becoming the foamy froth seen here.

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

Detailed statistics:

Name: Stirred
Date: January 7, 2010
Fractal: Discrete Volterra-Lotka Julia Set
Location: h = 1.00794139719, p = 1.11720348082
Depth: Very Shallow
Min Iterations: 1
Max Iterations: 9998
Layers: 2
Anti-aliasing: 3x3, threshold 0.0, depth 2
Preparation time: 5 minutes
Calculation time: 18 minutes (2.5GHz dual-core E5200)

There's already one posted, at this link, with more forthcoming...eventually.

I have used the M-set to pick some of the Julia sets actually.