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(http://u5789.direct.atpic.com/32751/0/1699236/1024.jpg) (http://pic.atpic.com/1699236/1024)

A Julia set of the discrete Volterra-Lotka map-family found in The Beauty of Fractals. This one has two attractors: a fixed point at infinity (pink basin) and a strange attractor (shown in white; blue basin).

This system exhibits strange attractors at the "crowns" of the "teeth" of the Mandelbrot structure. Periodic orbits become limit circle attractors, but there's another threshold. Approaching it, the circles become more and more convoluted and wiggly; then at the transition you get an attractor like this one, still roughly a circle but with folds and knots. This sort of attractor becomes even more convoluted, eventually nearly solidly filling a thick annulus with irregular borders, before disintegrating completely as the parameter point exits the M-set and the Julia set falls to pieces.

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Detailed statistics:

Name: Superstring Theory
Date: January 6, 2010
Fractal: Discrete Volterra-Lotka Julia Set
Location: h = 0.96789758067, p = 1.14927057191
Depth: Very Shallow
Min Iterations: 1
Max Iterations: 9998
Layers: 2
Anti-aliasing: 3x3, threshold 0.0, depth 1
Preparation time: 5 minutes
Calculation time: 1 hour (2.5GHz dual-core E5200)

looks nice :)

It's a dolphin-attractor :D

The one white pixel, not connected to the knoted circle is also part of the same strange attractor?

I like the reference to super strings, and the fact that the attractor takes this form. As it is related to the mandelbrot i suspect that this is still a sculpture and so represents a force folding and shaping space rather than space warping and shaping itself. For me the second description would underlie the force effects in space.

Well, it's an eat-or-get-eaten-space, I guess...

Thanks.

The isolated whitish spot is the repelling fixed point. The coloring in that basin is by closest approach of orbit to original pixel, with some iterations discarded. So, pixels on the attractor have the orbit return to them and have the minimum distance (color: white), pixels further away are blue, and pixels further still are black. The pixels very close to the repelling point, though, have the orbit slowly accelerate away from the repelling point, and after the pre-iterations the orbit may still be quite close to the starting point. If a pixel lands exactly on the repelling point it doesn't move at all and ends up bright white.

I see :)

Thanks for that. I am slowly getting the hang of the meaning behind the pictures. My analogy of a sculpting i have rethought slightly, as it limits analogy hunting, and these programmes are more complex than a simple analogy no matter how useful for the beginner. I see that this represents a repulsion attraction situation very much like a magnetic pole acting on an iron filing, which it is also slowly magnetising to a similar pole.

`i had the thought one day that biological space owes its shape in part to the biological instructions for growth, but also to inherent spatial properties in the spaces it wishes to grow into. So for example the leaf distribution pattern on a bush is not just a biological blueprint, but can be seen in the ditribution pattern of stars in a galaxy, or a cluster of galaxies in a super cluster.

I did not at that time understand about fractal entrainment, the causation of scale similarities in regions in space, i believe currently.
In any case the subtlety of sculpting most sculptors believe is in freeing the form that is in the block! that is to say that it is about warped and twisted space and discovering it. :gum: