Strange Attractors - Drawing the universe

One of my university projects currently involves me writing a Mandelbrot Explorer application, which is yielding some fairly cool results. I've been looking at multiple dimensions and different forms of the mandelbrot set, which just reinforces my amazement every time I run it.

The mandelbrot is a fractal set, so I thought it might be interesting to look at some other fractal sets. Below is a representation of a Strange Attractor - technically a system with chaotic dynamics and a non-integer dimension. The whole program was written in just a few lines of code and it is actually fairly straight forward to work out, just like the Mandelbrot set, but the results are spectacular. It really does seem like the universe is being drawn out in front of you - and it is true that a lot of the patterns found in fractal mathematics do appear in the structures of macroscopic objects, for example in the spiral arms of galaxies, or in nebula cloud formation.

One amazing thing about the program is that there are more possible combinations of what you can see than there are particles in the universe. Current astronomers put the number of particles in the universe at somewhere between 10⁷² and 10⁸⁷a number quite easy to write down. With accurate enough numbers there are infinitely many manifestations of the strange attractor, but practically for an image with 2000x2000 resolution - as the program has, and 256 colours per pixel the number of manifestations are of the order of 256^4000000 which is an incomprehensible figure! And thats just using  256 colours - ie red or green or blue, and not the whole spectrum available.

These numbers are a little bit scary but it is nice to know that some consistency and calm arises out of these. Its not all white noise! Anyway take a look at the program - It is constantly evolving - and you'll never ever see the same thing more than once! Just click the image below to launch it.

Or click here or here to run it in green or blue!