Strange Attractors
A long time ago, I stumbled on a page by Paul Bourke regarding random strange attractors. I've always been interested in fractal images, but these were something that I had not been exposed to before, and I quickly became enamored with them. Particularly fascinating about random strange attractors is the dependence on the parameters. Using his code to produce quadratic strange attractors, that is- plots of the iterations of:
ynew = b1x2 + b2xy + b3y2 + b4x + b5y + b6
Generally, 95% of randomly chosen parameters produce systems that diverge to infinity, 90% of those that remain become fixed or periodic, and a very slim number produce plots that have the intricate forms known as strange attractors. However, the parameters that produce the interesting systems are spread out considerably in the huge 12 dimensional parameter space described by the equations. This lead to the (seemingly) natural line of enquiry regarding what does the parameter space look like for strange attractors. These pages describe what I have found.