Lyapunov fractals
Experiments in Lyapunov space.

I am extending the basic Markus-Lyapunov algorithm to three and four variables (A, B, C and D) rather than the standard two variables A and B.

In addition, rather than plotting a function of the Lyapunov exponent at each point, I'm using the exponent to determine transparency: below a given threshold (eg. -1.125), convergent exponents are deemed opaque.

This is used in a simple ray casting routine written in OpenCL to render the opaque surfaces, and a basic Blinn-Phong function to shade them.
15 photos · 6 videos · 397 views