Visualizing Chaos: Lyapunov Surfaces and Volumes

Graphic techniques can be used to visualize chaos for a dual-parameter one-dimensional map. The technique that I have found useful demonstrates graphically interesting behavior in chaotic systems. This involves plotting the Lyapunov exponent with both height and color in a 3D map, as a function of the two parameters. Color is determined using a geographic lookup table. A graphics supercomputer can rotate the map in real time. © 1990 IEEE