Automatic generation of strange attractors

A pair of coupled quadratic difference equations with randomly chosen coefficients is repeatedly iterated by computer to produce a two-dimensional map that has considerable aesthetic appeal and a correlation is found with the Lyapunov exponent and correlation dimension.

Abstract

A pair of coupled quadratic difference equations with randomly chosen coefficients is repeatedly iterated by computer to produce a two-dimensional map. The map is tested for stability and sensitivity to initial conditions. The process is repeated until a chaotic solution is found. In this way a computer can generate a large collection of strange attractors that are all different, and most of which have considerable aesthetic appeal. A simple computer program and examples of its output are provided. Many of the attractors have been systematically evaluated for visual appeal, and a correlation is found with the Lyapunov exponent and correlation dimension.