Maximally complex simple attractors

A relatively small number of mathematically simple maps and flows are routinely used as examples of low-dimensional chaos. These systems typically have a number of parameters that are chosen for historical or other reasons. This paper addresses the question of whether a different choice of these parameters can produce strange attractors that are significantly more chaotic (larger Lyapunov exponent) or more complex (higher dimension) than those typically used in such studies. It reports numerical results in which the parameters are adjusted to give either the largest Lyapunov exponent or the largest Kaplan-Yorke dimension. The characteristics of the resulting attractors are displayed and discussed.