Box-counting dimension without boxes: computing D0 from average expansion rates.

We propose an efficient iterative scheme for calculating the box-counting (capacity) dimension of a chaotic attractor in terms of its average expansion rates. Similar to the Kaplan-Yorke conjecture for the information dimension, this scheme provides a connection between a geometric property of a strange set and its underlying dynamical properties. Our conjecture is demonstrated analytically with an exactly solvable two-dimensional hyperbolic map, and numerically with a more complicated higher-dimensional nonhyperbolic map.