Hausdorff Dimension and Uniformity Factor of Strange Attractors

The Hausdorff dimension $D_0$ of a strange attractor is argued to be the fixed point of a recursive relation, defined in terms of a suitable average of the smallest distances ${\delta }_i$ between points on the attractor. A fast numerical algorithm is developed to compute $D_0$. The spread $\lambda$ in the convergence rates towards zero of the distances ${\delta }_i$ (uniformity factor) as well as the stability of the fixed point are discussed in terms of the entropy of the ${\delta }_i$ distribution.