Fractal Dimension of Strange Attractors from Radius versus Size of Arbitrary Clusters

Abstract

A fractal dimension ${D}_{{F}^{\ensuremath{'}}}$ of strange attractors is estimated as follows. Clusters of $n$ nearest-neighbor points are sampled from a time series; ${D}_{{F}^{\ensuremath{'}}}$ is found from ${\overline{R}}^{{D}_{{F}^{\ensuremath{'}}}}\ensuremath{\sim}n$ where $\overline{R}$ is the average cluster's radius. The estimation of ${D}_{{F}^{\ensuremath{'}}}$ is shown to be especially efficient for high dimensional systems.