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

• Received 2 May 1983

DOI:https://doi.org/10.1103/PhysRevLett.51.1265