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

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3 October 1983

journal article
research article
Published by American Physical Society (APS) in Physical Review Letters

Vol. 51 (14) , 1265-1268
https://doi.org/10.1103/physrevlett.51.1265

Abstract

A fractal dimension

D_{F^{'}}

of strange attractors is estimated as follows. Clusters of

n

nearest-neighbor points are sampled from a time series;

D_{F^{'}}

is found from

{\bar{R}}^{D_{F^{'}}} \sim n

where

\bar{R}

is the average cluster's radius. The estimation of

D_{F^{'}}

is shown to be especially efficient for high dimensional systems.

Keywords

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