Estimating the Fractal Dimension of Chaotic Time Series

Fractals arise from a variety of sources: they have been observed in nature and on computer screens. An intriguing characteristic offractals is that they can be described by noninteger dimensions. The geometry of fractals and the mathematics of fractal dimension provide useful tools for a variety of scientific disciplines-in particular, the study of chaos. A chaotic dynamical system exhibits trajectories that converge to a strange attrac-tor. The fractal dimension of this attractor counts the effective number of degrees of freedom in the dynamical system and thus quantifies the system's complexity. This article reviews the numerical methods that have been developed to estimate the dimension of a physical system directly from the system's observed behavior.

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