Easily calculable measure for the complexity of spatiotemporal patterns

  • Kaspar F
  • Schuster H
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We demonstrate by means of several examples that an easily calculable measure of algorithmic complexity c which has been introduced by Lempel and Ziv IEEE Trans. Inf. Theory IT-22, 25 (1976) is extremely useful for characterizing spatiotemporal patterns in high-dimensionality nonlinear systems. It is shown that, for time series, c can be a finer measure for order than the Liapunov exponent. We find that, for simple cellular automata, pattern formation can be clearly separated from a mere reduction of the source entropy and different types of automata can be distinguished. For a chain of coupled logistic maps, c signals pattern formation which cannot be seen in the spatial correlation function alone.

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  • F. Kaspar

  • H. G. Schuster

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