Automatic Filters for the Detection of Coherent Structure in Spatiotemporal Systems

Details Automatic Filters for the Detection of Coherent Structure in Spatiotemporal Systems Automatic Filters for the Detection of Coherent Structure in Spatiotemporal Systems

2005-07-29

arxiv.org/abs/nlin/0508001v1

Physical Review E 73 (2006): 036104

Nonlinear Sciences

Cellular Automata and Lattice Gases

16 pages, 21 figures. Figures considerably compressed to fit arxiv requirements; write first author for higher-resolution vers

Scientific paper

10.1103/PhysRevE.73.036104

Most current methods for identifying coherent structures in spatially-extended systems rely on prior information about the form which those structures take. Here we present two new approaches to automatically filter the changing configurations of spatial dynamical systems and extract coherent structures. One, local sensitivity filtering, is a modification of the local Lyapunov exponent approach suitable to cellular automata and other discrete spatial systems. The other, local statistical complexity filtering, calculates the amount of information needed for optimal prediction of the system's behavior in the vicinity of a given point. By examining the changing spatiotemporal distributions of these quantities, we can find the coherent structures in a variety of pattern-forming cellular automata, without needing to guess or postulate the form of that structure. We apply both filters to elementary and cyclical cellular automata (ECA and CCA) and find that they readily identify particles, domains and other more complicated structures. We compare the results from ECA with earlier ones based upon the theory of formal languages, and the results from CCA with a more traditional approach based on an order parameter and free energy. While sensitivity and statistical complexity are equally adept at uncovering structure, they are based on different system properties (dynamical and probabilistic, respectively), and provide complementary information.

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