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Most current methods for identifying coherent structures inspatially-extended systems rely on prior information about the form which thosestructures take. Here we present two new approaches to automatically filter thechanging configurations of spatial dynamical systems and extract coherentstructures. One, local sensitivity filtering, is a modification of the localLyapunov exponent approach suitable to cellular automata and other discretespatial systems. The other, local statistical complexity filtering, calculatesthe amount of information needed for optimal prediction of the system'sbehavior in the vicinity of a given point. By examining the changingspatiotemporal distributions of these quantities, we can find the coherentstructures in a variety of pattern-forming cellular automata, without needingto guess or postulate the form of that structure. We apply both filters toelementary and cyclical cellular automata (ECA and CCA) and find that theyreadily identify particles, domains and other more complicated structures. Wecompare the results from ECA with earlier ones based upon the theory of formallanguages, and the results from CCA with a more traditional approach based onan order parameter and free energy. While sensitivity and statisticalcomplexity are equally adept at uncovering structure, they are based ondifferent system properties (dynamical and probabilistic, respectively), andprovide complementary information.Comment: 16 pages, 21 figures. Figures considerably compressed to fit arxiv  requirements; write first author for higher-resolution version

Automatic filters for the detection of coherent structure in spatiotemporal systems