James P. Crutchfield
Physics Department
University of California
Berkeley, California 94720, USA
A synthesis of elementary computation and dynamical system theories leads to a constructive approach to discovering coherent structures in spatial systems and to quantifying a pattern's complexity. The basic technique reviewed here builds probabilistic automata from temporal and spatial data series generated by a simple nonlinear spatial system. In this way, a given pattern's unpredictability and structure are measured by the entropy rate and complexity, respectively, of the ``machine'' reconstructed from the pattern data. Ancillary remarks indicate how the analysis gives a global view of the high-dimensional state space structures associated with spatial systems and, in particular, the geometry of coherent structure interactions. The bulk of the review, though, emphasizes practical results on inferring coherent space-time structures and on building detectors to track particle-like objects.
J. P. Crutchfield, Discovering Coherent Structures in Nonlinear Spatial Systems, in Nonlinear Dynamics of Ocean Waves, A. Brandt, S. Ramberg, and M. Shlesinger, editors, World Scientific, Singapore (1992) 190-216.Santa Fe Institute Working Paper 91-09-034.
Based on a talk given at at the Applied Physics Laboratory Symposium on the Nonlinear Dynamics of Ocean Waves, Johns Hopkins University, Maryland, 30-31 May 1991.