Discovering Coherent Structures in Nonlinear Spatial Systems

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. also in Complexity in Physics and Technology, R. Vilela-Mendes, editor, World Scientific, Singapore (1992) 1.