9320200 Crutchfield The proposed work is concerned with exploring algorithms: evolving cellular automata (CA) and related systems to perform specified computations. This project will have three major contributions: (i) Advances in the study of how to perform computation with spatially extended dynamical systems; (ii) Advances in the theory and practice of genetic algorithms; and (iii) Applications to parallel computation problems such as image processing, noise reduction, texture detection, and the automatic discovery of coherent structures in spatial pattern time series. This project is highly interdisciplinary in that it will call on very recent results in dynamical systems theory, computation theory, the statistical mechanics of phase transitions, and genetic algorithms.