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Cellular automata are regular uniform networks of locally-connected finite-state machines. They are discrete systems with non-trivial behaviour. Cellular automata are ubiquitous: they are mathematical models of computation and computer models of natural systems. The book presents results of cutting edge research in cellular-automata framework of digital physics and modelling of spatially extended non-linear systems; massive-parallel computing, language acceptance, and computability; reversibility of computation, graph-theoretic analysis and logic; chaos and undecidability; evolution, learning and cryptography. The book is unique because it brings together unequalled expertise of inter-disciplinary studies at the edge of mathematics, computer science, engineering, physics and biology.