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Preface to Cellular Automata (1984) |
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Although originally introduced thirty years ago, it is only very recently that research in many fields has led to widespread interest in cellular automata. Part of this growth in interest may be attributed to the recent availability of computing resources sufficient for extensive simulations of cellular automata. The next few years could see several important advances in the study of cellular automata.
On the mathematical side, the classes of cellular automaton behaviour identified by Wolfram should be more completely characterized and delineated. There are indications that computation and formal language theory, together with ergodic theory, may provide the appropriate mathematical tools for this purpose. From successful analyses along these lines, one may hope to abstract a powerful mathematical theory which generalizes the second law of thermodynamics. In addition, further elucidation of the mathematical basis for complex behaviour in continuous dynamical systems should be obtained.
The theoretical connections between the computational and statistical properties of cellular automata should be studied. Investigations such as those discussed by Margolus, in which physical concepts are applied to computation, and computational concepts to physics, can potentially yield important insights into the nature of computation and the bases of physical phenomena.
Explicit cellular automaton models of natural systems should be constructed and analysed. Aggregation phenomena, such as snowflake growth, follow simple local rules, but yield complex patterns, and are potentially modelled by cellular automata. Since cellular automata idealize partial differential equations, they may be appropriate as models for turbulent fluids, both at an abstract mathematical level, and perhaps at a more explicit physical level. In biology, cellular automata should provide explicit models for pattern formation in the growth of organisms.
Particular cellular automaton computers should be constructed, and methods for their programming should be devised. Whereas most parallel processing computer projects involve a small number of high level computers, cellular automata suggest the construction of systems with a very large number of simple computers, perhaps along the lines described by Hillis or along the complementary lines described by Toffoli. Such systems are closer in architecture to natural systems but their programming remains a significant challenge.
Probabilistic cellular automata should be investigated, and their analogies with spin systems studied.
Systems related to cellular automata, such as those described by Kauffman, may provide other classes of models for natural systems, and their mathematical analysis and application should be carried forward.
The study of cellular automata is in many respects only just beginning. Judging from history, it will be many years before there will be an understanding of the theory and applications of cellular automata comparable to that of differential equations today.
