Algebraic properties of cellular automata |
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| Authors: | Olivier Martin Andrew M Odlyzko Stephen Wolfram |
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| Institution: | (1) California Institute of Technology, 91125 Pasadena, CA, USA;(2) Bell Laboratories, 07974 Murray Hill, NJ, USA;(3) The Institute for Advanced Study, 08540 Princeton, NJ, USA;(4) Present address: Physics Department, Columbia University, 10027 New York, NY, USA |
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| Abstract: | Cellular automata are discrete dynamical systems, of simple construction but complex and varied behaviour. Algebraic techniques are used to give an extensive analysis of the global properties of a class of finite cellular automata. The complete structure of state transition diagrams is derived in terms of algebraic and number theoretical quantities. The systems are usually irreversible, and are found to evolve through transients to attractors consisting of cycles sometimes containing a large number of configurations.Address from January 1983 |
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