Algebraic properties of cellular automata

Olivier Martin, Andrew M. Odlyzko, Stephen Wolfram

Research output: Contribution to journalArticlepeer-review

285 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)219-258
Number of pages40
JournalCommunications in Mathematical Physics
Issue number2
StatePublished - Jun 1984


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