Abstract
In this paper we study Automata Networks whose local rules are “compatibles” with the Potts Hamiltonian. We prove that there exists compatible local rules with a very complex global behaviour (automata configurations may code any logic function) and that Maximal Local Rules admit a Lyapunov functional derived from the Potts Hamiltonian. Furthermore, in the last case, the steady-state behaviour is very simple: fixed points and/or two cycles.
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References
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© 1989 Kluwer Academic Publishers
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Goles, E. (1989). Potts Model and Automata Networks. In: Tirapegui, E., Villarroel, D. (eds) Instabilities and Nonequilibrium Structures II. Mathematics and Its Applications, vol 50. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2305-8_7
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DOI: https://doi.org/10.1007/978-94-009-2305-8_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7535-0
Online ISBN: 978-94-009-2305-8
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