Phenomenology of nonlocal cellular automata
 Wentian Li
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Dynamical systems with nonlocal connections have potential applications to economic and biological systems. This paper studies the dynamics of nonlocal cellular automata. In particular, all twostate, threeinput nonlocal cellular automata are classified according to the dynamical behavior starting from random initial configurations and random wirings, although it is observed that sometimes a rule can have different dynamical behaviors with different wirings. The nonlocal cellular automata rule space is studied using a meanfield parametrization which is ideal for the situation of random wiring. Nonlocal cellular automata can be considered as computers carrying out computation at the level of each component. Their computational abilities are studied from the point of view of whether they contain many basic logical gates. In particular, I ask the question of whether a threeinput cellular automaton rule contains the three fundamental logical gates: twoinput rules AND and OR, and oneinput rule NOT. A particularly interesting “edgeofchaos” nonlocal cellular automaton, the rule 184, is studied in detail. It is a system of coupled “selectors” or “multiplexers.” It is also part of the Fredkin's gate—a proposed fundamental gate for conservative computations. This rule exhibits irregular fluctuations of density, large coherent structures, and long transient times.
 Title
 Phenomenology of nonlocal cellular automata
 Journal

Journal of Statistical Physics
Volume 68, Issue 56 , pp 829882
 Cover Date
 199209
 DOI
 10.1007/BF01048877
 Print ISSN
 00224715
 Online ISSN
 15729613
 Publisher
 Kluwer Academic PublishersPlenum Publishers
 Additional Links
 Topics
 Keywords

 Nonlocal cellular automata
 automata networks
 classification of cellular automata
 cellular automata rule space
 critical hypersurface
 selforganized criticality
 meanfield theory
 universal computation
 “game of life”
 Fredkin's gate
 coupled selectors or coupled multiplexers
 edgeofchaos dynamics
 density fluctuations
 long transient behaviors
 cooperative dynamics
 Industry Sectors
 Authors

 Wentian Li ^{(1)}
 Author Affiliations

 1. Santa Fe Institute, 87501, Santa Fe, New Mexico