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Journal of Statistical Physics

, Volume 59, Issue 1–2, pp 171–193 | Cite as

A Toom rule that increases the thickness of sets

  • Peter Gács
Articles

Abstract

Toom's north-east-self voting cellular automaton ruleR is known to suppress small minorities. A variant,R+, is also known to turn an arbitrary initial configuration into a homogeneous one (without changing the ones that were homogeneous to start with). Here it is shown thatR+ always increases a certain property of sets called thickness. This result is intended as a step toward a proof of the fast convergence toward consensus underR+. The latter is observable experimentally, even in the presence of some noise.

Key words

Cellular automata Toom's rule statistical mechanics 

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References

  1. 1.
    P. Gács, Self-correcting two-dimensional arrays, inRandomness in Computation, S. Micali, ed. (JAI Press, Greenwich, Connecticut, 1989), pp. 233–326.Google Scholar
  2. 2.
    P. Gács and J. Reif, A simple three-dimensional real-time reliable cellular array,J. Computer System Sci. 36(2):125–147 (1988).Google Scholar
  3. 3.
    A. L. Toom, Stable and attractive trajectories in multicomponent systems, inMulticomponent Systems, R. L. Dobrushin, ed. (Dekker, New York, 1980), pp. 549–575.Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • Peter Gács
    • 1
  1. 1.Boston University and IBM Almaden Research CenterBoston

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