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.
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References
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A. L. Toom, Stable and attractive trajectories in multicomponent systems, inMulticomponent Systems, R. L. Dobrushin, ed. (Dekker, New York, 1980), pp. 549–575.
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Gács, P. A Toom rule that increases the thickness of sets. J Stat Phys 59, 171–193 (1990). https://doi.org/10.1007/BF01015567
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DOI: https://doi.org/10.1007/BF01015567