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A Toom rule that increases the thickness of sets

Peter Gacs
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Abstract

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

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Peter Gacs. 2001-02-08. A Toom rule that increases the thickness of sets. https://doi.org/10.1007/bf01015567

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