A Toom rule that increases the thickness of sets |
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Authors: | Peter Gács |
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Institution: | (1) Boston University and IBM Almaden Research Center, Boston |
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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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Keywords: | Cellular automata Toom's rule statistical mechanics |
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