Number-conserving cellular automata with a von Neumann neighborhood of range one

(2) KERMIT; Adam Dzedzej (1); Barbara Wolnik (1); Bernard De Baets (2) ((1) Institute of Mathematics; Bioinformatics; Department of Mathematical Modelling; Faculty of Mathematics; Ghent University); Informatics; Jan M. Baetens (2)

arxiv: 1705.00725 · v1 · pith:2XWMLLZWnew · submitted 2017-05-01 · 🧮 math.DS · nlin.CG

Number-conserving cellular automata with a von Neumann neighborhood of range one

Barbara Wolnik (1) , Adam Dzedzej (1) , Jan M. Baetens (2) , Bernard De Baets (2) ((1) Institute of Mathematics , Faculty of Mathematics , Physics , Informatics , University of Gda\'nsk

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(2) KERMIT Department of Mathematical Modelling Statistics Bioinformatics Ghent University)

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classification 🧮 math.DS nlin.CG

keywords conditionsneighborhoodneumanncellularnumber-conservingrangeallowsautomata

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We present necessary and sufficient conditions for a cellular automaton with a von Neumann neighborhood of range one to be number-conserving. The conditions are formulated for any dimension and for any set of states containing zero. The use of the geometric structure of the von Neumann neighborhood allows for computationally tractable conditions even in higher dimensions.

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Number-conserving cellular automata with a von Neumann neighborhood of range one

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