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

Barbara Wolnik , Adam Dzedzej , Jan M. Baetens , Bernard De Baets


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.
Author Barbara Wolnik (FMPI / IM)
Barbara Wolnik,,
- Institute of Mathematics
, Adam Dzedzej (FMPI / IM)
Adam Dzedzej,,
- Institute of Mathematics
, Jan M. Baetens
Jan M. Baetens,,
, Bernard De Baets
Bernard De Baets,,
Journal seriesJournal of Physics A-Mathematical and Theoretical, ISSN 1751-8113, (A 25 pkt)
Issue year2017
Publication size in sheets0.8
Keywords in Englishcellular automata, number-conservation, von Neumann neighborhood
Languageen angielski
Score (nominal)30
ScoreMinisterial score = 25.0, 20-12-2017, ArticleFromJournal
Ministerial score (2013-2016) = 30.0, 20-12-2017, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 1.857 (2) - 2016=1.605 (5)
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