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 30 pkt)
Issue year2017
Publication size in sheets0.8
Article number435101
Keywords in Englishcellular automata, number-conservation, von Neumann neighborhood
ASJC Classification2610 Mathematical Physics; 2611 Modelling and Simulation; 2613 Statistics and Probability; 3100 General Physics and Astronomy; 3109 Statistical and Nonlinear Physics
Languageen angielski
Score (nominal)30
Score sourcejournalList
ScoreMinisterial score = 30.0, 29-05-2020, ArticleFromJournal
Publication indicators WoS Citations = 2; Scopus Citations = 5; Scopus SNIP (Source Normalised Impact per Paper): 2017 = 0.963; WoS Impact Factor: 2017 = 1.963 (2) - 2017=1.766 (5)
Citation count*7 (2020-06-03)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
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