A two-layer representation of four-state reversible number-conserving 2D cellular automata

Adam Dzedzej , Barbara Wolnik , Maciej Dziemiańczuk , Anna Nenca , Jan M. Baetens , Bernard De Baets

Abstract

We present a novel representation of 1D reversible and number-conserving cellular automata with four states. Carrying this view over to two dimensions, we are able to construct 65 four-state reversible and number-conserving 2D cellular automata with the von Neumann neighborhood. A clever use of the split-and-perturb decomposition of number-conserving CAs allows to prove by elimination that this list is complete.
Author Adam Dzedzej (FMPI / IM)
Adam Dzedzej,,
- Institute of Mathematics
, Barbara Wolnik (FMPI / IM)
Barbara Wolnik,,
- Institute of Mathematics
, Maciej Dziemiańczuk (FMPI / II)
Maciej Dziemiańczuk,,
- Institute of Informatics
, Anna Nenca (FMPI / II)
Anna Nenca,,
- Institute of Informatics
, Jan M. Baetens
Jan M. Baetens,,
-
, Bernard De Baets
Bernard De Baets,,
-
Journal seriesJournal of Statistical Mechanics-Theory and Experiment, ISSN 1742-5468, (A 35 pkt)
Issue year2019
Vol2019
Pages1-17
Publication size in sheets0.8
Article number073202
Keywords in Englishcellular automata, dynamical processes, exact results
ASJC Classification1804 Statistics, Probability and Uncertainty; 2613 Statistics and Probability; 3109 Statistical and Nonlinear Physics
DOIDOI:10.1088/1742-5468/ab25df
URL https://doi.org/10.1088/1742-5468/ab25df
Languageen angielski
Score (nominal)35
ScoreMinisterial score = 35.0, 24-07-2019, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2016 = 0.461; WoS Impact Factor: 2017 = 2.404 (2) - 2017=2.228 (5)
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