All binary number-conserving cellular automata based on adjacent cells are intrinsically one-dimensional

Barbara Wolnik , Bernard De Baets

Abstract

A binary number-conserving cellular automaton is a discrete dynamical system that models the movement of particles in a d-dimensional grid. Each cell of the grid is either empty or contains a particle. In subsequent timesteps the particles move between the cells, but in one cell there can be at most one particle at a time. In thispaper, the von Neumann neighborhood is considered, which means that in each time step a particle can moveto an adjacent cell only. It is proven that regardless of the dimensiond, all of these cellular automata are trivial,as they are intrinsically one-dimensional. Thus, for givend, there are only 4d+1 binary number-conserving cellular automata with the von Neumann neighborhood: the identity rule and the shift and traffic rules in each ofthe 2d possible directions.
Author Barbara Wolnik (FMPI/IM)
Barbara Wolnik,,
- Institute of Mathematics
, Bernard De Baets
Bernard De Baets,,
-
Journal seriesPhysical Review E, ISSN 1539-3755, (N/A 140 pkt)
Issue year2019
Vol100
No2
Pages1-6
Publication size in sheets0.50
Article number022126
Keywords in Englishmulti-dimensional cellular automata, number conservation
ASJC Classification3104 Condensed Matter Physics; 2613 Statistics and Probability; 3109 Statistical and Nonlinear Physics
DOIDOI:10.1103/PhysRevE.100.022126
URL https://journals.aps.org/pre/pdf/10.1103/PhysRevE.100.022126
Languageen angielski
Score (nominal)140
Score sourcejournalList
ScoreMinisterial score = 140.0, 27-07-2020, ArticleFromJournal
Publication indicators WoS Citations = 1.000; Scopus Citations = 1.000; Scopus SNIP (Source Normalised Impact per Paper): 2016 = 0.896; WoS Impact Factor: 2018 = 2.353 (2) - 2018=2.380 (5)
Citation count*1 (2020-06-30)
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