Seven-state rotation-symmetric number-conserving cellular automaton that is not isomorphic to any septenary one
- Author
- Barbara Wolnik (UGent) , Anna Nenca, Adam Dzedzej and Bernard De Baets (UGent)
- Organization
- Abstract
- We consider two-dimensional cellular automata with the von Neumann neighborhood that satisfy two proper-ties of interest from a modeling viewpoint: rotation symmetry (i.e., the local rule is invariant under rotation of the neighborhood by 90 degrees) and number conservation (i.e., the sum of all the cell states is conserved upon every update). It is known that if the number of states k is smaller than or equal to six, then each rotation-symmetric number-conserving cellular automaton is isomorphic to some k-ary one, i.e., one with state set {0, 1, ... , k - 1}. In this paper, we exhibit an example of a seven-state rotation-symmetric number-conserving cellular automaton that is not isomorphic to any septenary one. This example strongly supports our plea that research into multistate cellular automata should not only focus on those that have {0, 1, ... , k - 1} as a state set.
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01GT90CA45J7KCCNY7R94G5KS7
- MLA
- Wolnik, Barbara, et al. “Seven-State Rotation-Symmetric Number-Conserving Cellular Automaton That Is Not Isomorphic to Any Septenary One.” PHYSICAL REVIEW E, vol. 107, no. 2, 2023, doi:10.1103/physreve.107.024211.
- APA
- Wolnik, B., Nenca, A., Dzedzej, A., & De Baets, B. (2023). Seven-state rotation-symmetric number-conserving cellular automaton that is not isomorphic to any septenary one. PHYSICAL REVIEW E, 107(2). https://doi.org/10.1103/physreve.107.024211
- Chicago author-date
- Wolnik, Barbara, Anna Nenca, Adam Dzedzej, and Bernard De Baets. 2023. “Seven-State Rotation-Symmetric Number-Conserving Cellular Automaton That Is Not Isomorphic to Any Septenary One.” PHYSICAL REVIEW E 107 (2). https://doi.org/10.1103/physreve.107.024211.
- Chicago author-date (all authors)
- Wolnik, Barbara, Anna Nenca, Adam Dzedzej, and Bernard De Baets. 2023. “Seven-State Rotation-Symmetric Number-Conserving Cellular Automaton That Is Not Isomorphic to Any Septenary One.” PHYSICAL REVIEW E 107 (2). doi:10.1103/physreve.107.024211.
- Vancouver
- 1.Wolnik B, Nenca A, Dzedzej A, De Baets B. Seven-state rotation-symmetric number-conserving cellular automaton that is not isomorphic to any septenary one. PHYSICAL REVIEW E. 2023;107(2).
- IEEE
- [1]B. Wolnik, A. Nenca, A. Dzedzej, and B. De Baets, “Seven-state rotation-symmetric number-conserving cellular automaton that is not isomorphic to any septenary one,” PHYSICAL REVIEW E, vol. 107, no. 2, 2023.
@article{01GT90CA45J7KCCNY7R94G5KS7,
abstract = {{We consider two-dimensional cellular automata with the von Neumann neighborhood that satisfy two proper-ties of interest from a modeling viewpoint: rotation symmetry (i.e., the local rule is invariant under rotation of the neighborhood by 90 degrees) and number conservation (i.e., the sum of all the cell states is conserved upon every update). It is known that if the number of states k is smaller than or equal to six, then each rotation-symmetric number-conserving cellular automaton is isomorphic to some k-ary one, i.e., one with state set {0, 1, ... , k - 1}. In this paper, we exhibit an example of a seven-state rotation-symmetric number-conserving cellular automaton that is not isomorphic to any septenary one. This example strongly supports our plea that research into multistate cellular automata should not only focus on those that have {0, 1, ... , k - 1} as a state set.}},
articleno = {{024211}},
author = {{Wolnik, Barbara and Nenca, Anna and Dzedzej, Adam and De Baets, Bernard}},
issn = {{2470-0045}},
journal = {{PHYSICAL REVIEW E}},
language = {{eng}},
number = {{2}},
pages = {{4}},
title = {{Seven-state rotation-symmetric number-conserving cellular automaton that is not isomorphic to any septenary one}},
url = {{http://doi.org/10.1103/physreve.107.024211}},
volume = {{107}},
year = {{2023}},
}
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