Number-conserving cellular automata with a von Neumann neighborhood of range one
- Author
- Barbara Wolnik, Adam Dzedzej, Jan Baetens (UGent) and Bernard De Baets (UGent)
- Organization
- Abstract
- 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.
- Keywords
- cellular automata, number-conservation, von Neumann neighborhood, UNIVERSALITY
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8535688
- MLA
- Wolnik, Barbara, et al. “Number-Conserving Cellular Automata with a von Neumann Neighborhood of Range One.” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol. 50, no. 43, 2017, doi:10.1088/1751-8121/aa89cf.
- APA
- Wolnik, B., Dzedzej, A., Baetens, J., & De Baets, B. (2017). Number-conserving cellular automata with a von Neumann neighborhood of range one. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 50(43). https://doi.org/10.1088/1751-8121/aa89cf
- Chicago author-date
- Wolnik, Barbara, Adam Dzedzej, Jan Baetens, and Bernard De Baets. 2017. “Number-Conserving Cellular Automata with a von Neumann Neighborhood of Range One.” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 50 (43). https://doi.org/10.1088/1751-8121/aa89cf.
- Chicago author-date (all authors)
- Wolnik, Barbara, Adam Dzedzej, Jan Baetens, and Bernard De Baets. 2017. “Number-Conserving Cellular Automata with a von Neumann Neighborhood of Range One.” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 50 (43). doi:10.1088/1751-8121/aa89cf.
- Vancouver
- 1.Wolnik B, Dzedzej A, Baetens J, De Baets B. Number-conserving cellular automata with a von Neumann neighborhood of range one. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. 2017;50(43).
- IEEE
- [1]B. Wolnik, A. Dzedzej, J. Baetens, and B. De Baets, “Number-conserving cellular automata with a von Neumann neighborhood of range one,” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol. 50, no. 43, 2017.
@article{8535688,
abstract = {{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.}},
articleno = {{435101}},
author = {{Wolnik, Barbara and Dzedzej, Adam and Baetens, Jan and De Baets, Bernard}},
issn = {{1751-8113}},
journal = {{JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL}},
keywords = {{cellular automata,number-conservation,von Neumann neighborhood,UNIVERSALITY}},
language = {{eng}},
number = {{43}},
title = {{Number-conserving cellular automata with a von Neumann neighborhood of range one}},
url = {{http://doi.org/10.1088/1751-8121/aa89cf}},
volume = {{50}},
year = {{2017}},
}
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