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Number-conserving cellular automata with a von Neumann neighborhood of range one

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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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Chicago
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).
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).
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).
MLA
Wolnik, Barbara et al. “Number-conserving Cellular Automata with a Von Neumann Neighborhood of Range One.” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 50.43 (2017): n. pag. Print.
@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},
  language     = {eng},
  number       = {43},
  title        = {Number-conserving cellular automata with a von Neumann neighborhood of range one},
  url          = {http://dx.doi.org/10.1088/1751-8121/aa89cf},
  volume       = {50},
  year         = {2017},
}

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