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Three-dimensional rotation-symmetric number-conserving cellular automata

Barbara Wolnik, Nikodem Mrozek, Adam Dzedzej and Bernard De Baets (UGent)
(2020) JOURNAL OF CELLULAR AUTOMATA. 15(4). p.243-259
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Abstract
We study three-dimensional rotation-symmetric cellular automata with the von Neumann neighborhood that conserve the sum of states. We show that any non-trivial such automaton requires at least seven states, which agrees with intuition based on the known results for the one and two-dimensional cases. We also give a full characterization of these cellular automata with a seven-element state set and the result is quite surprising.
Keywords
RULES

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Citation

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MLA
Wolnik, Barbara, et al. “Three-Dimensional Rotation-Symmetric Number-Conserving Cellular Automata.” JOURNAL OF CELLULAR AUTOMATA, vol. 15, no. 4, 2020, pp. 243–59.
APA
Wolnik, B., Mrozek, N., Dzedzej, A., & De Baets, B. (2020). Three-dimensional rotation-symmetric number-conserving cellular automata. JOURNAL OF CELLULAR AUTOMATA, 15(4), 243–259.
Chicago author-date
Wolnik, Barbara, Nikodem Mrozek, Adam Dzedzej, and Bernard De Baets. 2020. “Three-Dimensional Rotation-Symmetric Number-Conserving Cellular Automata.” JOURNAL OF CELLULAR AUTOMATA 15 (4): 243–59.
Chicago author-date (all authors)
Wolnik, Barbara, Nikodem Mrozek, Adam Dzedzej, and Bernard De Baets. 2020. “Three-Dimensional Rotation-Symmetric Number-Conserving Cellular Automata.” JOURNAL OF CELLULAR AUTOMATA 15 (4): 243–259.
Vancouver
1.
Wolnik B, Mrozek N, Dzedzej A, De Baets B. Three-dimensional rotation-symmetric number-conserving cellular automata. JOURNAL OF CELLULAR AUTOMATA. 2020;15(4):243–59.
IEEE
[1]
B. Wolnik, N. Mrozek, A. Dzedzej, and B. De Baets, “Three-dimensional rotation-symmetric number-conserving cellular automata,” JOURNAL OF CELLULAR AUTOMATA, vol. 15, no. 4, pp. 243–259, 2020.
@article{8685839,
  abstract     = {{We study three-dimensional rotation-symmetric cellular automata with the von Neumann neighborhood that conserve the sum of states. We show that any non-trivial such automaton requires at least seven states, which agrees with intuition based on the known results for the one and two-dimensional cases. We also give a full characterization of these cellular automata with a seven-element state set and the result is quite surprising.}},
  author       = {{Wolnik, Barbara and Mrozek, Nikodem and Dzedzej, Adam and De Baets, Bernard}},
  issn         = {{1557-5969}},
  journal      = {{JOURNAL OF CELLULAR AUTOMATA}},
  keywords     = {{RULES}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{243--259}},
  title        = {{Three-dimensional rotation-symmetric number-conserving cellular automata}},
  volume       = {{15}},
  year         = {{2020}},
}
Web of Science
Times cited: