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A two-layer representation of four-state reversible number-conserving 2D cellular automata

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Abstract
We present a novel representation of 1D reversible and number-conserving cellular automata with four states. Carrying this view over to two dimensions, we are able to construct 65 four-state reversible and number-conserving 2D cellular automata with the von Neumann neighborhood. A clever use of the split-and-perturb decomposition of number-conserving CAs allows to prove by elimination that this list is complete.
Keywords
cellular automata, dynamical processes, exact results

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Chicago
Dzedzej, Adam, Barbara Wolnik, Maciej Dziemiańczuk, Anna Nenca, Jan Baetens, and Bernard De Baets. 2019. “A Two-layer Representation of Four-state Reversible Number-conserving 2D Cellular Automata.” Journal of Statistical Mechanics-theory and Experiment.
APA
Dzedzej, A., Wolnik, B., Dziemiańczuk, M., Nenca, A., Baetens, J., & De Baets, B. (2019). A two-layer representation of four-state reversible number-conserving 2D cellular automata. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT.
Vancouver
1.
Dzedzej A, Wolnik B, Dziemiańczuk M, Nenca A, Baetens J, De Baets B. A two-layer representation of four-state reversible number-conserving 2D cellular automata. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT. 2019;
MLA
Dzedzej, Adam et al. “A Two-layer Representation of Four-state Reversible Number-conserving 2D Cellular Automata.” JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2019): n. pag. Print.
@article{8626849,
  abstract     = {We present a novel representation of 1D reversible and number-conserving cellular automata with four states. Carrying this view over to two dimensions, we are able to construct 65 four-state reversible and number-conserving 2D cellular automata with the von Neumann neighborhood. A clever use of the split-and-perturb decomposition of number-conserving CAs allows to prove by elimination that this list is complete.},
  articleno    = {073202},
  author       = {Dzedzej, Adam and Wolnik, Barbara and Dziemiańczuk, Maciej and Nenca, Anna and Baetens, Jan and De Baets, Bernard},
  issn         = {1742-5468},
  journal      = {JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT},
  keywords     = {cellular automata,dynamical processes,exact results},
  language     = {eng},
  pages        = {17},
  title        = {A two-layer representation of four-state reversible number-conserving 2D cellular automata},
  url          = {http://dx.doi.org/10.1088/1742-5468/ab25df},
  year         = {2019},
}

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