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Non-uniform number-conserving elementary cellular automata

(2023) INFORMATION SCIENCES. 626. p.851-866
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Abstract
In this paper, we investigate non-uniform elementary cellular automata (i.e., one-dimensional cellular automata whose cells can use different Wolfram rules to update their states) in the context of number conservation. As a result, we obtain an exhaustive characterization of such number-conserving cellular automata on all finite grids both with periodic and null boundary conditions. The characterization obtained allows, inter alia, to enumerate all number-conserving non-uniform elementary cellular automata, in particular those that are reversible. Surprisingly, the numbers obtained are closely related to the Fibonacci sequence.
Keywords
Artificial Intelligence, Information Systems and Management, Computer Science Applications, Theoretical Computer Science, Control and Systems Engineering, Software, Cellular automata, Non -uniform cellular automata, Number conservation, LATTICE-GAS, COMPLEXITY, DYNAMICS

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Citation

Please use this url to cite or link to this publication:

MLA
Wolnik, Barbara, et al. “Non-Uniform Number-Conserving Elementary Cellular Automata.” INFORMATION SCIENCES, vol. 626, 2023, pp. 851–66, doi:10.1016/j.ins.2023.01.033.
APA
Wolnik, B., Dziemiańczuk, M., & De Baets, B. (2023). Non-uniform number-conserving elementary cellular automata. INFORMATION SCIENCES, 626, 851–866. https://doi.org/10.1016/j.ins.2023.01.033
Chicago author-date
Wolnik, Barbara, Maciej Dziemiańczuk, and Bernard De Baets. 2023. “Non-Uniform Number-Conserving Elementary Cellular Automata.” INFORMATION SCIENCES 626: 851–66. https://doi.org/10.1016/j.ins.2023.01.033.
Chicago author-date (all authors)
Wolnik, Barbara, Maciej Dziemiańczuk, and Bernard De Baets. 2023. “Non-Uniform Number-Conserving Elementary Cellular Automata.” INFORMATION SCIENCES 626: 851–866. doi:10.1016/j.ins.2023.01.033.
Vancouver
1.
Wolnik B, Dziemiańczuk M, De Baets B. Non-uniform number-conserving elementary cellular automata. INFORMATION SCIENCES. 2023;626:851–66.
IEEE
[1]
B. Wolnik, M. Dziemiańczuk, and B. De Baets, “Non-uniform number-conserving elementary cellular automata,” INFORMATION SCIENCES, vol. 626, pp. 851–866, 2023.
@article{01GX3CB5TMA81YH7R8K3AS4Q60,
  abstract     = {{In this paper, we investigate non-uniform elementary cellular automata (i.e., one-dimensional cellular automata whose cells can use different Wolfram rules to update their states) in the context of number conservation. As a result, we obtain an exhaustive characterization of such number-conserving cellular automata on all finite grids both with periodic and null boundary conditions. The characterization obtained allows, inter alia, to enumerate all number-conserving non-uniform elementary cellular automata, in particular those that are reversible. Surprisingly, the numbers obtained are closely related to the Fibonacci sequence.}},
  author       = {{Wolnik, Barbara and Dziemiańczuk, Maciej and De Baets, Bernard}},
  issn         = {{0020-0255}},
  journal      = {{INFORMATION SCIENCES}},
  keywords     = {{Artificial Intelligence,Information Systems and Management,Computer Science Applications,Theoretical Computer Science,Control and Systems Engineering,Software,Cellular automata,Non -uniform cellular automata,Number conservation,LATTICE-GAS,COMPLEXITY,DYNAMICS}},
  language     = {{eng}},
  pages        = {{851--866}},
  title        = {{Non-uniform number-conserving elementary cellular automata}},
  url          = {{http://doi.org/10.1016/j.ins.2023.01.033}},
  volume       = {{626}},
  year         = {{2023}},
}

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