State-conserving one-dimensional cellular automata with radius one
- Author
- Barbara Wolnik (UGent) , Maciej Dziemianczuk and Bernard De Baets (UGent)
- Organization
- Abstract
- This paper presents a new way of looking at state-conserving one-dimensional cellular automata. Such cellular automata preserve the distribution of states, i.e., the number of cells in each state, throughout the entire evolution of the system. The tools introduced make it possible to fully characterize and enumerate all such cellular automata with radius one, regardless of the number of states. Surprisingly, it turns out that the number of state-conserving one-dimensional cellular automata with radius one and k states is very closely related to the number of labeled directed graphs with k vertices and not containing a directed path of length two.
- Keywords
- One-dimensional cellular automata, State-conserving cellular automata, State conservation, Multi-state cellular automata
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01JTFP8M07Z4EN71PY79NQSSSG
- MLA
- Wolnik, Barbara, et al. “State-Conserving One-Dimensional Cellular Automata with Radius One.” NONLINEAR DYNAMICS, vol. 113, no. 12, 2025, pp. 15393–405, doi:10.1007/s11071-025-10896-9.
- APA
- Wolnik, B., Dziemianczuk, M., & De Baets, B. (2025). State-conserving one-dimensional cellular automata with radius one. NONLINEAR DYNAMICS, 113(12), 15393–15405. https://doi.org/10.1007/s11071-025-10896-9
- Chicago author-date
- Wolnik, Barbara, Maciej Dziemianczuk, and Bernard De Baets. 2025. “State-Conserving One-Dimensional Cellular Automata with Radius One.” NONLINEAR DYNAMICS 113 (12): 15393–405. https://doi.org/10.1007/s11071-025-10896-9.
- Chicago author-date (all authors)
- Wolnik, Barbara, Maciej Dziemianczuk, and Bernard De Baets. 2025. “State-Conserving One-Dimensional Cellular Automata with Radius One.” NONLINEAR DYNAMICS 113 (12): 15393–15405. doi:10.1007/s11071-025-10896-9.
- Vancouver
- 1.Wolnik B, Dziemianczuk M, De Baets B. State-conserving one-dimensional cellular automata with radius one. NONLINEAR DYNAMICS. 2025;113(12):15393–405.
- IEEE
- [1]B. Wolnik, M. Dziemianczuk, and B. De Baets, “State-conserving one-dimensional cellular automata with radius one,” NONLINEAR DYNAMICS, vol. 113, no. 12, pp. 15393–15405, 2025.
@article{01JTFP8M07Z4EN71PY79NQSSSG,
abstract = {{This paper presents a new way of looking at state-conserving one-dimensional cellular automata. Such cellular automata preserve the distribution of states, i.e., the number of cells in each state, throughout the entire evolution of the system. The tools introduced make it possible to fully characterize and enumerate all such cellular automata with radius one, regardless of the number of states. Surprisingly, it turns out that the number of state-conserving one-dimensional cellular automata with radius one and k states is very closely related to the number of labeled directed graphs with k vertices and not containing a directed path of length two.}},
author = {{Wolnik, Barbara and Dziemianczuk, Maciej and De Baets, Bernard}},
issn = {{0924-090X}},
journal = {{NONLINEAR DYNAMICS}},
keywords = {{One-dimensional cellular automata,State-conserving cellular automata,State conservation,Multi-state cellular automata}},
language = {{eng}},
number = {{12}},
pages = {{15393--15405}},
title = {{State-conserving one-dimensional cellular automata with radius one}},
url = {{http://doi.org/10.1007/s11071-025-10896-9}},
volume = {{113}},
year = {{2025}},
}
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