All binary number-conserving cellular automata based on adjacent cells are intrinsically one-dimensional
- Author
- Barbara Wolnik and Bernard De Baets (UGent)
- Organization
- Abstract
- A binary number-conserving cellular automaton is a discrete dynamical system that models the movement of particles in a d-dimensional grid. Each cell of the grid is either empty or contains a particle. In subsequent time steps the particles move between the cells, but in one cell there can be at most one particle at a time. In this paper, the von Neumann neighborhood is considered, which means that in each time step a particle can move to an adjacent cell only. It is proven that regardless of the dimension d, all of these cellular automata are trivial, as they are intrinsically one-dimensional. Thus, for given d, there are only 4d+1 binary number-conserving cellular automata with the von Neumann neighborhood: the identity rule and the shift and traffic rules in each of the 2d possible directions.
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8626853
- MLA
- Wolnik, Barbara, and Bernard De Baets. “All Binary Number-Conserving Cellular Automata Based on Adjacent Cells Are Intrinsically One-Dimensional.” PHYSICAL REVIEW E, vol. 100, no. 2, 2019, doi:10.1103/physreve.100.022126.
- APA
- Wolnik, B., & De Baets, B. (2019). All binary number-conserving cellular automata based on adjacent cells are intrinsically one-dimensional. PHYSICAL REVIEW E, 100(2). https://doi.org/10.1103/physreve.100.022126
- Chicago author-date
- Wolnik, Barbara, and Bernard De Baets. 2019. “All Binary Number-Conserving Cellular Automata Based on Adjacent Cells Are Intrinsically One-Dimensional.” PHYSICAL REVIEW E 100 (2). https://doi.org/10.1103/physreve.100.022126.
- Chicago author-date (all authors)
- Wolnik, Barbara, and Bernard De Baets. 2019. “All Binary Number-Conserving Cellular Automata Based on Adjacent Cells Are Intrinsically One-Dimensional.” PHYSICAL REVIEW E 100 (2). doi:10.1103/physreve.100.022126.
- Vancouver
- 1.Wolnik B, De Baets B. All binary number-conserving cellular automata based on adjacent cells are intrinsically one-dimensional. PHYSICAL REVIEW E. 2019;100(2).
- IEEE
- [1]B. Wolnik and B. De Baets, “All binary number-conserving cellular automata based on adjacent cells are intrinsically one-dimensional,” PHYSICAL REVIEW E, vol. 100, no. 2, 2019.
@article{8626853,
abstract = {{A binary number-conserving cellular automaton is a discrete dynamical system that models the movement of particles in a d-dimensional grid. Each cell of the grid is either empty or contains a particle. In subsequent time steps the particles move between the cells, but in one cell there can be at most one particle at a time. In this paper, the von Neumann neighborhood is considered, which means that in each time step a particle can move to an adjacent cell only. It is proven that regardless of the dimension d, all of these cellular automata are trivial, as they are intrinsically one-dimensional. Thus, for given d, there are only 4d+1 binary number-conserving cellular automata with the von Neumann neighborhood: the identity rule and the shift and traffic rules in each of the 2d possible directions.}},
articleno = {{022126}},
author = {{Wolnik, Barbara and De Baets, Bernard}},
issn = {{2470-0045}},
journal = {{PHYSICAL REVIEW E}},
language = {{eng}},
number = {{2}},
pages = {{6}},
title = {{All binary number-conserving cellular automata based on adjacent cells are intrinsically one-dimensional}},
url = {{http://doi.org/10.1103/physreve.100.022126}},
volume = {{100}},
year = {{2019}},
}
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