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All binary number-conserving cellular automata based on adjacent cells are intrinsically one-dimensional

(2019) PHYSICAL REVIEW E. 100(2).
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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:

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.
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).
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).
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).
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://dx.doi.org/10.1103/physreve.100.022126}},
  volume       = {{100}},
  year         = {{2019}},
}

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