### Abstract

The directed-percolation (DP) hypothesis for stochastic, range-4 cellular automata with an acceptance rule y ≤ ∑_{j=-4}^{4} s_{i-j} ≤ 6, in the cases of y : {1, ⋯ , 5}, S_{i} {0,1} was investigated in one and two dimensions. Simulations, as well as mean-field renormalization-group and coherent-anomaly calculations, show that in one dimension the phase for y <4 are continuous and belong to the DP class, while for y = 4, 5 They are discontinuous. The same rules in two dimensions for y = 1 show (2 + 1)-dimensional DP university; but in the cases of y > 1 the transitions become first order.

Original language | English |
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Pages (from-to) | 2231-2238 |

Number of pages | 8 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 53 |

Issue number | 3 |

Publication status | Published - 1996 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics

### Cite this

**Directed-percolation conjecture for cellular automata.** / Ódor, G.; Szolnoki, A.

Research output: Contribution to journal › Article

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 53, no. 3, pp. 2231-2238.

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TY - JOUR

T1 - Directed-percolation conjecture for cellular automata

AU - Ódor, G.

AU - Szolnoki, A.

PY - 1996

Y1 - 1996

N2 - The directed-percolation (DP) hypothesis for stochastic, range-4 cellular automata with an acceptance rule y ≤ ∑j=-44 si-j ≤ 6, in the cases of y : {1, ⋯ , 5}, Si {0,1} was investigated in one and two dimensions. Simulations, as well as mean-field renormalization-group and coherent-anomaly calculations, show that in one dimension the phase for y <4 are continuous and belong to the DP class, while for y = 4, 5 They are discontinuous. The same rules in two dimensions for y = 1 show (2 + 1)-dimensional DP university; but in the cases of y > 1 the transitions become first order.

AB - The directed-percolation (DP) hypothesis for stochastic, range-4 cellular automata with an acceptance rule y ≤ ∑j=-44 si-j ≤ 6, in the cases of y : {1, ⋯ , 5}, Si {0,1} was investigated in one and two dimensions. Simulations, as well as mean-field renormalization-group and coherent-anomaly calculations, show that in one dimension the phase for y <4 are continuous and belong to the DP class, while for y = 4, 5 They are discontinuous. The same rules in two dimensions for y = 1 show (2 + 1)-dimensional DP university; but in the cases of y > 1 the transitions become first order.

UR - http://www.scopus.com/inward/record.url?scp=0000670935&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000670935&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0000670935

VL - 53

SP - 2231

EP - 2238

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 3

ER -