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The state of the collection of entities is updated at each discrete time according to some simple homogeneous rule. All entities' states are updated in parallel or synchronously. Stochastic cellular automata are CA whose updating rule is a
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Boas, Sonja E. M.; Jiang, Yi; Merks, Roeland M. H.; Prokopiou, Sotiris A.; Rens, Elisabeth G. (2018). "Chapter 18: Cellular Potts Model: Applications to
Vasculogenesis and Angiogenesis". In Louis, P.-Y.; Nardi, F. R. (eds.).
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Locally
Interacting Systems and their Application in Biology: Proceedings of the School-Seminar on Markov Interaction Processes in Biology, held in Pushchino, March 1976
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Fernandez, R.; Louis, P.-Y.; Nardi, F. R. (2018). "Chapter 1: Overview: PCA Models and Issues". In Louis, P.-Y.; Nardi, F. R. (eds.).
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one, which means the new entities' states are chosen according to some probability distributions. It is a discrete-time
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a finite neighbourhood of k. See for a more detailed introduction following the probability theory's point of view.
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Almeida, R. M.; Macau, E. E. N. (2010), "Stochastic cellular automata model for wildland fire spread dynamics",
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127:. From the spatial interaction between the entities, despite the simplicity of the updating rules,
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Studies in language classes defined by different types of time-varying cellular automata
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9th
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Agapie, A.; Andreica, A.; Giuclea, M. (2014), "Probabilistic
Cellular Automata",
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859:, Lecture Notes in Mathematics, vol. 653, Springer-Verlag, Berlin-New York,
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1161:(1972), "Real-time language recognition by one-dimensional cellular automata",
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Nishio, Hidenosuke; Kobuchi, Youichi (1975), "Fault tolerant cellular spaces",
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There is a strong connection between probabilistic cellular automata and the
461:{\displaystyle P(d\sigma |\eta )=\otimes _{k\in G}p_{k}(d\sigma _{k}|\eta )}
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676:{\displaystyle p_{k}(d\sigma _{k}|\eta )=p_{k}(d\sigma _{k}|\eta _{V_{k}})}
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139:. As mathematical object, it may be considered in the framework of
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Vichniac, G. (1984), "Simulating physics with cellular automata",
1198:. Emergence, Complexity and Computation. Vol. 27. Springer.
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Stochastic
Cellular Systems: Ergodicity, Memory, Morphogenesis
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in discrete-time. See for a more detailed introduction.
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749:{\displaystyle \eta _{V_{k}}=(\eta _{j})_{j\in V_{k}}}
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As discrete-time Markov process, PCA are defined on a
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R. L. Dobrushin; V. I. Kri︠u︡kov; A. L. Toom (1978).
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57:, without removing the technical details.
111:. Cellular automata are a discrete-time
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1128:Journal of Computer and System Sciences
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575:. In general some locality is required
200:{\displaystyle E=\prod _{k\in G}S_{k}}
1118:Indian Institute of Technology Madras
276:is a finite space, like for instance
55:make it understandable to non-experts
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227:is a finite or infinite graph, like
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151:PCA as Markov stochastic processes
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810:Relation to lattice random fields
548:is a probability distribution on
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814:PCA may be used to simulate the
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1196:Probabilistic Cellular Automata
1110:Mahajan, Meena Bhaskar (1992),
1004:Probabilistic Cellular Automata
916:Probabilistic Cellular Automata
893:. Manchester University Press.
320:{\displaystyle S_{k}=\{-1,+1\}}
90:probabilistic cellular automata
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365:{\displaystyle S_{k}=\{0,1\}}
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242:{\displaystyle \mathbb {Z} }
86:Stochastic cellular automata
18:Stochastic cellular automata
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800:majority cellular automaton
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220:{\displaystyle G}
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816:Ising model
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1271:Categories
1020:1887/69811
842:References
249:and where
121:stochastic
968:Physica D
732:∈
715:η
692:η
655:η
640:σ
614:η
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519:σ
479:∈
476:η
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414:∈
407:⊗
397:η
389:σ
300:−
180:∈
173:∏
63:June 2013
1261:24999557
1103:40847078
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1083:Bibcode
976:Bibcode
875:0479791
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494:and
131:may
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100:or
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