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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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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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1057:"A self-modifying cellular automaton model of historical urbanization in the San Francisco Bay area"
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116:. 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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Brazilian Conference on Dynamics, Control and their Applications, June 7–11, 2010
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Agapie, A.; Andreica, A.; Giuclea, M. (2014), "Probabilistic
Cellular Automata",
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1150:(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
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450:{\displaystyle P(d\sigma |\eta )=\otimes _{k\in G}p_{k}(d\sigma _{k}|\eta )}
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665:{\displaystyle p_{k}(d\sigma _{k}|\eta )=p_{k}(d\sigma _{k}|\eta _{V_{k}})}
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Vichniac, G. (1984), "Simulating physics with cellular automata",
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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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738:{\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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530:{\displaystyle p_{k}(d\sigma _{k}|\eta )}
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62:Learn how and when to remove this message
46:, without removing the technical details.
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100:. Cellular automata are a discrete-time
1153:Journal of Computer and System Sciences
1117:Journal of Computer and System Sciences
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189:{\displaystyle E=\prod _{k\in G}S_{k}}
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265:is a finite space, like for instance
44:make it understandable to non-experts
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537:is a probability distribution on
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803:PCA may be used to simulate the
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1185:Probabilistic Cellular Automata
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309:{\displaystyle S_{k}=\{-1,+1\}}
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231:{\displaystyle \mathbb {Z} }
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805:Ising model
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1260:Categories
1009:1887/69811
831:References
238:and where
110:stochastic
957:Physica D
721:∈
704:η
681:η
644:η
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396:⊗
386:η
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289:−
169:∈
162:∏
52:June 2013
1250:24999557
1092:40847078
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864:0479791
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