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On the dynamics of stochastic elementary cellular automata

(2017) JOURNAL OF CELLULAR AUTOMATA. 12(1-2). p.63-80
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Abstract
In this paper the dynamics of stochastic elementary cellular automata (SECAs) is investigated and compared to that of their deterministic counterparts. We observe that moving away from the determinism in von Neumann's original design impacts CA dynamics to such an extent that sensitive dependence on initial conditions might get lost abruptly, or also the other way around, might arise suddenly. As such, the behavior in a deterministic setting can be unrepresentative for the dynamics one gets in a stochastic setting. In the case of SECAs, it turns out that the involved probabilities should be understood as bifurcation parameters steering the nature of such SECAs, i.e. whether or not they are unstable.
Keywords
TRANSITIONS, MODELS, COMPLEXITY, TOPOLOGY, LYAPUNOV EXPONENTS, stochastic cellular automaton, stability, sensitive dependence on initial conditions, Lyapunov exponent

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Citation

Please use this url to cite or link to this publication:

Chicago
Baetens, Jan, Wouter Van der Meeren, and Bernard De Baets. 2017. “On the Dynamics of Stochastic Elementary Cellular Automata.” Journal of Cellular Automata 12 (1-2): 63–80.
APA
Baetens, Jan, Van der Meeren, W., & De Baets, B. (2017). On the dynamics of stochastic elementary cellular automata. JOURNAL OF CELLULAR AUTOMATA, 12(1-2), 63–80.
Vancouver
1.
Baetens J, Van der Meeren W, De Baets B. On the dynamics of stochastic elementary cellular automata. JOURNAL OF CELLULAR AUTOMATA. 2017;12(1-2):63–80.
MLA
Baetens, Jan, Wouter Van der Meeren, and Bernard De Baets. “On the Dynamics of Stochastic Elementary Cellular Automata.” JOURNAL OF CELLULAR AUTOMATA 12.1-2 (2017): 63–80. Print.
@article{8197320,
  abstract     = {In this paper the dynamics of stochastic elementary cellular automata (SECAs) is investigated and compared to that of their deterministic counterparts. We observe that moving away from the determinism in von Neumann's original design impacts CA dynamics to such an extent that sensitive dependence on initial conditions might get lost abruptly, or also the other way around, might arise suddenly. As such, the behavior in a deterministic setting can be unrepresentative for the dynamics one gets in a stochastic setting. In the case of SECAs, it turns out that the involved probabilities should be understood as bifurcation parameters steering the nature of such SECAs, i.e. whether or not they are unstable.},
  author       = {Baetens, Jan and Van der Meeren, Wouter and De Baets, Bernard},
  issn         = {1557-5969},
  journal      = {JOURNAL OF CELLULAR AUTOMATA},
  language     = {eng},
  number       = {1-2},
  pages        = {63--80},
  title        = {On the dynamics of stochastic elementary cellular automata},
  volume       = {12},
  year         = {2017},
}

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