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A complete description of the dynamics of legal outer-totalistic affine continuous cellular automata

Barbara Wolnik (UGent) , Marcin Dembowski, Antoni Augustynowicz and Bernard De Baets (UGent)
(2022) NONLINEAR DYNAMICS. 110(1). p.589-610
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Abstract
This paper presents an investigation into the evolution and dynamics of the simplest generalization of binary cellular automata: Affine continuous cellular automata (ACCAs), with [0,1] as state set and local rules that are affine in each variable. The focus lies on legal outer-totalistic ACCAs, an interesting class of dynamical systems that exhibit some behavior that is not observed in the binary case. A unique combination of computer simulations (sometimes quite advanced) and a panoply of analytical methods allows to lay bare the dynamics of each and every one of these continuous cellular automata. The results also show that in the class of ACCAs considered, all types of sensitivity can be observed: sensitivity to a change of the number of cells in the grid, sensitivity to slight changes in the parameters of a local rule and sensitivity to the change of a single value in an initial configuration.
Keywords
Affine, Continuous, Outertotalistic, Cellular automata, Dynamical systems, Sensitivity, CONWAYS, GAME

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MLA
Wolnik, Barbara, et al. “A Complete Description of the Dynamics of Legal Outer-Totalistic Affine Continuous Cellular Automata.” NONLINEAR DYNAMICS, vol. 110, no. 1, 2022, pp. 589–610, doi:10.1007/s11071-022-07642-w.
APA
Wolnik, B., Dembowski, M., Augustynowicz, A., & De Baets, B. (2022). A complete description of the dynamics of legal outer-totalistic affine continuous cellular automata. NONLINEAR DYNAMICS, 110(1), 589–610. https://doi.org/10.1007/s11071-022-07642-w
Chicago author-date
Wolnik, Barbara, Marcin Dembowski, Antoni Augustynowicz, and Bernard De Baets. 2022. “A Complete Description of the Dynamics of Legal Outer-Totalistic Affine Continuous Cellular Automata.” NONLINEAR DYNAMICS 110 (1): 589–610. https://doi.org/10.1007/s11071-022-07642-w.
Chicago author-date (all authors)
Wolnik, Barbara, Marcin Dembowski, Antoni Augustynowicz, and Bernard De Baets. 2022. “A Complete Description of the Dynamics of Legal Outer-Totalistic Affine Continuous Cellular Automata.” NONLINEAR DYNAMICS 110 (1): 589–610. doi:10.1007/s11071-022-07642-w.
Vancouver
1.
Wolnik B, Dembowski M, Augustynowicz A, De Baets B. A complete description of the dynamics of legal outer-totalistic affine continuous cellular automata. NONLINEAR DYNAMICS. 2022;110(1):589–610.
IEEE
[1]
B. Wolnik, M. Dembowski, A. Augustynowicz, and B. De Baets, “A complete description of the dynamics of legal outer-totalistic affine continuous cellular automata,” NONLINEAR DYNAMICS, vol. 110, no. 1, pp. 589–610, 2022.
@article{8767653,
  abstract     = {{This paper presents an investigation into the evolution and dynamics of the simplest generalization of binary cellular automata: Affine continuous cellular automata (ACCAs), with [0,1] as state set and local rules that are affine in each variable. The focus lies on legal outer-totalistic ACCAs, an interesting class of dynamical systems that exhibit some behavior that is not observed in the binary case. A unique combination of computer simulations (sometimes quite advanced) and a panoply of analytical methods allows to lay bare the dynamics of each and every one of these continuous cellular automata. The results also show that in the class of ACCAs considered, all types of sensitivity can be observed: sensitivity to a change of the number of cells in the grid, sensitivity to slight changes in the parameters of a local rule and sensitivity to the change of a single value in an initial configuration.}},
  author       = {{Wolnik, Barbara and Dembowski, Marcin and Augustynowicz, Antoni and De Baets, Bernard}},
  issn         = {{0924-090X}},
  journal      = {{NONLINEAR DYNAMICS}},
  keywords     = {{Affine,Continuous,Outertotalistic,Cellular automata,Dynamical systems,Sensitivity,CONWAYS,GAME}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{589--610}},
  title        = {{A complete description of the dynamics of legal outer-totalistic affine continuous cellular automata}},
  url          = {{http://doi.org/10.1007/s11071-022-07642-w}},
  volume       = {{110}},
  year         = {{2022}},
}
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