[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ skip to main content
10.1007/978-3-031-14926-9_10guideproceedingsArticle/Chapter ViewAbstractPublication PagesConference Proceedingsacm-pubtype
Article

Lyapunov Profiles of Three-State Totalistic Cellular Automata

Published: 12 September 2022 Publication History

Abstract

Inspired by the theory of continuous dynamical systems, Lyapunov exponents have been previously defined in the framework of cellular automata (CAs) in order to quantify a CA’s sensitive dependence on initial conditions, i.e. a CA’s sensitivity to a perturbation of an initial configuration. However, the application of these Lyapunov exponents is currently limited to two-state CAs, which limits their usefulness in the framework of CA-based models since these typically involve more than two states. This paper proposes an extension of the existing methodological framework to three-state CAs. Our method is illustrated for some interesting totalistic three-state rules, although it is generally applicable. Our proposed extension to the existing framework reveals some interesting features regarding CAs classified as class IV according to Wolfram’s classification.

References

[1]
Baetens JM and Gravner J Introducing Lyapunov profiles of cellular automata J. Cell. Autom. 2015 13 267-286
[2]
Bagnoli, F., Rechtman, R., Ruffo, S.: Damage spreading and Lyapunov exponents in cellular automata. Phys. Lett. A 172(1), 34–38 (1992)., http://www.sciencedirect.com/science/article/pii/037596019290185O
[3]
Bhattacharjee K, Naskar N, Roy S, and Das S A survey of cellular automata: types, dynamics, non-uniformity and applications Nat. Comput. 2018 19 2 433-461
[4]
Courbage, M., Kaminski, B.: Space-time directional Lyapunov exponents for cellular automata. J. Stat. Phys. 124 (2006).
[5]
Pfeifer B et al. A cellular automaton framework for infectious disease spread simulation Open Med. Inform. J. 2008 2 70-81
[6]
Reyes L and Laroze D Cellular automata for excitable media on a complex network: the effect of network disorder in the collective dynamics Physica A 2021 588 126552
[7]
Shereshevsky, M.A.: Lyapunov exponents for one-dimensional cellular automata. J. Nonlinear Sci. 2, 1–8 (1992).
[8]
Tisseur P Cellular automata and Lyapunov exponents Nonlinearity 2000 13 5 1547-1560
[9]
Vallejo, J., Sanjuán, M.: Predictability of Chaotic Dynamics: A Finite-time Lyapunov Exponents Approach. Springer, Cham (2019).
[10]
Vichniac G Boolean derivatives on cellular automata Physica D 1990 45 1–3 63-74
[11]
Vispoel M, Daly AJ, and Baetens JM Progress, gaps and obstacles in the classification of cellular automata Physica D 2022 432 133074
[12]
Wolfram S Universality and complexity in cellular automata Physica D 1984 10 37
[13]
Wuensche A Classifying cellular automata automatically: finding gliders, filtering, and relating space-time patterns, attractor basins, and the Z parameter Complexity 1999 4 47-66

Recommendations

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image Guide Proceedings
Cellular Automata: 15th International Conference on Cellular Automata for Research and Industry, ACRI 2022, Geneva, Switzerland, September 12–15, 2022, Proceedings
Sep 2022
372 pages
ISBN:978-3-031-14925-2
DOI:10.1007/978-3-031-14926-9

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 12 September 2022

Author Tags

  1. Cellular automata
  2. Lyapunov exponents
  3. Multi-state systems

Qualifiers

  • Article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • 0
    Total Citations
  • 0
    Total Downloads
  • Downloads (Last 12 months)0
  • Downloads (Last 6 weeks)0
Reflects downloads up to 30 Dec 2024

Other Metrics

Citations

View Options

View options

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media