Skip to main content
SpringerLink
Log in
Book cover

International Conference on Cellular Automata

ACRI 2008: Cellular Automata pp 174–183Cite as

Controlling the Dynamics of the Fuzzy Cellular Automaton Rule 90, I.

  • Conference paper

  • 1636 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5191))

Abstract

Control problems on Cellular Automata (CA) models have been introduced in a rigorous mathematical framework [10]. In this paper, we attempt to apply the control theory concept to the special class of fuzzy CA for which more freedom is gained using a continuum state space. Focusing on the case of fuzzy rule 90, we investigate the possibility of finding a control u = (u 0, u 1, ⋯ , u T − 1) which forces the system at a localized cell, to achieve a given desired state at time T. The problem is studied starting from an initial configuration consisting of a single seed on a zero background.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bunimovich, L.A.: Coupled Map Lattices: one Step Forward and two Steps Back. Physica D 86, 248–255 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  2. Cattaneo, G., Flocchini, P., Mauri, G., Santoro, N.: Cellular automata in fuzzy backgrounds. Physica D 105, 105–120 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chopard, B., Droz, M.: Cellular automata modelling of physical systems. In: Collection Alea-Sacley. Cambridge University Press, Cambridge (1998)

    Google Scholar 

  4. Conway, J. H.: Game of life (1976)

    Google Scholar 

  5. Culik II, K., Yu, S.: Undecidability of CA classification schemes. Complex Systems 2, 177–190 (1988)

    MATH  MathSciNet  Google Scholar 

  6. El Yacoubi, S., El Jai, A.: Notes on control and observation in Cellular automata models. WSEAS Transaction on Computers 4(2), 1086–1092 (2003)

    Google Scholar 

  7. El Yacoubi, S., El Jai, A., Ammor, N.: Regional controllability with cellular automata models. In: Bandini, S., Chopard, B., Tomassini, M. (eds.) ACRI 2002. LNCS, vol. 2493, pp. 357–367. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  8. El Yacoubi, S., El Jai, A.: Cellular Automata and Spreadability. Journal of Mathematical and Computer Modelling 36, 1059–1074 (2002)

    Article  MATH  Google Scholar 

  9. El Yacoubi, S., Jacewicz, P.: A genetic programming approach to structural identification of cellular automata models. Journal Of Cellular Automata

    Google Scholar 

  10. El Yacoubi, S.: A Mathematical method for control problems on Cellular Automata models. International Journal of Systems Sciences 39(5), 529–538 (2008)

    Google Scholar 

  11. Flocchini, P., Geurts, F., Mingarelli, A., Santoro, N.: Convergence and aperiodicity in fuzzy cellular automata: revisiting rule 90. Physica D 42, 20–28 (2000)

    Article  MathSciNet  Google Scholar 

  12. Flocchini, P., Santoro, N.: The chaotic evolution of information in the interaction between knowledge and uncertainty. In: Stonier, R.J., Yu, X.H. (eds.) Complex Systems: Mechanism of Adaptation, pp. 337–343. IOS Press, Amsterdam (1994)

    Google Scholar 

  13. Garzon, M.: Models of massive parallelism. Analysis of cellular automata and neural networks. Springer, Heidelberg (1995)

    MATH  Google Scholar 

  14. Hedlund, G.A.: Endomorphisms and automorphisms of the shift dynamical systems. Mathematical Systems Theory 3, 320–375 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  15. Mingarelli, A.B.: The global evolution of general fuzzy cellular automata. J. Cellular Automata 1(2), 141–164 (2006)

    MATH  MathSciNet  Google Scholar 

  16. Mingarelli, A.B., El Yacoubi, S.: On the decidability of the evolution of the fuzzy cellular automaton, FCA 184. In: Alexandrov, V.N., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds.) ICCS 2006. LNCS, vol. 3993, pp. 360–366. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  17. Von Neumann, J.: Theory of Self-Reproducing Automata. University of Illinois Press, Urbana (1966)

    Google Scholar 

  18. Sontag, E.D.: Mathematical Control Theory: Deterministic Finite Dimensional Systems, 2nd edn. Springer, Heidelberg (1998)

    MATH  Google Scholar 

  19. Sipper, M.: Non-Uniform Cellular Automata: Evolution in Rule Space and Formation of Complex Structures. In: Brooks, R.A., Maes, P. (eds.) Artificial Life IV, pp. 394–399. MIT Press, Cambridge (1994)

    Google Scholar 

  20. Toffoli, T.: Cellular automata as an alternative to differential equation in modeling physics. Physica D 10, 117–127 (1984)

    Article  MathSciNet  Google Scholar 

  21. Vichniac, G.Y.: Simulating physics with cellular automata. Physica D 10, 96–115 (1984)

    Article  MathSciNet  Google Scholar 

  22. Wolfram, S.: Cellular Automata and Complexity. Collected Papers. World Scientific, Singapore (1994)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of Mathematics, Physics and Systems, University of Perpignan, 52, Paul Alduy Avenue, 66860, Perpignan, Cedex, France

    Samira El Yacoubi

  2. School of Mathematics and Statistics, Carleton University, Ottawa, Canada, K1S 5B6

    Angelo Mingarelli

Authors
  1. Samira El Yacoubi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Angelo Mingarelli
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Hiroshi Umeo Shin Morishita Katsuhiro Nishinari Toshihiko Komatsuzaki Stefania Bandini

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

El Yacoubi, S., Mingarelli, A. (2008). Controlling the Dynamics of the Fuzzy Cellular Automaton Rule 90, I.. In: Umeo, H., Morishita, S., Nishinari, K., Komatsuzaki, T., Bandini, S. (eds) Cellular Automata. ACRI 2008. Lecture Notes in Computer Science, vol 5191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79992-4_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-79992-4_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79991-7

  • Online ISBN: 978-3-540-79992-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation