Advertisement

Journal of Statistical Physics

, Volume 77, Issue 3–4, pp 889–897 | Cite as

A note on inherent replication properties of local cellular automata transition functions

  • Heinrich Rust
Short Communications

Abstract

Local transition functions of elementary cellular automata show different tendencies to replicate parts of a configuration in a later generation. This is seen as regularities in the time-space diagram. This replication depends on both the configuration and the local transition function. A possibility to isolate the influence of the local transition function is shown.

Key Words

Cellular automata discrete dynamical systems elementary cellular automata entropy 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Stephen Wolfram, Statistical mechanics of cellular automata,Rev. Mod. Phys. 55(3):601–644 (1983).Google Scholar
  2. 2.
    Noam Chomsky and George A. Miller, Finite state languages,Information Control 1:91–112 (1958).Google Scholar
  3. 3.
    Stephen Wolfram, Computation theory of cellular automata,Commun. Math. Phys. 96:15–57 (1984).Google Scholar
  4. 4.
    Andrew Wuensche and Mike Lesser,The Global Dynamics of Cellular Automata (Addison-Wesley, 1992).Google Scholar
  5. 5.
    Erica Jen, Linear cellular automata and recurring sequences in finite fields,Commun. Math. Phys. 119:13–28 (1988).Google Scholar
  6. 6.
    Erica Jen, Transience and dislocations in one-dimensional cellular automata, inCellular Automata and Cooperative Systems, N. Boccara, E. Goles, S. Martinez, and P. Picco, eds. (Kluwer, 1993), pp. 299–310.Google Scholar
  7. 7.
    Heinrich Rust, Relatively invertible local transition functions of elementary cellular automata, submitted for publication.Google Scholar
  8. 8.
    Stephen Wolfram, ed.,Theory and Applications of Cellular Automata (World Scientific, Singapore, 1986).Google Scholar
  9. 9.
    Nino Boccara, Eric Goles, Servez Martinez, and Pierre Picco, eds.,Cellular Automata and Cooperative Systems (Kluywer, 1993).Google Scholar
  10. 10.
    O. Martin, A. M. Odlyzko, S. Wolfram, Algebraic properties of cellular automata,Commun. Math. Phys. 93:219–258 (1984).Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Heinrich Rust
    • 1
  1. 1.Informatik für Ingenieure and NaturwissenschaftlerUniversität Karlsruhe (TH)KarlsruheGermany

Personalised recommendations