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Related Experiment Videos

Traveling patterns in cellular automata.

Jesus Urias1, G. Salazar-Anaya, Edgardo Ugalde

  • 1Instituto de Investigacion en Comunicacion Optica, Universidad Autonoma de San Luis Potosi, 78000, San Luis Potosi, SLP, MexicoDepartment of Mathematics and Statistics, Carleton University, Ottawa, Ontario, CanadaCPT, Luminy, Case 907, F-13288 Marseille, Cedex 9, FranceEscuela de Fisica, Universidad Autonoma de Zacatecas, 98000 Zacatecas, Zac., Mexico.

Chaos (Woodbury, N.Y.)
|September 1, 1996
PubMed
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This study introduces a method to identify cellular automaton (CA) configurations that move at constant speeds. It reveals that domain interactions dominate dynamics when configurations exhibit non-zero topological entropy.

Area of Science:

  • Complex Systems
  • Theoretical Computer Science
  • Dynamical Systems

Background:

  • Cellular automata (CA) are discrete dynamical systems with applications in physics and computation.
  • Understanding the long-term behavior and emergent patterns in CA is crucial for theoretical analysis.
  • Identifying invariant subsets and their propagation dynamics is key to characterizing CA behavior.

Purpose of the Study:

  • To develop a method for identifying invariant subsets of bi-infinite CA configurations propagating at constant velocity.
  • To analyze causal traveling configurations and their associated topological entropy.
  • To investigate the role of domain interactions in CA dynamics.

Main Methods:

  • Description of a method to identify invariant subsets of CA configurations.

Related Experiment Videos

  • Analysis of causal traveling configurations with speeds up to the automaton range.
  • Representation of configuration sets using finite automata.
  • Calculation of topological entropy for these sets.

    • Main Results:

    • Sets of traveling configurations and domains are characterized by finite automata.
    • Non-zero topological entropy indicates dynamics dominated by domain interactions.
    • End-resolving CA typically exhibit spatially periodic traveling configurations with zero entropy, except possibly at maximum speed.

    Conclusions:

    • The study provides a framework for analyzing propagating patterns in cellular automata.
    • Topological entropy serves as a key indicator of complex dynamics driven by domain interactions.
    • Elementary CA behavior is exhaustively examined through this lens.