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Alexandru Agapie1, Anca Andreica, Marius Giuclea

  • 11 Department of Applied Mathematics, University of Economic Studies , Bucharest, Romania .

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Summary
This summary is machine-generated.

This study investigates synchronous cellular automata, exploring their long-term behavior. It connects configuration probabilities to zero-one borders, offering new insights into deterministic and probabilistic models.

Keywords:
binary latticecellular automatadetailed balance equationfinite homogeneous Markov chainstationary distribution

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Area of Science:

  • Complex Systems
  • Computational Science
  • Statistical Mechanics

Background:

  • Cellular automata model dynamical systems using local rules on binary lattices.
  • Automata can be synchronous or asynchronous, deterministic or probabilistic.
  • Predicting the end configuration from an initial state is a key theoretical challenge.

Purpose of the Study:

  • To provide numerical and theoretical insights into the long-term behavior of synchronous cellular automata.
  • To extend previous findings on asynchronous automata to synchronous models.
  • To analyze the relationship between configuration probabilities and zero-one borders.

Main Methods:

  • Analysis of synchronous cellular automata dynamics.
  • Application of concepts from finite homogeneous Markov chains for probabilistic models.
  • Numerical simulations and theoretical derivations.

Main Results:

  • The study offers insights into the stationary distribution of probabilistic synchronous automata.
  • A connection is established between configuration probabilities and the number of zero-one borders.
  • The long-term behavior of synchronous automata is characterized.

Conclusions:

  • The findings contribute to understanding the complex dynamics of synchronous cellular automata.
  • The research bridges theoretical analysis with numerical insights.
  • The work advances the prediction of end configurations in cellular automata models.