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<p>This work explores a new cellular automaton model, where two rules, say <i>f</i> and <i>g</i> are applied with some probability to each cell temporarily. Rule <i>f</i> acts as default rule of the model, whereas rule <i>g</i> is treated as a noise rule and applied with probability <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\tau\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation>. This class of cellular automata is called <i>Temporally Stochastic Cellular Automata</i> (TSCAs). The dynamical behaviour of these automata is studied to identify the list of convergent TSCAs. This work identifies the similarities between TSCAs and Markov chains, and shows that the dynamics of the TSCAs are Markovian. We utilise absorbing Markov chain as a tool to study the convergence of TSCAs. Finally, we study the theoretical aspects behind the convergence of TSCAs to validate the experimental outcomes of dynamical studies.</p>

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On convergence of temporally stochastic cellular automata

  • 期刊论文

  • 发表日期：

    2026年1月20日

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  • Subrata Paul,
  • Souvik Roy,
  • Sukanta Das

摘要

This work explores a new cellular automaton model, where two rules, say f and g are applied with some probability to each cell temporarily. Rule f acts as default rule of the model, whereas rule g is treated as a noise rule and applied with probability \(\tau\) τ . This class of cellular automata is called Temporally Stochastic Cellular Automata (TSCAs). The dynamical behaviour of these automata is studied to identify the list of convergent TSCAs. This work identifies the similarities between TSCAs and Markov chains, and shows that the dynamics of the TSCAs are Markovian. We utilise absorbing Markov chain as a tool to study the convergence of TSCAs. Finally, we study the theoretical aspects behind the convergence of TSCAs to validate the experimental outcomes of dynamical studies.