This work reports a study on the dynamics of k non-uniform cellular automata (CA), where the cellular system is associated with two elementary CA (ECA) rules \(\mathcal {R}_1\) and \(\mathcal {R}_2\) (non-uniform couples). The \(\mathcal {R}_1\) is the default rule, and the noise rule \(\mathcal {R}_2\) is applied to the rule vector of the CA with a perturbation rate of “k” to shatter the deterministic notion of (hybrid) non-uniform CA system. It explores the dynamics of chaotic and locally chaotic non-uniform couples following the qualitative (space-time diagrams) and quantitative (density and Kolmogorov-Sinai entropy) experimental approach and establishes the fact that (a) Some chaotic non-uniform couples show strong resistance against the k perturbation; (b) The chaotic ECA 18 depicts dominating nature during interaction with the locally chaotic systems, however, ECA 126 is dominated due such perturbation; and (c) The class transition -that is, locally chaotic to chaotic and locally chaotic to fixed point exists during evolution of the k non-uniform system.

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First Experiments on Chaotic k Non-Uniform Cellular Automata

  • Souvik Roy,
  • Aryan Sukhadia,
  • Harsh Modi,
  • Tanay Shah,
  • Biplab K. Sikdar

摘要

This work reports a study on the dynamics of k non-uniform cellular automata (CA), where the cellular system is associated with two elementary CA (ECA) rules \(\mathcal {R}_1\) and \(\mathcal {R}_2\) (non-uniform couples). The \(\mathcal {R}_1\) is the default rule, and the noise rule \(\mathcal {R}_2\) is applied to the rule vector of the CA with a perturbation rate of “k” to shatter the deterministic notion of (hybrid) non-uniform CA system. It explores the dynamics of chaotic and locally chaotic non-uniform couples following the qualitative (space-time diagrams) and quantitative (density and Kolmogorov-Sinai entropy) experimental approach and establishes the fact that (a) Some chaotic non-uniform couples show strong resistance against the k perturbation; (b) The chaotic ECA 18 depicts dominating nature during interaction with the locally chaotic systems, however, ECA 126 is dominated due such perturbation; and (c) The class transition -that is, locally chaotic to chaotic and locally chaotic to fixed point exists during evolution of the k non-uniform system.