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This work investigates finite non-uniform asynchronous cellular automata (NUACAs) under periodic boundary condition, following fully asynchronous update scheme. Based on the nature of recurrent configurations, these NUACAs are categorized into convergent, strongly non-convergent and weakly non-convergent. Furthermore, the convergent ACA rules are ranked from 1 to 8 based on the proportion of active RMTs. It is shown that NUACAs are strongly non-convergent even if they are composed by solely convergent rules. Moreover, this work identifies the minimal proportion of ranks 1 and 2 rules necessary to generate strongly non-convergent NUACAs.

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A Study of Non-uniform Cellular Automata with Fully Asynchronous Updating : First Results on the Non-convergent Cases

  • 会议论文

  • 发表日期：

    2026年

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  • Sukanya Mukherjee,
  • Mayukh Chatterjee,
  • Ahana Majumdar

摘要

This work investigates finite non-uniform asynchronous cellular automata (NUACAs) under periodic boundary condition, following fully asynchronous update scheme. Based on the nature of recurrent configurations, these NUACAs are categorized into convergent, strongly non-convergent and weakly non-convergent. Furthermore, the convergent ACA rules are ranked from 1 to 8 based on the proportion of active RMTs. It is shown that NUACAs are strongly non-convergent even if they are composed by solely convergent rules. Moreover, this work identifies the minimal proportion of ranks 1 and 2 rules necessary to generate strongly non-convergent NUACAs.