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<p>We investigate number conservation in non-uniform one-dimensional binary cellular automata with a neighborhood of size four. In this setting, cells may follow distinct local rules, leading to a wide range of dynamic behaviors. It is known that one way to synthesize such cellular automata on a finite grid of a given length is to use concatenation of smaller blocks, which are themselves number-conserving. By introducing new mathematical tools, we were able to find and describe in detail the dynamics of all such blocks of length less than five.</p>

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Exploration of number-conserving non-uniform cellular automata with a neighborhood of size four: barriers and blocks

  • 期刊论文

  • 发表日期：

    2026年2月14日

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  • Bartosz Makuracki,
  • Maciej Dziemiańczuk,
  • Barbara Wolnik,
  • Bernard De Baets

摘要

We investigate number conservation in non-uniform one-dimensional binary cellular automata with a neighborhood of size four. In this setting, cells may follow distinct local rules, leading to a wide range of dynamic behaviors. It is known that one way to synthesize such cellular automata on a finite grid of a given length is to use concatenation of smaller blocks, which are themselves number-conserving. By introducing new mathematical tools, we were able to find and describe in detail the dynamics of all such blocks of length less than five.