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This work studies Cellular Automata (CAs) over Cayley tree of order 2, where each vertex of the tree is considered as a cell and the nearest connected vertices are considered as its neighbors. The proposed CA follows a two-state, four-neighborhood structure, where each cell updates its state using a local update rule. In this work, we mainly focus on the fixed points of a CA. When a CA reaches to a fixed point, say c, the CA remains at c forever during evolution. We investigate the fixed points by introducing the Fixed Point Graph (FPG) of a CA. Finally, we propose an algorithm that computes the number of fixed points of a CA.

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Finding Fixed Points of Cellular Automata over Cayley Tree of Order 2

  • 会议论文

  • 发表日期：

    2026年

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  • Bipul Patra,
  • Subrata Paul

摘要

This work studies Cellular Automata (CAs) over Cayley tree of order 2, where each vertex of the tree is considered as a cell and the nearest connected vertices are considered as its neighbors. The proposed CA follows a two-state, four-neighborhood structure, where each cell updates its state using a local update rule. In this work, we mainly focus on the fixed points of a CA. When a CA reaches to a fixed point, say c, the CA remains at c forever during evolution. We investigate the fixed points by introducing the Fixed Point Graph (FPG) of a CA. Finally, we propose an algorithm that computes the number of fixed points of a CA.