Scholarlink

<p>This paper presents a new way of looking at state-conserving one-dimensional cellular automata. Such cellular automata preserve the distribution of states, i.e., the number of cells in each state, throughout the entire evolution of the system. The tools introduced make it possible to fully characterize and enumerate all such cellular automata with radius one, regardless of the number of states. Surprisingly, it turns out that the number of state-conserving one-dimensional cellular automata with radius one and <i>k</i> states is very closely related to the number of labeled directed graphs with <i>k</i> vertices and not containing a directed path of length two.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

State-conserving one-dimensional cellular automata with radius one

  • 期刊论文

  • 发表日期：

    2025年1月26日

查看全文
  • Barbara Wolnik,
  • Maciej Dziemiańczuk,
  • Bernard De Baets

摘要

This paper presents a new way of looking at state-conserving one-dimensional cellular automata. Such cellular automata preserve the distribution of states, i.e., the number of cells in each state, throughout the entire evolution of the system. The tools introduced make it possible to fully characterize and enumerate all such cellular automata with radius one, regardless of the number of states. Surprisingly, it turns out that the number of state-conserving one-dimensional cellular automata with radius one and k states is very closely related to the number of labeled directed graphs with k vertices and not containing a directed path of length two.