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This chapter provides a summary of recent results on number-conserving cellular automata, along with a general introduction to the field. We cover results in arbitrary dimensions, with particular attention to the von Neumann neighborhood, while also addressing specific classes of cellular automata, such as Wolfram’s well-known elementary cellular automata and non-uniform variants thereof, affine continuous cellular automata and cellular automata on triangular grids.

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Recent Insights into Number-Conserving Cellular Automata

  • 章节

  • 发表日期：

    2025年

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  • Barbara Wolnik,
  • Witold Bołt,
  • Bernard De Baets

摘要

This chapter provides a summary of recent results on number-conserving cellular automata, along with a general introduction to the field. We cover results in arbitrary dimensions, with particular attention to the von Neumann neighborhood, while also addressing specific classes of cellular automata, such as Wolfram’s well-known elementary cellular automata and non-uniform variants thereof, affine continuous cellular automata and cellular automata on triangular grids.