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March 3, 2026Natural ComputingOpen Access

On the surjunctivity and the Garden of Eden theorem for non-uniform cellular automata

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KPKatariina PaturiJKJarkko Kari

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Overview

Analysis reveals the conditions for the Garden of Eden theorem in non-uniform cellular automata, indicating their broader implications.

Key Points

  • Garden of Eden theorem holds for uniformly recurrent local rules in non-uniform cellular automata.
  • A non-recurrent one-dimensional rule distribution can be substituted to create a NUCA that fails the theorem.
  • Non-uniform cellular automata with asymptotic recurrent distributions can exhibit surjunctivity under specific conditions.
  • Findings expand understanding of local rule configurations and their effects on cellular automata behavior.

Cite This Study

Paturi et al. (2026) studied this question.

synapsesocial.com/papers/69a7612ac6e9836116a2ed82https://doi.org/10.1007/s11047-026-10067-8
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