Lattice-driven cellular automata implementing local semantics

Daisuke Uragami*, Yukio Pegio Gunji

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


We propose a model based on Elementary Cellular Automata (ECA) where each cell has its own semantics defined by a lattice. Semantics play the following two roles: (1) a state space for computation and (2) a mediator generating and negotiating the discrepancy between the rule and the state. We call semantics playing such roles 'local semantics'. A lattice is a mathematical structure with certain limits. Weakening the limits reveals local semantics. Firstly, we implement local semantics for ECA and call the result 'Lattice-Driven Cellular Automata' (LDCA). In ECA rules are common and invariant for all cells, and uniquely determine the state changes, whereas in LDCA rules and states interplay with each other dynamically and directly in each cell. Secondly, we compare the space-time patterns of LDCA with those of ECA with respect to the relationship between the mean value and variance of the 'input-entropy'. The comparison reveals that LDCA generate complex patterns more universally than ECA. Lastly, we discuss the observation that the direct interplay between levels yields wholeness dynamically.

Original languageEnglish
Pages (from-to)187-197
Number of pages11
JournalPhysica D: Nonlinear Phenomena
Issue number2
Publication statusPublished - 2008 Feb
Externally publishedYes


  • Cellular automaton
  • Hierarchy
  • Lattice
  • Semantics
  • Wholeness

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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