Lattice-driven cellular automata implementing local semantics

Daisuke Uragami, Yukio Gunji

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

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
Volume237
Issue number2
DOIs
Publication statusPublished - 2008 Feb
Externally publishedYes

Fingerprint

semantics
cellular automata
Cellular automata
Cellular Automata
Semantics
Cell
cells
Mediator
Mean Value
Discrepancy
State Space
Entropy
Space-time
entropy
Model-based
Invariant

Keywords

  • Cellular automaton
  • Hierarchy
  • Lattice
  • Semantics
  • Wholeness

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

Lattice-driven cellular automata implementing local semantics. / Uragami, Daisuke; Gunji, Yukio.

In: Physica D: Nonlinear Phenomena, Vol. 237, No. 2, 02.2008, p. 187-197.

Research output: Contribution to journalArticle

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