Complete Characterization of Structure of Rule 54

نویسندگان

  • Genaro Juárez Martínez
  • Andrew Adamatzky
  • Harold V. McIntosh
چکیده

The dynamics of the rule 54 one-dimensional, two-state cellular automaton (CA) are a discrete analog of a space-time dynamics of excitations in a nonlinear active medium with mutual inhibition. A cell switches its state 0 to state 1 if one of its two neighbors is in state 1 (propagation of a perturbation), and a cell remains in state 1 only if its two neighbors are in state 0. A lateral inhibition is because a 1-state neighbor causes a 1-state cell to switch to state 0. The rule produces a rich spectrum of space-time dynamics, including gliders and glider guns just from four primitive gliders. We construct a catalog of gliders and describe them by tiles. We calculate a subset of regular expressions YR54 to encode gliders. The regular expressions are derived from de Bruijn diagrams, tile-based representation of gliders, and cycle diagrams sometimes. We construct an abstract machine that recognizes regular expressions of gliders in rule 54 and validate YR54. We also propose a way to code initial configurations of gliders to depict any type of collision between the gliders and explore self-organization of gliders, formation of larger tiles, and soliton-like interactions of gliders and computable devices.

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عنوان ژورنال:
  • Complex Systems

دوره 23  شماره 

صفحات  -

تاریخ انتشار 2014