Complete characterization of structure of rule 54

Martinez, G. J., Adamatzky, A. and McIntosh, H. V. (2014) Complete characterization of structure of rule 54. Complex Systems, 23 (3). pp. 259-293. ISSN 0891-2513 Available from:


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The dynamics of rule 54 one-dimensional two-state cellular automaton (CA) are a discrete analog of a space-time dynamics of excitations in 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 catalogue of gliders and describe them by tiles. We calculate a subset of regular expressions $\Psi_{R54}$ 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 $\Psi_{R54}$. 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.

Item Type:Article
Uncontrolled Keywords:elementary cellular automata, rule 54, complex systems, gliders, collisions, regular language
Faculty/Department:Faculty of Environment and Technology > Department of Computer Science and Creative Technologies
ID Code:24105
Deposited By: Dr G. Martinez
Deposited On:13 Oct 2014 09:43
Last Modified:15 Nov 2016 21:41

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