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ACRI
2008
Springer

On the Representation of Gliders in Rule 54 by De Bruijn and Cycle Diagrams

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On the Representation of Gliders in Rule 54 by De Bruijn and Cycle Diagrams
Abstract. Rule 54, in Wolfram’s notation, is one of elementary yet complexly behaving one-dimensional cellular automata. The automaton supports gliders, glider guns and other non-trivial long transients. We show how to characterize gliders in Rule 54 by diagram representations as de Bruijn and cycle diagrams; offering a way to present each glider in Rule 54 with particular characteristics. This allows a compact encoding of initial conditions which can be used in implementing non-trivial collision-based computing in one-dimensional cellular automata. 1 Preliminaries Amongst one-dimensional cellular automata (CA) studied by Wolfram in [15, 16], one can find a few evolution rules supporting gliders (particles or mobile self-localizations); rules 110 and 54 exhibit particularly rich and somewhat complex behaviour.3 Interaction between gliders can be employed to execute logical operations, and thus ultimately to perform universal computation [1]. Collisionbased computing schemes are ver...
Genaro Juárez Martínez, Andrew Adama
Added 01 Jun 2010
Updated 01 Jun 2010
Type Conference
Year 2008
Where ACRI
Authors Genaro Juárez Martínez, Andrew Adamatzky, Harold V. McIntosh
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