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...

• Type: Conference
• Year: 2008
• Where: ACRI
• Authors: Genaro Juárez Martínez, Andrew Adamatzky, Harold V. McIntosh
• Keywords: ACRI 2008, Artificial Intelligence, Glider, One-dimensional Cellular Automata, Rule 54