Pattern Graphs of Cellular Automata and Reaction Systems

Abstract

We introduce a framework that connects two discrete models of natural computing, cellular automata (CA) and reaction systems (RS). We define pattern graphs of a CA as one-out digraphs where vertices correspond to totally periodic configurations and edges reflect CA evolution. Using pattern graphs based on periodic configurations we show that every one-dimensional binary CA can be transformed into an RS via its zero-context graph and provide counterexamples for the converse. Modified techniques, such as increasing the number of states and subgraphs of pattern graphs, are used to transform arbitrary RS into CA.