The Algebraic Structure of Cellular Automata

0.Introduction The effort to effectively model and better understand complexity in all of its varied phenomenal permutations is one of the foremost goals of modern science. Recently, cellular automata and related computational models have been used to successfully explore the complexity of general abstract systems. Contemporary research suggests that there are universal principles – a fortiori, simple atomic “programs” – that apply operationally to systems throughout the natural world.[9] This paper is a modest attempt to taxonomize a small subset of these abstract systems using algebraic techniques. The results that follow are based primarily on John Pedersen‟s paper “Cellular Automata as Algebraic Systems” and Stephen Wolfram‟s related work with Cellular Automata.