Algebraic properties of cellular automata

Algebraic Properties of Cellular Automata

Cellular automata are discrete dynamical systems, of simple construction but complex and varied behaviour. Algebraic techniques are used to give an extensive analysis of the global properties of a class of finite cellular automata. The complete structure of state transition diagrams is derived in terms of algebraic and number theoretical quantities. The systems are usually irreversible, and are...

Algebraic Properties of the Block Transformation on Cellular Automata

By grouping several sites together into one a cellular automaton can be transformed into another with more states and a smaller neighbor hood if the neighborhood has just two sites we can think of the resulting CA rule as a binary operation We show that if the blocked rule satis es an identity which holds for a broad class of algebras then the underly ing rule must have essentially the same str...

Cellular Automata as Algebraic Systems

Infinite cellular automata have been studied mostly using empirical and sta tistical techniques, with some combinatorial analysis. Here we show how concepts of universal algebra such as subdirect decomposition and chains of varieties can be applied to their study. Cellular automata with ultimately periodic behavior are shown to correspond to varieties of groupoids. Relat ionships between these ...

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,...

Additive Cellular Automata and Algebraic Series