On algebraic cellular automata

On Elementary and Algebraic Cellular Automata

In this paper we study elementary cellular automata from an algebraic viewpoint. The goal is to relate the emergent complex behavior observed in such systems with the properties of corresponding algebraic structures. We introduce algebraic cellular automata as a natural generalization of elementary ones and discuss their applications as generic models of complex systems. There is a great divers...

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 ...

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...

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