On the Dynamical Behaviour of Cellular Automata

TL;DR

This paper investigates the dynamics of 1D and 2D cellular automata using 2-adic representations, introducing a graphical method for periodic solutions, analyzing continuity, and computing entropy.

Contribution

It presents a novel graphical technique for identifying periodic solutions and explores the continuity and entropy of 2-adic systems associated with cellular automata.

Findings

Graphical method effectively finds periodic solutions.

Continuity properties of 2-adic systems are characterized.

Entropy of cellular automata systems is computed.

Abstract

In this paper we study the dynamics of 1- and 2- dimensional cellular automata, using a 2-adic representation of the states, we give a simple graphical technique for finding periodic solutions. We also study the continuity properties of the associated 2-adic system and show how to compute the entropy.