35 Cellular Automata: In-Depth Overview

Cellular Automata (CAs) are dynamical systems in which space and time are discrete, where each cell obeys the same rule and has a finite number of states. The Cellular Automata model is both general and simple. Generality relates to two things: (1) the model can perform universal computation and (2) the basic units are formed out of a general interaction and not because of a specialized function. The Cellular Automata model is one of the simplest and most general models available for observing and computing complex systems. In this paper we provide an in-depth snapshot of CA, its components that make up the system, rules that the cells follow to bring about dynamic behavior, the classification of CA based on their behavior towards certain rules, and we will also provide an analogy between CAs and Differential Equations as CAs are an extension to Partial Differential Equations. Due to the number of page limitations, topics covered in this paper are summarized. Interested readers are encouraged to refer to the references at the end of this paper.