ABSTRACT
This chapter begins the investigation of cellular automata as a class of mathematical models for certain behavior. It concentrates on the mathematical features of the simplest cellular automata, leaving for future study more complicated cellular automata and details of applications to specific systems. The chapter defines and introduces cellular automata and describes the qualitative behavior of elementary cellular automata. It gives a quantitative statistical analysis of the states generated in the time evolution of cellular automata, revealing several quantitative universal features. The chapter describes the global analysis of cellular automata and discusses the results in the context of dynamical systems theory and the formal theory of computation. Markovian master equation approximations to the density development were found inadequate because of the importance of "feedback" in the cellular automaton evolution. Starting even from an ensemble in which each possible configuration appears with equal probability, the cellular automaton evolution concentrates the probabilities for particular configurations, thereby reducing entropy.
