ABSTRACT
Cellular automata are simple mathematical systems that exhibit very complicated behaviour. Twenty central problems that remain unsolved are discussed. This chapter discusses some of the ones that have so far been identified. It concentrates on theoretical aspects of cellular automata. There is little discussion of models for actual natural systems. Cellular automata are a class of mathematical models that seem to capture the essential features of this phenomenon. Cellular automaton evolution may be considered to carry out a computation on data represented by the initial sequence of site values. Continuous dynamical systems provide analogues for the classes of behaviour seen in cellular automata. Dynamical systems theory gives a first approach to the quantitative characterization of cellular automaton behaviour. Various kinds of entropy may be defined for cellular automata. Coarse-graining in cellular automata may be achieved by applying an irreversible transformation, perhaps a cellular automaton rule, to the cellular automaton configurations.
