ABSTRACT
Two-dimensional cellular automata have a relatively ancient history, from von Neumann's self-reproducing automata of the 1940's to Conway's "game of life". This chapter discusses a simple model of crystal growth based on counter automata, and an application of cellular automata to hydrodynamics. It also discusses Conway's "game of life". The chapter provides lattices with square grids, or square lattices. In the case of the triangular lattice, 7 bits are sufficient to describe the input configuration, just as 7 bits can describe the output configuration. In the von Neumann neighborhood, each automaton has five inputs, consisting of itself and its four neighbors. In the Moore neighborhood, it has nine inputs, consisting of itself and its eight nearest neighbors. Growth happens on the facets, but from time to time an impurity, an imperfection of the lattice, or even an isolated atom "stuck" on the facet allow the growth of a new row of atoms on that facet.
