Cellular automata with regular behaviour.

The study of cellular automata (CA) was motivated recently by their application to systems whose complex behavior arises from the interaction among simple identical components. Actually, a CA consists of a linear biinfinite array of cells, each one connected with the r cells that precede it on the left-hand side and the r cells that follow it on the right-hand side neighborhood. Each cell is in one of finitely many states. The new state of a cell is computed according to a local rule that is a function of the states of the cells in the neighborhood, besides the old state of the cell. All cells are assumed to change state simultaneously. In [5] CA are classified with respect to their behavior. The great part of CA falls in the third class, that is, the one whose evolution leads to a chaotic pattern. Recently, however, Wilson [3] and Culik [1] exhibited some CA belonging to this class and having a very regular behavior, fractal-like on particular initial configurations. In this paper, we study a class we will call pseudototalistic cellular automata (PTCA).