Complex Systems

Cellular Automata with Regular Behavior Download PDF

E. Fachini
L. Vassallo
Dipartimento Informatica e Applicazioni, Universita' di Salerno,
84081 Baronissi (SA), Italy


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).