Elementary Cellular Automata with Elementary Memory Rules in Cells: The Case of Linear Rules

Cellular Automata (CA) are discrete, spatially explicit extended dynamic systems. A CA system is composed of adjacent cells or sites arranged as a regulard-dimensional lattice, which evolves in discrete time steps. Each cell is characterized by an internal state whose value belongs to a finite set. The updating of these states is made simultaneously according to a common local transition rule involving only a neighborhood of each cell. Thus, if σ (T ) i is taken to denote the value of cell i at time stepT , the