  A small-world cellular automaton network has been formulated to simulate the
long-range interactions of complex networks using unconventional computing
methods in this paper. Conventional cellular automata use local updating rules.
The new type of cellular automata networks uses local rules with a fraction of
long-range shortcuts derived from the properties of small-world networks.
Simulations show that the self-organized criticality emerges naturally in the
system for a given probability of shortcuts and transition occurs as the
probability increases to some critical value indicating the small-world
behaviour of the complex automata networks. Pattern formation of cellular
automata networks and the comparison with equation-based reaction-diffusion
systems are also discussed
