Journal of Statistical Physics, Vol. 54, Nos. 5/6, 1989. p. 1441-1458.
We discuss some recent results suggesting that certain spatially extended dynamical systems naturally evolve toward a state characterized by domains of all length scales. The analogy with second-order phase transitions has prompted the name "self-organized criticality"; specific results are available for cellular automaton models, which can be thought of as caricatures of a sandpile undergoing avalances. The potential generality of the results stems from the very simple (nonlinear) diffusion dynamics governing the system.