A new class of cellular automata is observed to evolve to a self-organized critical state. These ‘‘vector automata’’ obey a threshold relaxation condition that depends on the gradient of a scalar field, which is locally conserved except at the system boundaries. Both square and triangular lattices are studied and lead to virtually identical statistics; however, a particular (and natural) choice of boundary shape for the square lattice leads to trivial dynamics characteristic of a minimally stable configuration.

• Received 19 June 1989

DOI:https://doi.org/10.1103/PhysRevA.41.1867