Using Economy of Means to Evolve Transition Rules within 2D Cellular Automata

Running a cellular automaton (CA) on a rectangular lattice is a time-honored method for studying artificial life on a digital computer. Commonly, the researcher wishes to investigate some specific or general mode of behavior, say, the ability of a coherent pattern of points to glide within the lattice, or to generate copies of itself. This technique has a problem: how to design the transitions table-the set of distinct rules that specify the next content of a cell from its current content and that of its near neighbors. Often the table is painstakingly designed manually, rule by rule. The problem is exacerbated by the potentially vast number of individual rules that need be specified to cover all combinations of center and neighbors when there are several symbols in the alphabet of the CA. In this article a method is presented to have the set of rules evolve automatically while running the CA. The transition table is initially empty, with rules being added as the need arises. A novel principle drives the evolution: maximum economy of means-maximizing the reuse of rules introduced on previous cycles. This method may not be a panacea applicable to all CA studies. Nevertheless, it is sufficiently potent to evolve sets of rules and associated patterns of points that glide (periodically regenerate themselves at another location) and to generate gliding "children" that then "mate" by collision.