Cellular automata models can be developed to describe the evolution of emergent dynamical systems that maintain a discrete character, including those with an implicit hierarchical character. Moreover, these models can be related to directed graphs. These methods have found widespread application in condensed matter physics (e.g., diffusion limited aggregation and crystal growth, sandpiles andself-organized criticality) as well as in earth and environmental physics (e.g., models of earthquakes and river networks). In particular, models developed for forest fires are manifestly complex systems that show well-preserved scaling laws relating to the frequency of forest fires relative to their size. In sociological studies of conflict and deadly quarrels, similar statistical scaling laws have been observed, e.g., Richardson, with identical power-law indices. In earlier work, Gabrielov, Newman, and Turcotte (199?) succeeded in deriving from first principles those scaling laws. Here, we show that a simple redefinition of terms makes it possible for the statistics of gangs to be obtained from these other cellular automata models. In particular, by equivalencing the recruitment of gang members in the sociological problem with the planting of trees in the environmental problem, the observed statistics of gang populations and their prevalence can be derived.
Joint work with Donald L. Turcotte (UC Davis), and Andrei Gabrielov (Purdue)