Many natural systems, as social insects, perform complex computations collectively. In these groups, large numbers of individuals communicate in a local way and send information to its nearest neighbors. Interestingly, a general observation of these societies reveals that the computational capabilities of individuals are fairly limited, suggesting that the observed complex dynamics observed inside the collective is induced by the interactions among elements, and it is not defined at the individual level. In this paper we use globally coupled maps (GCM), as a generic theoretical model of a distributed system, and Crutchfield's statistical complexity, as our theoretical definition of complexity, to study the relation between the computational capabilities the collective is able to induce on the individual, and the complexity of the latter. It is conjectured that the observed patterns could be a generic property of complex dynamical nonlinear networks.
