Effects of Lattice Structure in the Dynamics of Coupled Elements

Abstract

We investigate the influence of lattice geometry in network dynamics, using a cellular automaton with nearest-neighbor interactions and two admissible local states. We show that there are significant geometric effects in the distribution of local states and in the distribution of clusters, even when the connection topology is kept constant. Moreover, we show that some geometric structures are more cohesive than others, tending to keep a given initial configuration. To characterize the dynamics, we determine the distributions of local states and introduce a cluster coefficient. The lattice geometry is defined from the number of nearest neighbors and their disposition in 'space', and here we consider four different geometries: a chain, a hexagonal lattice, a square lattice and a cubic lattice