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##### Effects of lattice structure in the dynamics of coupled elements

**Authors**: Andre S. Ribeiro, P.G. Lind

**Ref.**: Physica Scripta **71** (2005)

**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.