We give a combinatorial description of a family of 2-graphs which subsumes
those described by Pask, Raeburn and Weaver. Each 2-graph Ξ we consider
has an associated Cβ-algebra, denoted Cβ(Ξ), which is simple and
purely infinite when Ξ is aperiodic. We give new, straightforward
conditions which ensure that Ξ is aperiodic. These conditions are
highly tractable as we only need to consider the finite set of vertices of
Ξ in order to identify aperiodicity. In addition, the path space of
each 2-graph can be realised as a two-dimensional dynamical system which we
show must have zero entropy.Comment: 19 page