We give a combinatorial description of a family of 2-graphs which subsumes
those described by Pask, Raeburn and Weaver. Each 2-graph $\Lambda$ has an
associated $C^*$-algebra, denoted $C^*(\Lambda)$, which is simple and purely
infinite when $\Lambda$ is aperiodic. We give new, straightforward conditions
which ensure that $\Lambda$ is aperiodic. These conditions are highly tractable
as we only need to consider the finite set of vertices of $\Lambda$ in order to
identify aperiodicity.