From network topology to cultural forms. (A) Propagation of a broadband signal through a spatial network may result in clusters of nodes with converging conventions, but globally, competition between those clusters may cause instability (Centola and Baronchelli, 2015). (B) In a homogeneous network, a slow convergence due to interactions between distant nodes (red lines) may eventually result in a global adoption of a single convention. In the case of a binary signal (C), a spatial network topology may quickly filter out rare morphs and converge globally (Klar and Shmargad, 2016). However, in a homogeneous network (D) interactions between distant nodes may sustain the rare morph (blue lines).