A species of voter model driven by immigration

A geometric process is proposed in which a random political constituency map emerges through an influx of settlers to a region. At first there is a spatially dispersed native population with established political opinions. The settlers, in sequence, choose random locations in the region and each adopts the political opinion of its closest neighbour, whether native or fellow settler. Various qualitative properties of the resulting constituencies are derived for a planar case of the model. A linear case is also discussed.