In nature, barchan dunes typically exist as members of larger fields that display striking, enigmatic structures that cannot be readily explained by examining the dynamics at the scale of single dunes, or by appealing to patterns in external forcing. To explore the possibility that observed structures emerge spontaneously as a collective result of many dunes interacting with each other, we built a numerical model that treats barchans as discrete entities that interact with one another according to simplified rules derived from theoretical and numerical work and from field observations: (1) Dunes exchange sand through the fluxes that leak from the downwind side of each dune and are captured on their upstream sides; (2) when dunes become sufficiently large, small dunes are born on their downwind sides (“calving”); and (3) when dunes collide directly enough, they merge. Results show that these relatively simple interactions provide potential explanations for a range of field-scale phenomena including isolated patches of dunes and heterogeneous arrangements of similarly sized dunes in denser fields. The results also suggest that (1) dune field characteristics depend on the sand flux fed into the upwind boundary, although (2) moving downwind, the system approaches a common attracting state in which the memory of the upwind conditions vanishes. This work supports the hypothesis that calving exerts a first-order control on field-scale phenomena; it prevents individual dunes from growing without bound, as single-dune analyses suggest, and allows the formation of roughly realistic, persistent dune field patterns.