The Axelrod model of cultural dissemination is a convenient analogue to the description of archaeological cultures based on a series of material features, such as styles of pottery, agriculture, domestication, etc. Allowing a population to spread into uninhabited, or sparsely inhabited, territory, while undergoing cultural interaction, generates a wave front containing larger homogeneous cultures, with a backwater of diversity. A very similar process is observed in the neolithic transition -the arrival of the first farming technology at the end of the Mesolithic - in south- eastern Europe (c. 8000-6000 cBC), where the first observable neolithic cultures are large and homogeneous, and these are succeeded by greater diversity. The model presented here demonstrates how the dynamics of a spreading wave can explain the observed progression from large, spreading cultures to smaller, more diverse cultures.