Elementary processes governing the evolution of road networks.

Urbanisation is a fundamental phenomenon whose quantitative characterisation is still inadequate. We report here the empirical analysis of a unique data set regarding almost 200 years of evolution of the road network in a large area located north of Milan (Italy). We find that urbanisation is characterised by the homogenisation of cell shapes, and by the stability throughout time of high-centrality roads which constitute the backbone of the urban structure, confirming the importance of historical paths. We show quantitatively that the growth of the network is governed by two elementary processes: (i) 'densification', corresponding to an increase in the local density of roads around existing urban centres and (ii) 'exploration', whereby new roads trigger the spatial evolution of the urbanisation front. The empirical identification of such simple elementary mechanisms suggests the existence of general, simple properties of urbanisation and opens new directions for its modelling and quantitative description.