Elementary processes governing the evolution of road networks

Urbanization is a fundamental phenomenon which still remains poorly characterized in a quantitative way. The structure of street networks plays a crucial role in the development of urban areas. Here we report a study of almost 200 years evolution of the street network in a large area located in the north of Milan's metropolitan region (Italy). We present an empirical analysis of the transition from non-urbanized to urbanized land, attested by the regularization of cell shapes and by an increase of the fraction of intersections of degree four in the street network. We show that the evolution of the road network relies on a set of central points which are stable throughout time, and which constitute the backbone of the urban structure, conrming the importance of historical paths. Finally, our analysis led us to identify two elementary processes through which urbanization lls out space. The rst process is `densication', which corresponds to an increase in the local density of streets around the main existing central points and directions. The second process is `exploration', and consists in new roads and streets triggering the spatial evolution of the urbanization front. The quantitative identification of such simple elementary mechanisms suggests the existence of universal properties of urbanization processes, and opens up new possibilities to conceive more general and accurate models.