The recent availability of geolocalized historical data allows to address quantitatively spatial features of the time evolution of urban areas. Here, we discuss how the number of buildings evolves with population and we show on different datasets (Chicago, 1930−2010; London, 1900−2015; New York City, 1790−2013; Paris, 1861−2011) that this curve evolves in a ‘universal’ way with three distinct phases.
After an initial pre-urbanization phase, the first phase is a rapid growth of the number of buildings versus population. In a second regime, where residences are converted into offices and stores, the population decreases while the number of buildings stays approximatively constant. In another subsequent — modern — phase, the number of buildings and the population grow again and correspond to a re-densification of cities.
We propose a simple model based on these simple mechanisms to explain the first two regimes and show that it is in excellent agreement with empirical observations. These results bring evidences for the possibility of constructing a simple model that could serve as a tool for understanding quantitatively urbanization and the future evolution of cities.