Buildings as Species: Competition and Scaling Rules in Cities

Abstract

We look at buildings’ competition over space in cities following the distribution of the perimeters r of the buildings’ circumscribing ellipses. p(r) is shown to follow a power-law behavior beyond a critical threshold of the density of the built environment. In this regime, p(d), where d is the distance to the nearest competitor, defined to be a building with a larger r, bifurcates with the buildings’ number n. This reveals two different competition laws: one which is linked to spatial homogeneity and segregation, as opposed to another favoring spatial diversity and intermixing between buildings with different sizes.