Scaling and universality in the micro-structure of urban space

Abstract

We present a broad, phenomenological picture of the distribution of the length of open space linear segments, $l$, derived from maps of 36 cities in 14 different countries. By scaling the Zipf plot of $l$, we obtain two master curves for a sample of cities, which are not a function of city size. We show that a third class of cities is not easily classifiable into these two universality classes. The cumulative distribution of $l$ displays power-law tails with two distinct exponents, $α_B=2$ and $α_R=3$. We suggest a link between our data and the possibility of observing and modelling urban geometric structures using Levy processes.