We analyze the morphology of the modern urban skyline in terms of its roughness properties. This is facilitated by a database of ${10}^7$ building heights in cities throughout the Netherlands which allows us to compute the asymptotic height difference correlation function in each city. We find that in cities for which the height correlations display power-law scaling as a function of distance between the buildings, the corresponding roughness exponents are commensurate to the Edwards-Wilkinson and Kardar-Parisi-Zhang equations for kinetic roughening. Based on analogy to discrete deposition models, we argue that these two limiting classes emerge because of possible height restriction rules for buildings in some cities.

• Received 13 March 2020
• Accepted 8 May 2020

DOI:https://doi.org/10.1103/PhysRevE.101.050301