Kinetic roughening of the urban skyline

Abstract

\begin{abstract} In this Letter we follow the asymptotic spatial correlation of buildings' heights $G_{\infty }(r)$ in the whole of the Netherlands \cite{bag3d}, which comprises $\approx 10,000,000$ buildings, for the purpose of recovering its scaling with respect to space and time given respectively by the exponents $r^{2\alpha }$ and $t^{2\beta }$. This allows us to identify the universality class of the evolution of the urban skyline seen as a dynamically evolving interface. Two major classes of cities were identified based on the recovered value of $\alpha =0.4$ and $\alpha =0$, which correspond respectively to the KPZ and the EW universality classes. Picking a discrete model from each of these classes and mapping it to physical rules for constructions in cities we conclude that imposed restrictions on buildings' heights are reflected in the exponent $\alpha$ and thus have implications on how the skyline evolves.

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• Stirred Kardar-Parisi-Zhang equation with quenched random noise: Emergence of induced nonlinearity
• The non-perturbative sides of the Kardar-Parisi-Zhang equation
• Universal fluctuations of global geometrical measurements in planar clusters