Singularity cities

Yunfei Li, Diego Rybski and Jürgen P. Kropp
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Diego Rybski: 28412Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association, Potsdam, Germany
Jürgen P. Kropp: 28412Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association, Potsdam, Germany; Department of Environmental Sciences & Geography, University of Potsdam, Potsdam, Germany

Environment and Planning B, 2021, vol. 48, issue 1, 43-59

Abstract: We propose an upgraded gravitational model which provides population counts beyond the binary (urban/non-urban) city simulations. Numerically studying the model output, we find that the radial population density gradients follow power-laws where the exponent is related to the preset gravity exponent γ . Similarly, the urban fraction decays exponentially, again determined by γ . The population density gradient can be related to radial fractality and it turns out that the typical exponents imply that cities are basically zero-dimensional. Increasing the gravity exponent leads to extreme compactness and the loss of radial symmetry. We study the shape of the major central cluster by means of another three fractal dimensions and find that overall its fractality is dominated by the size and the influence of γ is minor. The fundamental allometry, between population and area of the major central cluster, is related to the gravity exponent but restricted to the case of higher densities in large cities. We argue that cities are shaped by power-law proximity. We complement the numerical analysis by economics arguments employing travel costs as well as housing rent determined by supply and demand. Our work contributes to the understanding of gravitational effects, radial gradients, and urban morphology. The model allows to generate and investigate city structures under laboratory conditions.

Keywords: Gravity models; population density; urban fraction; fractal geometry (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:sae:envirb:v:48:y:2021:i:1:p:43-59

DOI: 10.1177/2399808319843534

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