Atlas of urban scaling laws

Accurate estimates of the urban fractal dimension Df are obtained by implementing the detrended moving average algorithm on high-resolution multi-spectral satellite images from the WorldView2 (WV2) database covering the largest European cities. Fractal dimension Df varies between 1.65 and 1.90 with high values for highly urbanised urban sectors and low ones for suburban and peripheral ones. Based on recently proposed models, the values of the fractal dimension Df are checked against the exponents βs and βi of the scaling law Y ∼ N^β, respectively for socio-economic and infrastructural variables Y, with N the population size. The exponents βs and βi are traditionally derived as if cities were zero-dimensional objects, with the relevant feature Y related to a single homogeneous population value N, thus neglecting the microscopic heterogeneity of the urban structure. Our findings go beyond this limit. High sensitive and repeatable satellite records yield robust local estimates of the urban scaling exponents. Furthermore, the work discusses how to discriminate among different scaling theories, shedding light on the debated issue of scaling phenomena contradictory perspectives and pave paths to a more systematic adoption of the complex system science methods to urban landscape analysis.