Atlas of Urban Scaling Laws.

Highly accurate estimates of the urban fractal dimension $D_f$ are obtained by implementing the Detrended Moving Average algorithm (DMA) on WorldView2 satellite high-resolution multi-spectral images covering the largest European cities. Higher fractal dimensions are systematically obtained for urban sectors (centrally located areas) than for suburban and peripheral areas, with $Df$ values ranging from $1.65$ to $1.90$ respectively.The exponents $\beta_s$ and $\beta_i$ of the scaling law $N^{\beta}$ with $N$ the population size, respectively for socio-economic and infrastructural variables, are evaluated for different urban and suburban sectors in terms of the fractal dimension $D_f$.Results confirm the range of empirical values reported in the literature. Urban scaling laws have been traditionally derived as if cities were zero-dimensional objects with the relevant feature related to a single homogeneous population value, thus neglecting the microscopic heterogeneity of the urban structure. Our findings allow one to go beyond this limit. High sensitive and repeatable satellite records yield robust local estimates of the Hurst and scaling exponents. Furthermore, the approach allows one to discriminate among different scaling theories, shedding light on the open issue of scaling phenomena, reconciling contradictory scientific perspectives and pave paths to the systematic adoption of the complex system science approach to urban landscape analysis.