Fractal dimension of European Cities: A comparison of the patterns of built-up areas in the urban core and the peri-urban ring

This study compares the urban form of large European cities using fractal dimensions. Fractal dimensions are computed for built-up areas using data available in the Imperviousness High Resolution Layer dataset (EEA, 2012), and are estimated following two different methodologies; the binary approach which considers only two classes, developed land and non-developed land and the grayscale approach in which the built-up intensity, as expressed by the soil sealing degree is explicitly taken into account. Fractal dimensions are estimated for the 60 European cities with population exceeding one million. Using the boundaries defined in Urban Atlas the functional urban Area (FUA) is divided in two parts, the core of the urban area and the peri-urban ring area. Fractal dimensions are computed for each of these three spatial entities. Results show that the grayscale fractal dimension values at the FUA level are 1.18-1.55 and that the equivalent binary ones are always higher with values between 1.34 and 1.83. There is a high correlation between the two sets of fractal dimensions, as well as between the fractal dimension and the overall percentage of built-up area. Cities are also compared across regions (UK-Ireland, Scandinavia, Central, South, East). Significantly higher fractal values at the FUA level are reported in the cities located on the highly urbanized European corridor spanning from South UK to the Netherlands, Belgium, the Ruhr region and Northern Italy, while East European and Scandinavian cities form a distinct group with lower fractal dimension values.  Another group of cities with high FUA fractal dimensions includes the coastal South European cities Porto, Lisbon, Naples and Barcelona. At the CΟRE urban areas, the highest fractal values are observed in the largest cities (London, Paris, Berlin) which are compactly built-up.