Fractal Dimensions of the Built-up Footprint: Buildings versus Roads. Fractal Evidence from Antwerp (Belgium)

In this paper we explore further the use of fractal dimensions by comparing values for built-up spaces and values for road networks, both being estimated by the same method. This is done in an attempt to explain the differences theoretically and empirically, and to show how far both indices are complementary and useful in urban planning. Empirical analyses are performed at the scale of the townships within the urban region of Antwerp (Belgium). Fractal dimensions, curves of scaling behavior, and concordance analyses are computed and their usefulness explained. We conclude that both dimensions translate subtly different realities and that they should be used with caution in morphological analyses: the fractal dimension for built-up spaces indicates how uniformly buildings fill space when zooming to ever finer scales, while the fractal dimension for networks indicates the extent to which street segments are distributed more or less uniformly in the study area. The two are not the same, as roads can serve spaces that are not built up.