From Fractal Urban Pattern Analysis to Fractal Urban Planning Concepts - Computational Approaches for Urban Environments - page 23

data N (") obey a fractal law. 1 In general, the fractal approach is well suited for
characterizing the spatial organization of urban fabrics. The quality of adjustment
between empirical and theoretical curves is usually rather high.
Different authors emphasized that urban fabrics are generally a mixture of dif-
ferent scaling behavior, and hence, multifractal approach suits better for measuring
their morphology than unifractal ones (e.g., Chen and Wang 2013 ). We agree to this
point of view in that sense that considering an agglomeration as a whole, different
town sections may have different scaling properties. Hence, considering large urban
areas, multifractal behavior occurs since at this scale different types of patterns are
mixed. We focus here essentially on the intraurban scale of wards for which we
observed, e.g., by a recently developed special method we call multiradial analysis,
a rather stable scaling behavior reminding that of unifractals. Ariza-Villaverde et al.
( 2013 ) used multifractal analysis on an intraurban scale for street networks, but the
differences between the values of the different dimensions observed for two areas
are very small, what confirms rather unifractal behavior on this scale.
However, since the town sections we analyzed are chosen within a square-like
window and not according to local morphological properties, we do not exclude the
potential presence of a certain mix of scaling behavior.
This incited us comparing different measuring methods. It turned out that
correlation analysis provides the most robust results on a rather large range of
scales. However, the dimension values differ for this method from results obtained
with covering methods, which can be explained, as pointed out, by the fact that the
method takes into account the position of built-up sites across scales in a precise
way and follows a multifractal analysis logic.
All analyses presented were carried out with the open access software tool
Fractalyse, developed at Thema institute by Gilles Vuidel under the supervision of
Pierre Frankhauser and Cécile Tannier.
We first discuss some results obtained on the basis of rather coarse-grained data
for metropolitan areas as a whole (Frankhauser 2004 ). For the agglomerations of
Berlin and Stuttgart, surface dimensions are rather low, which expresses rather
contrasted patterns. Indeed, in both cases, the urban fabric is dominated by axial
growth along valleys for Stuttgart and alongside the suburban railway lines for
Berlin. We also determined the fractal dimension of the boundaries of the central
clusters of these agglomerations. The obtained value of Stuttgart is rather high,
reflecting its rather sinuous appearance (Fig. 2.1 ). The most compact situation is
observed for London, which can be explained by the green belt policy that attempted
to contain urban growth. We shall return to this aspect later (Table 2.1 ).
We now come to the results obtained by using GIS-data which take into account
the microstructure of the urban fabric, i.e., resolutions of 4 m minimum.
Several series of investigations have been realized for various European cities
in Italy, Finland, France, Germany, and Switzerland, but essentially Belgium and
1 The free software “fractalyse” was developed at the THEMA institute (Besançon) by Gilles
Vuidel. A version allowing GIS-data to be used directly is currently under development.