From Fractal Urban Pattern Analysis to Fractal Urban Planning Concepts - Computational Approaches for Urban Environments - page 14

Fig. 2.2 64 blocks distributed in two different ways: the pattern on ( a ) obeys fractal logic and the
pattern ( b ) is uniform (Thomas et al. 2008a )
of space. Accordingly, density is constant when the constituent parts of a structure,
in our case buildings, are distributed uniformly across space, which does not seem
to hold for urban patterns. Moreover, density does not really yield information about
spatial distribution. Figure 2.2 shows two patterns in which 64 blocks of the same
size are distributed in different ways within the same square: while the densities are
the same, the first pattern is a fractal-like structure, unlike the second one.
Obviously, the nonuniform distribution of buildings makes it difficult to grasp the
spatial organization of urban patterns. This is plain when looking for reliable criteria
on which to define urban boundaries. Looking at the simplified map in Fig. 2.1 a, it
might be thought that the urban boundary can be identified easily, but not so in the
real-world situation (Fig. 2.1 b). As pointed out, the distances between buildings
vary over a large range, particularly so for the fringes of sprawling urbanized
areas where recent detached housing estates and traditional rural settlement patterns
interdigitate. The criteria suggested by various administrative departments turn out
to be questionable.
However, despite the complexity of these patterns, regularities can be detected in
them, which seems paradoxical. For instance, if we measure the boundary lengths
and surface areas of urban clusters on a coarse-grained map like that in Fig. 2.1 a, the
twotendtobe proportional (Frankhauser and Sadler 1991 ). This clearly contradicts
the usual geometric assumption that the surface area should be proportional to the
square of the perimeter length, but it is consistent with fractal geometry, as will be
seen next.