From Fractal Urban Pattern Analysis to Fractal Urban Planning Concepts - Computational Approaches for Urban Environments - page 25

urban development influences fractal dimension values. At the scale of agglomera-
tions, axial development along valleys or transportation routes leads to more highly
contrasted patterns.
This also means that some fractal values refer rather to physical factors (coast)
or local historical contexts than to national planning rules, confirming Frankhauser
( 2003 , 2008 ). More generally, this also confirms that nineteenth-century cities have
higher fractal values than twentieth-century cities, and more generally, “historical
cities are fractal, whereas the twentieth-century city is not” (Salingaros 2003 )or
they are multifractal (see, e.g., Batty 2005 ).
On the scale of urban districts, different investigations have shown that it is
possible to identify different types of spatial organization which can be linked
to peculiar historical or geographical contexts. In Thomas et al. ( 2012 ), a ward
classification was applied to minimize intragroup variance. Four classes were
identified. The first one with very high D values close to D D 1.9 corresponds to
city centers with a high concentration of buildings, constructed in a continuous
way along the streets where blocks are always very clearly recognizable. A second
class comprises built-up neighborhoods composed of detached housing typical of
pericentral areas. These districts have a low or middling density of urbanization,
with quite a regular morphology, where houses are located alongside streets.
Fractal dimensions are lower here since the patterns are less compact and hence
more contrasted. Whereas in the previous patterns buildings follow the streets,
in the third class dwellings and nonresidential, buildings are mixed and do not
necessarily follow the street pattern. Such districts were often built during the
period 1950-1980. Since buildings are located rather arbitrarily, dimensions are
rather low (about D D 1.67). The most contrasted patterns are observed in French
new towns like Cergy-Pontoise and districts constructed on the Charte d'Athènes
(Le Corbusier 1971 ) principles. Here the spatial arrangement of buildings as well
as their forms is varied, and green areas of various sizes separate the large isolated
buildings.

2.5.2 Information Provided by the Curves of Scaling Behavior

Similar results were obtained in another way. In Thomas et al. ( 2010 ), we not only
used the values of fractal dimensions to distinguish different types of urban patterns,
but we looked at the shape of the curves of scaling behavior in order to distinguish
different types of urban patterns. Indeed, for correlation analysis, it turns out that
these curves often display a substantial fall before rising again for small distances
corresponding to the size of buildings, courtyards, etc. Here, fractality does not
come into play yet.
Figure 2.7 shows an example in which the lowest point corresponds to 28 m;
the stable situation is reached for 68 m. But for other districts, the shape of
the curves is quite different, e.g., smoother from the very beginning. Hence, we
used the k -medoid algorithm (Bishop 2006 ) for classifying curves by their shape.