From Fractal Urban Pattern Analysis to Fractal Urban Planning Concepts - Computational Approaches for Urban Environments - page 32

Fig. 2.10 ( a ) The Copenhagen finger plan (Source: Städtbauliches Institut Universität Stuttgart).
( b ) Schumacher's palm plan for Hamburg (Source: Güldner 1968 ). ( c ) A proposal by the architect
Schöfl for a “fractal” town outline (Schöfl 1986 )

Tabl e 2. 3 Change in the
fractal surface area dimension
of Basel

Basel Central city cluster Agglomeration

1880 1.42 -

1950 1.68 1.64

1990 1.7 1.74

famous Copenhagen finger plan (Fig. 2.10 a) or the Schumacher plan for Hamburg
(Fig. 2.10 b). The same logic inspired already Eberstadt et al. ( 1910 ) for developing
the Berlin metropolitan area.
But in many cases, we observe that in the course of urbanization, the fractal
dimension increases on the scale of metropolitan areas (see the example of Basel,
Tab le 2.3 ). This means that interstitial space between the main transportation routes
is increasingly filled since motorization provides good accessibility even to more
isolated villages.
This contributes not only to lengthening the daily commuting trips but is one of
the reasons for the deterioration of natural resources. Moreover, improving the street
network contributes largely to land consumption. For example, on the outskirts of
the urbanized area of the Paris metropolitan area, within the period of 1987-1997,
only 1.4 % of space was consumed by new residential and mixed use constructions,
whereas 50 % of space was used for improving the road network (Tourneux 2006 ).
Let us remind that dimensions close to D D 2 refer to a uniform distribution of
build-up space whatever the density, whereas lower fractal dimensions correspond
to higher local concentrations of build-up space across scales like in the example of
Figs. 2.2 and 2.4 . Hence, we may summarize that on the scale of agglomerations,
lower fractal dimensions of build-up space correspond to a lower degree of sprawl
since buildings are locally more concentrated and do not fill up space in a diffuse
more or less uniform way.
Chen and Feng ( 2010 ) showed that in Chinese agglomerations, fractal dimen-
sions increases sometimes rather dramatically since the 1980th, and they link this