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patterns may be seen as resulting from such demand. In the more rural Ardennes
region, the surface area dimensions vary between 0.54 and 1.00 and are rather low,
but the range of the boundary dimension is very large extending from 1.33 to 1.75.
Hence, some of them are rather compact, whereas others look rather tattered. Near
Luxembourg, the surface area dimensions are higher (1.00-1.23) as are the boundary
dimensions (1.68 and 1.75), and so they are reminiscent of the periurban periphery
of Brussels.
2.6
Fractals for Sustainable Planning
2.6.1
The General Concept
The previously presented results make it obvious that the spatial organization of
urban patterns is rather consistent with fractal order principles. This type of spatial
organization is in part linked to planning concepts as shown, say, for New Towns.
But usually urban fabrics arise from highly complex interactions among various
types of agents such as politicians and planners but also developers and landowners,
who react to social demand. Hence, urbanization is at least in part a self-organizing
process.
Without going into details, this leads us to consider briefly the socioeconomic
processes contributing to what is usually called urban sprawl. We should be aware
that this phenomenon is not just due to lower lot prices in the periphery than in
city centers. As already pointed out, households choose these areas since they
want to flee urban density and prefer to live in individual houses surrounded by
a garden and to enjoy a green and quiet environment. In France, for example, a
survey conducted in 2007 by the Département Stratégies d'Opinion de l'institut
d'études marketing et d'opinion TNS Sofres (Gault and Bedeau 2007 ) revealed that
56 % of French households want to live in detached individual houses surrounded
by a large garden. Individual houses belonging to housing estates are preferred by
20 % and semidetached housing in an urban environment by 11 %. It is obvious
that this residential choice behavior tends to generate diffused settlement patterns
where residential areas are localized far away from jobs as well as from retail
centers and services. This increases the number and the length of commuting trips
and hence energy consumption and pollution. The negative impact of this evolution
has essentially been made evident by Newman and Kenworthy ( 1989 ). Moreover,
natural areas risk becoming ever more fragmented, so lowering biodiversity.
This prompted numerous authors to recommend a return to compact cities in
order to limit urban sprawl. However, even if this lifestyle contributes to urban
sprawl (Von Hoffman and Felkner 2002 ) such households will reject densifying
(Breheny 1997 ; Gordon and Richardson 1997 ; Fouchier 1995 ).
Investigations showed that households integrate a couple of criteria concerning
accessibility to different types of sites frequented when choosing their residence.
Brun and Fagnani ( 1994 ) and McDowell ( 1997 ) showed that they try to minimize
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