From Fractal Urban Pattern Analysis to Fractal Urban Planning Concepts - Computational Approaches for Urban Environments - page 31

the distance or the travel time for acceding to their jobs, but also to retail centers
(Lerman 1976 ) and, too, to leisure areas (Guo and Bhat 2002 ). Hence, densifying
residential zones may prompt households to move to lower density areas (Schwanen
et al. 2004 ). Moreover, policies favoring the compact city have turned out to be
less efficient than expected. They induce an increase in housing costs and traffic
congestion and reduce the accessibility of leisure areas (Breheny 1997 ). As observed
by Levinson and Kumar ( 1994 ), trip time does decrease with population density but
increases again when a certain threshold is exceeded.
Investigations for Walloon communes have shown that, where substantial pro-
portions of households are dissatisfied with their immediate environment, D values
are commonly close to 2 (Thomas et al. 2008b ), whereas communes with large
percentages of very satisfied households have a high variety of D values (from 0.5
to 1.8). Of course, there is no simple relation between the fractal shape of the urban
fabric and household satisfaction since a large number of criteria come into play
and there is considerable diversity in housing environments and tastes. However,
in two papers on economic residential choice modeling, we explored the impact
of Sierpinski carpet-like urban patterns on household satisfaction. It turned out
that, for households which have preferences for both “urban amenities” and “green
amenities,” such a model provides advantages that can be measured by market-
induced lot prices (Cavailhès et al. 2004 ).
We showed, too, for a teragon, that the mean minimal distance from all sites
for acceding to the boundary falls to 56 % when passing from a square to the first
iteration step and is reduced to 91.5 % for the transition from the first to the second
step. The mean distance to the center increases, of course, but for the first step, we
obtain 112.5 % with respect to the initial square and 104 % for second step with
respect to the first one (Frankhauser 2000 ). Hence, the “loss of centrality” is less
important than the gain in acceding to the urban boundary.
These reflections prompted us to ask whether the emerging fractal order principle
cannot be made operational for managing urban sprawl, which means that instead
of rejecting the non-compact shape of urban patterns, we may use this approach
to structure urban fabrics. The goal is to develop a planning concept that takes
account of household preferences but that reduces energy consumption and prevents
fragmentation of both built-up and open landscape. Hence, one of the most crucial
objectives is to improve accessibility to the different kinds of sites residents frequent
more or less regularly. On a local scale, we saw that a fractal shape of an urbanized
area can provide leisure areas in the neighborhood of residential zones thereby
satisfying residents' desired quality of life. But one of the most criticized impacts of
urban sprawl is that urbanization increasingly affects rural areas far from jobs and
shopping facilities and so generates large traffic flows.
Returning to urban history, we must be aware that, after the industrial revolution,
market-determined growth generated irregular urban patterns. However, during
the “trolley period,” i.e., before motorization, urban growth remained restricted
to ribbon-like development beside public transportation routes. Particularly in
Northern metropolitan areas, planning strategies deliberately oriented urbanization
in this direction on the scale of metropolitan areas. Let us cite as examples the