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Conceptually defining the city as a place of concentration of inhabitants, jobs,
services, etc. allows making a mental representation of it. The aim is then to
formalize this representation in terms of observables, and the path is still a long one
before having made the whole construction process explicit that then leads to a
representation in computing terms. This process is based on the categories presented
above. Among the possible choices, a city can be defined as a political entity
(municipality, metropolitan region, agglomeration community...), or as a
morphological entity (dense space and/or built in a continuous manner), or even as a
functional entity (employment center, area drawn by daily commuters...). If we rely
on the first design of the city, there are only few questions to ask: indeed, the city in
this case is an object of the fiat type, defined by convention or politico-
administrative decision. In the case of the morphological definition, the first
question that arises concerns without doubt the conceptualization of space: can we
apprehend the city and its dynamics through the bias of a density field (Figure 1.2),
where the city appears as a “spatial singularity”, distinguishable from its
environment, and introducing a “discontinuity” in this environment, as in the
example of a hill in an altitude area? Or is it preferable to envisage the city from an
object perspective? In this case, it concerns an object of the fiat and composite type,
constructed from lower level objects or fields (Figure 1.2). It is then important to
recognize the type of relationships and criteria that will be taken into account in the
case of a morphological definition to identify where in the built space are located the
discontinuities that allow demarcating the city.
Figure 1.2. The morphological city: a peak in the density surface or an
aggregation/composition of buildings. For a color version of the figure, see
www.iste.co.uk/mathian/spatiotemporal.zip
In practice, the first morphological delimitations in France have been made on
the basis of aerial photos (field source), and the discontinuity of built area is
detected through a proximity criterion based on a spacing threshold of 200 m. This
criterion implies that the city incorporates, starting from the center, all the built-up
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