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much wider interaction. There has been little or no research into such possibilities; in fact, it is the
development of CA in this context which has raised the idea of these effects - so long taken for
granted as exogenous - being endogenous to and emergent from such computation. As cells evolve
and change, building their overall spatial potential through local neighbourhood action or decision,
it is possible to conceive of all system-wide effects as being embodied in this potential. Therefore,
it is only necessary to ever act behaviourally according to what this potential is within its local
neighbourhood for this potential takes account of wider action at a distance effects. Simply by
examining the position of a cell in the system, these effects are known. This is an issue that clearly
requires considerable research.
The first CA models came from Tobler's (1979) algebras, from Couclelis's (1985) theoretical
speculations, from Batty and Longley's (1986) initial work on fractals, from Batty and Xie's (1994)
work on urban simulation, from White and Engelen's (1993) applications to Cincinnati and from
the Clarke et al. (1997) generalisation of the forest fire models to the fractal growth of the San
Francisco Bay area. These latter two applications spawned the only two long-standing CA mod-
els applied to urban development, namely, SLEUTH developed by Clarke and his colleagues and
the White-Engelen Metronamica models that have found widespread development in Europe. A
midterm summary of these developments is given by Batty and Xie (2005), and more recent spe-
cial issues of journals and conferences have been devoted to the basic ideas in an applied context
(Dragićević, 2008; Marceau and Benenson, 2011). As far as we know, no one has yet produced a
summary of applications, with perhaps the short summary by Dragićević (2008) being the excep-
tion, and there is now a sense in which CA models applied to city systems are simply one of many
approaches which have, like all urban models, considerable limitations. One of the major limitations
is the fact that such models really generate qualitative changes in state rather than numerical predic-
tions. This makes their use in policy making problematic. Moreover, these models tend to lack an
explicit transportation sector, and as transportation is still one of the essential components in urban
structure, this makes their application to problems of sprawl and urban growth - for which they are
devised in the first place - limited. Growth is intimately linked to transportation, and thus there
are very few urban agencies that have adopted CA-like models, preferring older and large-scale and
more comprehensive land use-transportation interaction (LUTI) models.
The flurry of recently developed applications can be divided into those which deal with hypo-
thetical in contrast to real systems, as well as those which are strict CA in contrast to CS models
where definitions of local neighbourhood and transition rules are relaxed. Other significant features
involve relationships with GIS software, the extent to which multiple states are dealt with and the
starting points for such simulations based on limited numbers of seeds or already developed land-
scapes. There are now upwards of 50 or more applications of CA to cities. Most deal with hypotheti-
cal examples which emphasise some aspect of urban structure or dynamics such as the segregation
of land uses and the diffusion or migration of resident populations. As we have noted, applications
to urban policy problems are few and far between, but there are several proof of concept examples
in real cities now existing.
We will not review the many applications here but it is worth illustrating a typical example of
CA to urban development that the authors have been involved in (Stanilov and Batty, 2011). We have
applied the Metronamica model to the growth of west London at a fairly detailed fine spatial scale
where development is articulated as the sequence of development decisions associated with land
parcels and streets. A simulation since the mid-nineteenth century has been developed using data
from old maps and related census sources, and the application shows that CA models at this scale
produce rather good patterns of development, explaining the importance of local rules to the way
sites are developed. In fact, it appears from this example that the real power of CA in urban model-
ling is at the fine physical scale where the performance of this particular model is good. At broader
scales, the performance of these models is more problematic, and the fact that transportation is so
important but largely missing from such models and that the idea of a local neighbourhood is lim-
ited in real cities tends to limit the relevance of these models.
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