Geoscience Reference
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the notion of cells being affected by changes in their immediate vicinity (Hagerstrand, 1967). These
were not strict CA but CS models in the terminology adopted here. In the early 1960s, CA were
implicit in the wave of computer models designed for land use-transportation planning. Chapin
and his colleagues at North Carolina in their modelling of the land development process articulated
CS models where changes in state were predicted as a function of a variety of factors affecting
each cell, some of which embodied neighbourhood effects (Chapin and Weiss, 1968). Lathrop and
Hamburg (1965) proposed similar CS simulations for the development of western New York state.
The idea that the effect of space should be neutralised in such models by adopting regular lattice
structures such as grids also encouraged CA-like representations.
However, strict CA models came from another source - from theoretical quantitative geography.
These were largely due to Waldo Tobler (1970, 1975, 1979) who during the 1970s worked at the
University of Michigan where Arthur Burks and his Logic of Computers Group were keeping the
field alive. Tobler himself first proposed CS models for the development of Detroit but, in 1974,
formally began to explore the way in which strict CA might be applied to geographical systems,
culminating in his famous paper
Cellular Geography
published in 1979. At Santa Barbara in the
1980s, Couclelis (1985, 1988, 1989), influenced by Tobler, continued these speculations, until the
early 1990s when applications really began to take off as computer graphics, fractals, chaos and
complexity, all generated the conditions in which CA have now become an important approach to
GeoComputation.
It is perhaps surprising that CA models were not explored earlier as a basis for GeoComputation
in urban and related simulations, but other approaches held sway, particularly those that emphasised
time rather than space
per se
. Dynamics has always held a fascination in spatial modelling. Early
attempts at embodying time into operational urban models were always plagued by a simplistic view
of dynamics or by difficulties of embedding appropriate dynamics within spatial representations
(Forrester, 1969; Batty 1971). By the early 1980s, however, several groups had begun to explore
how developments in non-linear dynamics might be adapted to the simulation of urban change.
Wilson (1981) building on catastrophe theory, Allen (1982) on adaptations of Prigogine's approach
to bifurcation through positive feedback, White (1985) on notions of discontinuity in the behaviour
of regional systems and Dendrinos (1991) on predator-prey models and latterly with Sonis on cha-
otic dynamics (Dendrinos and Sonis, 1990) all set the pace. But this work downplayed the spatial
element which was considered simply as a starting point. The emphasis was upon new conceptions
of time. The dynamics of how spatial morphologies evolved and changed took much longer to gain
the attention of researchers following this new paradigm. Nevertheless, it was from these develop-
ments in dynamics that the first explicit application of CA to real urban systems came. White and
Engelen's (1993) application of CA in the light of their own work in non-linear urban dynamics
was to the development of US cities such as Cincinnati where they showed how urban form could
be modelled through time and how these forms were consistent with fractal geometry and urban
density theory (Batty and Longley, 1994).
Strict CA of course does not appear immediately applicable to real systems where the definition
of states, neighbourhoods and transition rules is much more general than the theory suggests.
Clear statements of the theory of CA have only been produced since Wolfram's (1984, 1994) work,
and even now, there is no definitive discussion of the ways in which strict CA might be relaxed
and adapted to real systems, with the possible exception of Toffoli and Margolus' (1987) topic.
The key problem of adapting strict CA to generalised GeoComputation involves the issue of
action
at a distance
. Much GeoComputation, which has spatial analysis as its foundation, articulates spa-
tial behaviour as the product of
action at a distance
, building on notions of gravitation, spatial
autocorrelation and network connectivity. But such notions are invariably developed from models
of static systems where distance relations have clearly evolved through time. The situation for
dynamic urban theory is much more confused because there is a strong argument that action at a
distance
emerges
in such systems as the consequence of local action through time, as a product of
the successive build-up and compounding of local effects which give rise to structures that reflect
