Geoscience Reference
In-Depth Information
Action at a distance is the central organising principle behind spatial modelling. Consequently,
most applications of CA break with the rule that truly local neighbourhoods condition growth and
change, preferring to embody some action at a distance within larger neighbourhoods within which
the effect of individual cells might embody some distance decay. These CS models are writ large
in empirical applications but strict CA is still invoked in some applications such as the SLEUTH
models. Moreover, in several applications, the scale of space - the size of the cells - and the extent
to which these contain all interaction within are rarely explicit. Couclelis (1985, 1988, 1989) has
emphasised many times in her papers that, at best, CA must be primarily seen as a metaphor for
urban growth and change: '… systems of the kind considered here have such volatile behaviour that
models representing them may be more useful as “metaphors” or conceptual organising schemata,
than as quantitative planning models' (Couclelis, 1989, p.142).
There are however ways in which CA might provide much more sophisticated representations of
urban systems than anything so far. When systems grow in space, they invariably diffuse, and the
repeated action of local rules can be so structured as to represent the cumulative build-up of interac-
tion potential. This might be no more than when a cell is occupied, it interacts locally with all other
occupied cells in its neighbourhood from thenceforth and thus cells which are occupied first always
have the greatest cumulative
potential
interaction through time. Potential might thus vary directly
with the age of a cell - when it was first occupied - and in this way, centrality can be reinforced as
action at a distance
emerges
from such repeated local actions across space. The various applications
to hypothetical urban systems which dominate the field all stress different aspects of the theory of
CA. There are several strong links to GIS based on the notion that CA and CS models use a form
of representation which is the same as raster-based/pixel-based GIS. Standard CA models can be
represented and modelled within the raster-based systems such as
IDRISI
, but contemporary GIS
systems such as
ArcGIS
now embrace CA-style applications that can easily be embedded into the
overlay capabilities and modelling structures within such software.
2.10 CONCLUSIONS
CA clearly brings many unique aspects to GeoComputation and modelling, as much to define the
limits of what is modellable and what is computable as to define new methods of GeoComputation
per se
. Moreover, it picks up on the notion that spatial form is intrinsically fractal and CA methods
provide the basis for their generation. But as a basis for urban modelling which is geared to policy
analysis, these techniques are limited. Emphasis on the principles of locality and transition in neigh-
bourhoods, on the question of action at a distance, strikes at the very heart of the issue of the way
in which potential and density are created temporally in spatial systems and the way new foci of
potential such as edge cities emerge through positive feedback and bifurcations in the development
process. Scale and space are still confused within such modelling for there has been little research
into appropriate levels at which urban systems might be constituted as automata. Applications show
scales of cell and neighbourhood which range across as many as three orders of magnitude, while
the competition and interaction between different states in cells, which often represent different uses
of land or buildings in an urban context, still remain largely to be worked out. CA imposes a degree
of regularity on the world which must be modified whenever applications are developed, but as yet,
the effect of irregular cell shapes and disconnected neighbourhoods and the representation of streets
and linear features as cells and their interaction with areal features all define the research frontier.
2.11 FURTHER READING
Although no one has yet written a general expository text on CA which gradually builds up basic
ideas and translates these into generic applications - something we have tried to do here for
geographic systems, albeit very briely - Toffoli and Margolus' (1987) topic
Cellular Automata
Machines: A New Environment for Modeling
is by far the best exposition to date. Notwithstanding
