Geoscience Reference
In-Depth Information
kinds of patterns that are generated by CA giving various examples in the 2D domain, and we
then illustrate how these kinds of models have been used to simulate urban development pat-
terns. We develop a number of critiques of this modelling approach, review the key historical
and contemporary literature and then present relevant references.
2.1 CELLULAR AUTOMATA, GEOCOMPUTATION
AND FRACTAL MORPHOLOGIES
Cellular automata, or CAs for short, are computable objects existing in time and space whose char-
acteristics, usually called states, change discretely and uniformly as a function of the states of
neighbouring objects, that is, those that are in their immediate vicinity. The objects are usually
conceived as occupying spaces which are called cells, with processes for changing the state of each
cell through time and space usually articulated as simple rules which control the influence of the
neighbourhood on each cell. This formulation is quite general and many systems can be represented
as CA, but the essence of such modelling consists of ensuring that changes in space and time are
always generated locally, by cells which are strictly adjacent to one another. From such a represen-
tation comes the important notion that CA simulate processes where local action generates global
order, where global or centralised order
emerges
as a consequence of applying local or decentralised
rules which in turn embody local processes. Systems which cannot be reduced to models of such
local processes are therefore not likely to be candidates for CA, and although this might seem to
exclude a vast array of geographical processes where change seems to be a function of action at a
distance, this criterion is not so restrictive as might appear at first sight.
In this characterization, CA embody processes that operate locally in such a way that order
emerges globally at higher scales in space or time or both which are defined in any number of
dimensions. These generate forms that are globally similar in some sense to the elements of the
local form that often represent the modules that form the basis for the automata. For example, let
us start with a 2D cellular space where one of the cells in the space is occupied; we can then define
a rule that says that any occupied cell generates another occupied cell immediately adjacent to the
cell in question at, say, positions to the northwest and the northeast of the starting cell. If we apply
this local rule over and over again to the growing structure, we generate a tree-like form whose
structure at any scale is represented as a compact intertwined lattice of trees which manifest self-
similarity on all scales. We show this in Figure 2.1 where we see the original space which is the
initial condition (Figure 2.1a), the rule for generating the morphology in terms of any occupied
cells (Figure 2.1b) and the growing structure at subsequent levels of scale, up to the seventh order.
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FIGURE 2.1
Basic elements of a CA: generating a fractal. (a)
The initiator
. (b)
The generator
- if this is
applied systematically, it generates
the fractal
. (c)
The fractal
- as an intertwined set of trees.
