Environmental Engineering Reference
In-Depth Information
4
Non-Linear Dynamics,
Self-Organization and Cellular
Automata Models
David Favis-Mortlock
Environmental Change Institute, Oxford, UK
There are three great frontiers in science: the very big, the very small, and the very complex.
(Martin Rees, Our Cosmic Habitat , 2002)
If politics is the art of the possible, research is surely the art of the soluble. Both are intensely practical-minded
affairs.
(Peter Medawar, 'The Act of Creation', 1964)
'The best material model of a cat is another, or preferably
the same, cat' (Rosenblueth and Wiener, 1945).
This problem results in a tension between the desire
for the maximum possible applicability of our models,
and the apparently inevitable tradeoff: model complexity
and comprehensibility. This tension is the focus of this
chapter. The chapter has two aims. First, it summarizes
current knowledge of self-organization in complex sys-
tems (including self-organized criticality), which has it
roots in earlier work on nonlinear dynamics, including
chaos and fractals. The second aim is to show how this
knowledge may be used in a practical way to construct
spatial environmental models. The resulting approach
(cellular automata modelling) is one that appears to have
great promise for lessening this tension in future spatial
models of all kinds.
While many of the examples presented here are drawn
from physical geography, as that is the area of science
in which the author works, the ideas and approaches
discussed are of wide applicability (cf. Wolfram, 2002).
4.1 Introduction
The environment can be very complex. Models are one of
the main tools available to help us to understand our envi-
ronment, and to attempt to predict what will happen in
it. Indeed, as early as 1962, Ackoff et al . (1962: 108) noted
that 'The control [which] science gives us over reality,
we normally obtain by the application of models.' Many
aspects of the environment, however, are too complex for
mere humans to fully grasp: if this is the case, we are forced
to simplify, in effect to fall back on making analogies. The
aim of an analogy is to highlight similarities between
the things compared, and in the same way environmental
models aim to link the more easily understood system (the
model) with the less comprehensible system (some aspect
of the environment). Analogies, though, are never perfect,
and in the same way models are always less than perfect in
making this link. To return to the original point, it could
hardly be otherwise, since a model which is as complicated
as the thing it represents would be no easier to understand.
 
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