Non-Linear Dynamics, Self-Organization and Cellular Automata Models - Environmental Modelling: Finding Simplicity in Complexity - page 50

generate a power-law, and Newman (2005) gives at least
six mechanisms for generating power-law relationships,
none of which involve SOC.
Despite (or perhaps because of) this ongoing con-
troversy, several geomorphological studies have focused
on the possible role of SOC. For example, Boardman
and Favis-Mortlock (1999) speculated that power-law
frequency-magnitude relationships in a wide range of soil
loss and sediment yield data might indicate the workings
of SOC in the erosional system. Self-organized criticality
has also been a theme in the work of Phillips (1995, 1996,
1997, 1999a, 1999b, 2006), Dikau (1999), and others.
Interestingly, Sidorchuk (2006) makes use of a modelling
approach in investigating the role of SOC in gully devel-
opment. Van De Wiel and Coulthard (2010) speculate
that, in addition to the usual SOC fingerprints of power
law frequency-magnitude relationships, 1/f properties of
time-series data, and spatial fractality, a SOC system
must also possess a cascading process mechanism which
enables the system to initiate both low-magnitude and
high-magnitude events. Finally, Eadie and Favis-Mortlock
(submitted) warn that even when a power law line is an
apparently good fit to measured frequency-magnitude
data, this fit may be somewhat illusory and thus is cer-
tainly, by itself, no reason to infer the operation of SOC.
The importance of SOC in environmental systems, and
for environmental modelling, remains controversial.

acquaintance the notion of self-organization is distinctly
counterintuitive (Bar-Yam, 1997: 623).
This counterintuitivity is probably to some extent a
matter of preconceptions: an everyday observation that
the hot cappuccino always cools to muddy uniformity. It
is perhaps this kind of much-repeated experience which
colours our expectations of 'the way things are'. But
equally, we see living things - plants and animals - come
into being and maintain their organization for some
time (i.e. as long as they are alive). Accustomed to these
observations since infancy, we unquestioningly intuit that
these 'kinds' of system are different in some fundamental
way (although we may seldom ask ourselves what this
difference is). So: why do these two kinds of systems
behave so differently?
Distinctions between living and nonliving systems were
much discussed at the end of the nineteenth century, when
the laws of thermodynamics were being formulated by
physicists such as Ludwig Boltzmann. These laws express
some of the most profound scientific truths yet known, in
particular the universal inexorability of dissolution and
decay. To develop an understanding of self-organization,
it is essential to comprehend the implications of the sec-
ond law of thermodynamics, which states that entropy, or
disorder, in a closed system can never decrease. It can be
colloquially expressed as 'There is no such thing as a free
lunch.' Thus in a 'closed' finite universe, the end result is
a kind of cold-cappuccino uniformity, often described in
studies of chemical equilibrium (Chorley, 1962). How-
ever, pioneering work by Ilya Prigogine and colleagues at
the Free University of Brussels in the 1960s (for example,
Nicolis and Prigogine, 1989; Ruelle, 1993; Klimontovich,
2001) focused on systems that are 'open' from a ther-
modynamic perspective. In a thermodynamically open
system (also called a 'dissipative system': ¸ ambel, 1993:
56), there is a continual flow of matter and energy through
the system. This continuous flow of matter and energy
permits the system to maintain itself in a state far from
thermodynamic equilibrium (Huggett, 1985) - at least
while the flow continues. This situation is in contrast
to the thermodynamically closed (or 'conservative') sys-
tem, such as the cup of cappuccino together with its
immediate surroundings: here there is no such flow of
matter and energy into the system, only a movement of
energy between the coffee and its surroundings. Thus
the coffee and its environment gradually equilibrate, with
the coffee cooling and mixing, and the surrounding air
warming slightly. Living systems, though, maintain their
structure and do not equilibrate, as long as food, oxygen
and so forth are available. So, in a sense, the second law

4.2.5 Thecounterintuitiveuniversalityof
self-organization

Self-organizing systems have been proposed or identified
all around us:

In purely physical systems, for example crackling noise
(Sethna et al ., 2001), chemical reactions (Tam, 1997),
and sand-dune dynamics (Hansen et al ., 2001).

•

In biological systems, for example population dynamics
(Sole et al ., 1999), bacterial patterns (Ben-Jacob and
Levine, 2001), embryonic pattern formation (Goodwin,
1997), ecology (Laland et al . 1999; Peterson, 2000),
evolutionary dynamics (Lewin, 1997), and Gaia theory
(Lenton, 1998).

•

In human systems, for example urban structure (Portu-
gali et al ., 1997), social networks (Watts, 1999; Winder,
2000), and the discipline of geography (Clifford, 2001).

•

Yet since our common experience is that bricks do
not spontaneously organize themselves into houses, or
a child's bedroom spontaneously tidy itself, at first