Non-Linear Dynamics, Self-Organization and Cellular Automata Models - Environmental Modelling: Finding Simplicity in Complexity - page 47

be very difficult to go from the data to a description of
the underlying dynamics (e.g. Wilcox et al ., 1991), even
though simple models may be devised that produce
simulated data closely resembling the measured values.
But since there may be many such models, what
certainty can we have that any one of them has
captured the workings of the real-world system? (Again
cf. Beven's 'model equifinality': Beven, 1993.)

and Highfield (1995), Kauffman (1995), and Holland
(1998), amongst others.
These early studies demonstrated that responses which
are both complex and highly structured may result
from relatively simple interactions (but very many of
them) between the components of a system. Interactions
between such components are governed by 'local' rules,
but the whole-system ('global') response is to manifest
some higher-level 'emergent' organization, following the
formation of ordered structures within the system. The
system thus moves from a more uniform ('symmetri-
cal') state to a less uniform - but more structured - state:
this is so-called 'symmetry-breaking'. Several aspects of
the phenomenon of self-organization are summarized
in Figure 4.2. Note the definition of emergence which
is given: 'emergent responses cannot be simply inferred
from the behaviour of the system's components'.

For a while, it seemed that deterministic chaos and frac-
tals might remain little more than interesting diversions
for environmental modellers.

4.2.2 Earlyworkonself-organization

Pioneering research carried out from the late 1980s,
however, strongly supported the notion that struc-
tured complexity does not always require an underlying
complexity of process. A major centre for this work was
the Santa Fe Institute (Waldrop, 1994). Overviews of this
diverse body of early research on self-organization and
emergence in complex systems are presented by Coveney

4.2.3 Attributesof self-organizingsystems

Three key concepts that characterize self-organizing
systems are feedback, complexity, and emergence. All are
interlinked.

Characteristics of Complex Systems

A 'complex' system

Emergent behavior that cannot
be simply inferred from the
behavior of the components

Complex Systems

Chaos

Involve:

Emergence

Fine Scales Influence
Large Scale Behavior

Hlerarchles

Many
Components

Self-Organization

Control Structures

Dynamically
Interacting

Composites
Substructure
Decomposability

and giving rise to

Evolution

A Number of
Levels or Scales

A 'simple'
system

which exhibit

Common
Behaviors

Transdisciplinary Concepts

Across Types of System,
Across Scales, and thus
Across Disciplines

Figure 4.2 Schematic representation of some attributes of self-organizing complex systems. Graphic by Marshall Clemens
(www.idiagram.com), from the 'Visualizing Complex Systems Science' project at http://necsi.org/projects/mclemens/viscss.html.
Used by permission.