Complicated things are often confused
with Complex things, but there is a subtle distinction:
- Complicated -- comprises many
parts
- Complex -- involves many
interactions
Which is not to say that one cannot also
be the other. Also it should be noted that complex systems are NOT
random systems. They may display chaotic behaviors but there is an
underlying structure to be found.
The Canonical Examples
section shows some "simple"
complex systems, the Logistic Equation and the Lorenz Attractor. They
illustrate the ideas that Complexity lurks in what seem to be very
straight-forward models and where, while being completely deterministic,
the end results are often so dependent on the starting state that they
are not predictable in advance (sensitive dependence on initial
conditions).
One area of great interest is that of Multi-Agent Systems. These are
environments containing many (more or less) independent individuals
that interact with one another, often in very simple ways. When viewed
on a grander scale these systems can sometimes exhibit aggregate behaviors that are
very surprising. Complex systems can arise as the result of many simple
interactions.
All of this leads us to the idea of Emergent Behavior. This can be
anything from finding a new metric for a system quality that doesn't
actually exist within the underlying components, to observing behaviors
that are more than the sum of their parts. In many cases behaviors
emerge solely from low level interactions and disappear when the system
is reduced to it's component parts. For these systems the old scientific reductionist paradigm breaks down.