When complexity is defined as a function of
structure, entropy and granularity, examining its dynamics reveals its
fantastic depth and phenomenal properties. The process of complexity
computation materializes in a particular mapping of a state vector onto a
scalar. What is surprising is how a simple process can enshroud such an
astonishingly rich spectrum of features and characteristics. Complexity
does not possess the properties of an energy and yet it expresses the
"life potential" of a system in terms of the modes of behaviour it can
deploy. In a sense, complexity, the way we measure it, reflects the
amount of fitness of an autonomous dynamical system that operates
in a given Fitness Landscape. This statement by no means implies that
higher complexity leads to higher fitness. In fact, our research shows
the existence of an upper bound on the complexity a given system may
attain. We call this limit critical complexity. We know that in
proximity of this limit, the system in question becomes delicate and
fragile and operation close to this limit is dangerous. There surely
exists a "good value" of complexity - which corresponds to a fraction,
ß, of the upper limit - that maximizes fitness:
Cmax fitness = ß Ccritical
We don't know what the value of ß is for a given
system and we are not sure on how it may be computed. However, we think
that the fittest systems are able to operate around a good value of ß.
Fit systems can potentially deploy a sufficient variety of modes of
behaviour so as to respond better to a non-stationary environment
(ecosystem). The dimension of the modal space of a system ultimately
equates to its degree of adaptability. Close to critical
complexity the number of modes, as we observe, increases rapidly but, at
the same time, the probability of spontaneous (and unwanted) mode
transitions also increases quickly. This means the system can suddenly
undertake unexpected and potentially self-compromising actions (just
like adolescent humans).
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