International Encyclopedia of Systems and Cybernetics

An exploration of some concrete or abstract space without any determining guidance.

S LEVY reminds us of the probability theorem that states that "Starting from any point in a random walk restricted to a finite space, we can reach any other point any number of times" (1992, p.303).

The conditon for a random walk is that no attractor should exist within the space considered or, in other words, that no gradient be present.

Once some reinforcement factor appears within the explored space, the "explorers" search tends to become organized. This is basic for the appearence of self-organization in networks, for instance of social robots.

It is also the case for many seemingly aperiodic oscillations: markets fluctuations for example cannot be satisfactorily modelized by random walks, because while their behavior is chaotic, it is however not perfectly undetermined.

In human generated more or less periodic processes (for ex. stock markets evolution) a loosely deterministic factor is present and active. This factor is psychological in each participating individual, but at the same time psychosocial among the group of investors as a whole. Markets, for ex. are not only fluctuating in relation to economic indicators, but also according to investors and speculators moods and beliefs, as they are not purely rational agents, nor omniscient.. If the majority are optimistic, the prices rise; if they turn pessimistic, the prices fall.

Moreover the shifts present two other defining characteristics:

- they are self-organizing processes, with critical thresholds of unstability

- as shown by ELLIOTT in the 1930's, long term movements can be graphically split into alterning medium and short component waves which appear to be grossly self-similar.

→ ELLIOTT's waves; Self-similarity in the WEIERSTRASS function