Abstract

Complexity is a multifarious concept; different researchers focus on different aspects. For instance, a system can be considered complex because it has many interacting parts, yet its behavior can be relatively simple, that is, easy to predict, control and manipulate: car engines and watches would be examples. On the other hand, a system with few interacting parts can exhibit behavior considered complex, that is, hard to predict: three billiard balls on a torus would be an example (Krámli, Simányi, and Szász 1991). Also note that both the terms “complexity” and “emergence” often are used for two seemingly different cases. One case involves simple rules governing uniform elements that generate unpredictable (“complex”) behavior such as strikingly stable patterns in finite automata. Another case involves “complex,” seemingly random, often nonlinear interactions of uniform elements that generate robust and stable large-scale patterns that are therefore, at least from a particular level of analysis, largely predictable, for example, Rayleigh-Bénard convection (RBC). The idea is that in the first kind of case we have complexity from relative simplicity, while in the second kind of case we have simplicity from relative complexity.