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Complex Systems: Criticality and Scaling


At different temporal and spatial scales in nature systems far from equilibrium often undergo wide fluctuations and intermittent bouts of activity and stasis (quiescent behavior). Complexity notions have been advanced for explaining these phenomena through the application of concepts and theories developed in the study of self-organized criticality (see the subject self-organization above). According to this view broad fluctuations occur spontaneously without the need of triggering events from outside the system.

The characteristic scaling properties of fractal geometrical objects mathematically describe self-organized systems at their critical points as structures that display self-similarity. Self-similarity is a basic invariance (symmetry) of some naturally occurring arrangements of parts in which at all scales the parts resemble the whole structure in all details except for their size. Fractal mathematical methods are applied to discern and investigate self- similar hierarchical organization in many biological forms of aggregation, such as forests, coral reefs, the movement patterns displayed by populations of organisms, the concentration of plankton patches in the ocean, etc.