Self-Organized Criticality

The causes and possible relations between the abundance of fractal structures and 1/f signals found in nature have puzzled scientists for years. Based on observations of computer simulations of the cellular automata sandpile model, the term, self-organized criticality (SOC) was invented by theoretical physicists Bak and coworkers (1987) and was used to explain a universal dynamic organizing process governing various fractal growths in space and time. SOC describes that systems organize themselves so that their internal dynamics produce critical behavior over a very wide range of length scales. The term consists of two parts. Self-organization has been used to describe the ability of certain nonequilibrium systems to develop structures and patterns often without explicit pressure or involvement from outside the systems (Prigogine, 1997). In other words, the constraints on form (i.e., organization) of interest to us are internal to the system, resulting from the interactions among the components and usually independent of the physical nature of those components. The organization can evolve in either time or space, maintain a stable form or show transient phenomena. Criticality is a technical word used in connection with phase transitions (strictly speaking, continuous or second-order transitions), and has a very precise meaning, in which the system becomes critical in the sense that all members of the system influence each other and events of all sizes occur. The key point of view in Bak et al. (1987) is that they suggest that there are important analogies between the marginal stability reached at the critical point of a phase transition and the complex self-organized features that arise from the marginal stability of a dynamic system.