Self-Organized Criticality and ComplexityTheory

Self-organized criticality (abbreviated as SOC from here on) describes a large and varied body of phenomenological data and theoretical work. As is the case with many such catch-all terms, its current meaning has evolved far from any initial precise meaning the term may have had. This chapter will attempt to elucidate the basic concepts behind SOC, describe some of the relevant experimental and theoretical findings, and indicate possible future research directions. The functional focus that I will choose to adopt is the understanding and description of broad classes of pattern formation in nature. The original motivation for SOC came from recursive mathematics. Iterative maps produced fascinating images--fractals--which are now in common usage in popular culture. Some of them produced patterns which looked tantalizingly similar to patterns found in nature, such as river erosion patterns, plant and leaf structure, and geological landscapes. The question then presented itself, What kind of dynamical mechanism would be required to produce such patterns in nature? In addition to being able to produce complex patterns, this mechanism would also have to be simple, because if the mechanism were as complex as the pattern produced, very little would be gained by such an “explanation.”