complexity

complexity in science, field of study devoted to the process of self-organization. The basic concept of complexity is that all things tend to organize themselves into patterns, e.g., ant colonies, immune systems, and human cultures; further, they go through cycles of growth, mass extinction, regeneration, and evolution. Complexity looks for the mathematical equations that describe the middle ground between equilibrium (see statics ) and chaos (see chaos theory ), such as the interplay between supply and demand in an economy or the relationship among living organisms in an ecosystem.

Complexity theory had its beginnings with American mathematician Norbert Wiener's development of cybernetics , Canadian biologist Ludwig von Bertalanffy's development of general system theory, and American mathematician John H. Holland's development of a computerized artificial life simulation. More recent efforts are centered at the Santa Fe Institute in New Mexico, which was established in 1984, and are found in the work of multidisciplinary researchers such as American economist Kenneth Arrow and American physicist Murray Gell-Mann. Because complex systems typically cross the boundaries of traditional disciplines, the study of complexity is an interdisciplinary science. Much of the progress in the field can be attributed to advances in nonlinear dynamics , in the power of computers and in computer graphics , and in adaptive programs and fuzzy logic .

Bibliography: See M. M. Waldrop, Complexity: The Emerging Science at the Edge of Order and Chaos (1992); R. Lewin, Complexity: Life at the Edge of Chaos (1993); J. H. Holland, Hidden Order (1995).

complex See LITHOSTRATIGRAPHIC UNIT.

complexity The “ease” or “difficulty” of solving computational problems, measured in terms of some resource consumed during computation. The resource can be an abstract measure, or something specific like space or time. The analysis of the complexity of computational problems is a very active and large area of research at present and has important practical implications. See also complexity classes, complexity measure.