complexity definition of complexity in the Free Online Encyclopedia.

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 statics, branch of mechanics concerned with the maintenance of equilibrium in bodies by the interaction of forces upon them (see force ). It incorporates the study of the center of gravity (see center of mass ) and the moment of inertia.
..... Click the link for more information. ) and chaos (see chaos theory chaos theory, in mathematics, physics, and other fields, a set of ideas that attempts to reveal structure in aperiodic, unpredictable dynamic systems such as cloud formation or the fluctuation of biological populations.
..... Click the link for more information. ), 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 Wiener, Norbert, 1894–1964, American mathematician, educator, and founder of the field of cybernetics, b. Columbia, Mo., grad. Tufts College, 1909, Ph.D. Harvard, 1913.
..... Click the link for more information. development of cybernetics cybernetics [Gr.,=steersman], term coined by American mathematician Norbert Wiener to refer to the general analysis of control systems and communication systems in living organisms and machines.
..... Click the link for more information. , 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 Arrow, Kenneth Joseph, 1921–, American economist, b. New York City, grad. City College of New York (B.S. 1940), Columbia (M.A. 1941, Ph.D. 1951). He taught economics at the Univ. of Chicago (1947–49) and Stanford Univ.
..... Click the link for more information. 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 nonlinear dynamics, study of systems governed by equations in which a small change in one variable can induce a large systematic change; the discipline is more popularly known as chaos (see chaos theory ).
..... Click the link for more information. , in the power of computers computer, device capable of performing a series of arithmetic or logical operations. A computer is distinguished from a calculating machine, such as an electronic calculator , by being able to store a computer program (so that it can repeat its operations and make
..... Click the link for more information. and in computer graphics, and in adaptive programs and fuzzy logic fuzzy logic, a multivalued (as opposed to binary) logic developed to deal with imprecise or vague data. Classical logic holds that everything can be expressed in binary terms: 0 or 1, black or white, yes or no; in terms of Boolean algebra , everything is in one set
..... Click the link for more information. .

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).

(algorithm)

complexity - The level in difficulty in solving mathematically posed problems as measured by the time, number of steps or arithmetic operations, or memory space required (called time complexity, computational complexity, and space complexity, respectively).

The interesting aspect is usually how complexity scales with the size of the input (the "scalability"), where the size of the input is described by some number N. Thus an algorithm may have computational complexity O(N^2) (of the order of the square of the size of the input), in which case if the input doubles in size, the computation will take four times as many steps. The ideal is a constant time algorithm (O(1)) or failing that, O(N).

See also NP-complete.

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Bibliography

complexity