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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 staticsstatics,
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.
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) and chaos (see chaos theorychaos 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.
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), 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'sWiener, Norbert,
1894–1964, American mathematician, educator, and founder of the field of cybernetics, b. Columbia, Mo., grad. Tufts College, 1909, Ph.D. Harvard, 1913.
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 development of cyberneticscybernetics
[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.
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, 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 ArrowArrow, Kenneth Joseph,
1921–2017, American economist, b. New York City, grad. City College of New York (B.S. 1940), Columbia (M.A. 1941, Ph.D. 1951). He was on the faculties of the Univ.
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 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 dynamicsnonlinear 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).
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, in the power of computerscomputer,
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 logical
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 and in computer graphicscomputer graphics,
the transfer of pictorial data into and out of a computer. Using analog-to-digital conversion techniques, a variety of devices—such as curve tracers, digitizers, and light pens—connected to graphic computer terminals, computer-aided design
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, and in adaptive programs and fuzzy logicfuzzy 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 or another but
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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).


Consisting of various parts united or connected together, formed by a combination of different elements; intricate, interconnecting parts that are not easily disentangled.


(computer science)
The number of elementary operations used by a program or algorithm to accomplish a given task.


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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