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).

---

complexity [kəm′plek·səd·ē]

(computer science)

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

---

(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.