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Latin complexus, past participle of complect, to entwine.

A whole composed of interconnected or interwoven parts: a complex of cities and suburbs; the military-industrial complex.

Consisting of interconnected or interwoven parts; composite.

The process of increase of variety may be called differentiation, the process of increase in the number or strength of connections may be called integration. We will now show that evolution automatically produces differentiation and integration, and this at least along the dimensions of space, spatial scale, time and temporal scale.

We may conclude that complexity increases when the variety (distinction), and dependency (connection) of parts or aspects increase, and this in several dimensions. These include at least the ordinary 3 dimensions of spatial, geometrical structure, the dimension of spatial scale, the dimension of time or dynamics, and the dimension of temporal or dynamical scale. In order to show that complexity has increased overall, it suffices to show, that - all other things being equal - variety and/or connection have increased in at least one dimension.

The aspects of distinction and connection determine two dimensions characterizing complexity. Distinction corresponds to variety, to heterogeneity, to the fact that different parts of the complex behave differently. Connection corresponds to constraint, to redundancy, to the fact that different parts are not independent, but that the knowledge of one part allows the determination of features of the other parts. Distinction leads in the limit to disorder, chaos or entropy, like in a gas, where the position of any gas molecule is completely independent of the position of the other molecules. Connection leads to order or negentropy, like in a perfect crystal, where the position of a molecule is completely determined by the positions of the neighbouring molecules to which it is bound. Complexity can only exist if both aspects are present: neither perfect disorder (which can be described statistically through the law of large numbers), nor perfect order (which can be described by traditional deterministic methods) are complex. It thus can be said to be situated in between order and disorder, or, using a recently fashionable expression, "on the edge of chaos".

To join by weaving or twining together; interweave.

In mathematics, nonlinear systems represent systems whose behavior is not expressible as a sum of the behaviors of its descriptors. In particular, the behavior of nonlinear systems is not subject to the principle of superposition, as linear systems are. Crudely, a nonlinear system is one whose behavior is not simply the sum of its parts or their multiples.

Reductionism in philosophy is the theory that asserts that the nature of complex things can always be reduced to (explained by) simpler or more fundamental things.

Part of systems theory, system dynamics is a method for understanding the dynamic behavior of complex systems. The basis of the method is the recognition that the structure of any system — the many circular, interlocking, sometimes time-delayed relationships among its components — is often just as important in determining its behavior as the individual components themselves.

Systems theory focuses on organization and interdependence of relationships. A system is composed of regularly interacting or interdependent groups of activities/parts the emergent relationship(s) of which form the (a) whole.

A complex is a whole that comprehends a number of parts, especially one with interconnected or mutually related parts

In mathematics and physics, chaos theory describes the behavior of certain nonlinear dynamical systems that under certain conditions exhibit a phenomenon known as chaos. Among the characteristics of chaotic systems, described below, is sensitivity to initial conditions (popularly referred to as the butterfly effect). As a result of this sensitivity, the behavior of systems that exhibit chaos appears to be random, even though the system is deterministic in the sense that it is well defined and contains no random parameters

complex systems specifically consist of a large number of mutually interacting dynamical parts.

The term complex system formally refers to a system of many parts which are coupled in a nonlinear fashion