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For other uses, see Complexity (disambiguation).

In general usage, complexity tends to be used to characterize something with many parts in intricate arrangement. In science there are at this time a number of approaches to characterizing complexity, many of which are reflected in this article. Seth Lloyd of M.I.T. writes that he once gave a presentation which set out 32 definitions of complexity.^[1]

Definitions are often tied to the concept of a ‘system’ – a set of parts or elements which have relationships among them differentiated from relationships with other elements outside the
relational regime. Many definitions tend to postulate or assume that complexity expresses a condition of numerous elements in a system and numerous forms of relationships among the elements. At the same time, what is complex and what is simple is relative and changes with time.

Some definitions key on the question of the probability of encountering a given condition of a system once characteristics of the system are specified. Warren Weaver has posited that the complexity of a particular system is the degree of difficulty in predicting the properties of the system if the properties of the system’s parts are given. In Weaver's view, complexity comes in two forms: disorganized complexity, and organized complexity. ^[2] Weaver’s paper has influenced contemporary thinking about complexity. ^[3]

The approaches which embody concepts of systems, multiple elements, multiple relational regimes, and state spaces might be summarized as implying that complexity arises from the number of distinguishable relational regimes (and their associated state spaces) in a defined
system.

Some definitions relate to the algorithmic basis for the expression of a complex phenomenon or model or mathematical expression, as is later set out herein.

http://en.wikipedia.org/wiki/Complexity