Concepts used in the scientific study of complex systems have become so
widespread that their use and abuse has led to ambiguity and confusion in their
meaning. In this paper we use information theory to provide abstract and
concise measures of complexity, emergence, self-organization, and homeostasis.
The purpose is to clarify the meaning of these concepts with the aid of the
proposed formal measures. In a simplified version of the measures (focusing on
the information produced by a system), emergence becomes the opposite of
self-organization, while complexity represents their balance. Homeostasis can
be seen as a measure of the stability of the system. We use computational
experiments on random Boolean networks and elementary cellular automata to
illustrate our measures at multiple scales.Comment: 42 pages, 11 figures, 2 table