In the
Center for Complexity and Collective Computation at the Wisconsin Institute for Discovery

Complex systems are all characterized by adaptive behavior emerging from the coordinated, collective dynamics of large populations of agents. Research in C4 on complex systems integrates insights from the theory of strategic interactions in game theory with the theory of frustrated systems, drawing for example, from the statistical mechanics of spin glasses. Agents can be molecules in cells, cells in bodies, individuals in societies and computers in networks.

All complex systems form natural hierarchies consisting of modular structures capable of achieving high degrees of functional differentiation and specialization.  C4 scientists are developing measures of complexity that might reveal dynamical or structural characteristics of hierarchical systems and afford us with some means of comparison. A range of characteristic time and space scales also allow classification of these hierarchies.  For example, the concept of multi-information arises as a natural measure of complexity when considering stochastic interdependence among a set of measured valued obtained from an empirical observation.  

C4 scientists are also interested in theories for the evolution of complex systems. This includes explaining why and how systems characterized by these properties come into existence, and how they are able to persist in the face of great uncertainty and noise.

Support for our complexity projects is generously provided by the John Templeton Foundation through a grant to the Santa Fe Institute.