A Macro-Level Order Metric for Self-Organizing Adaptive Systems

Analyzing how agent interactions affect macro-level self-organized behaviors can yield a deeper understanding of how complex adaptive systems work. The dynamic nature of complex systems makes it difficult to determine if, or when, a system has reached a state of equilibrium or is about to undergo a major transition reflecting the appearance of self-organized states. Using the notion of local neighborhood entropy, this paper presents a metric for evaluating the macro-level order of a system. The metric is tested in two dissimilar complex adaptive systems with self-organizing properties: an autonomous swarm searching for multiple dynamic targets and Conway's Game of Life. In both domains, the proposed metric is able to graphically capture periods of increasing and decreasing self-organization (i.e. changes in macro-level order), equilibrium and points of criticality; displaying its general applicability in identifying these behaviors in complex adaptive systems.