Discrete Dynamical Networks and Their Attractor Basins

A key notion in the study of network dynamics is that state-space is connected into basins of attraction. Convergence in attractor basins correlates with order-complexity-chaos measures on space-time patterns. A network's "memory," its ability to categorize, is provided by the configuration of its separate basins, trees and sub-trees. Based on computer simulations using the software Discrete Dynamics Lab, this paper provides an overview of recent work describing some of the issues, methods, measures, results, applications and conjectures.<p> To appear in the proceedings of Complex Systems '98University of New South Wales, Sidney, Australia.