Active Walks: The First Twelve Years (Part I)

Active walk is a paradigm for self-organization and pattern formation in simple and complex systems, originated by Lam in 1992. In an active walk, the walker (an agent) changes the deformable landscape as it walks and is influenced by the changed landscape in choosing its next step. Active walk models have been applied successfully to various biological, chemical and physical systems from the natural sciences, and to economics and many other systems from the social sciences. More recently, it has been used to model human history. In this review, the history, basic concepts, formulation, theories, applications, new developments and open problems of active walk are summarized and discussed. New experimental, theoretical and computer modeling results are included.