Abstract
Active Walk (AW) is a paradigm for self-organization and pattern formation in simple and complex systems, originated by Lam in 1992. In an AW, the walker 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, physical, geological and economic systems from both the natural and social sciences. More recently, it has been used to model human history. In Part I of this review, the birth of the AW paradigm, its basic concepts and formulations, a solvable two-site model, and the experiments and AW modeling of surface-reaction filamentary patterns are presented. Part II here continues with properties of AW, and applications of AW in nonliving and living systems — including those from the social sciences and human history. (In particular, unsuspected quantitative laws and a prediction about the Chinese history are given.) A comment on the relationship between physics, social science and complex systems is provided. The review concludes with open problems in the form of workable research projects and general discussions.
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