Agent-Based Social Simulation: A Dynamical-Systems Viewpoint JULYAN H. E. CARTWRIGHT Instituto Andaluz de Ciencias de la Tierra, CSIC–Universidad de Granada, Granada, Spain Physics is expanding outward from its traditional base; nowadays many physicists work on phenomena involving biology, economics, and sociology. How can we get to grips with physics in these fields where traditional equation-based modelling is difficult to imple- ment? The so-called audience or Mexican Wave in sports stadia, in which participants jump up and raise their arms in a coordinated manner so that a wave propagates around the stadium, is an instance where structures familiar to physicists— nonlinear waves or solitons—appear in the novel context of socio- physics. Using the example of the Mexican Wave, I discuss new approaches based on cellular automata and agent-based models, and how these may be related to classical continuum physics. KEYWORDS agent-based modelling, cellular-automaton compu- tation, Mexican wave, sociophysics INTRODUCTION In a so-called audience or Mexican Wave, the participants—the crowd at a sports event—jump up and raise their arms in a coordinated manner so that a wave propagates around the stadium (Figure 1). Recently it has been described as a wave in an excitable medium (Farkas et al., 2002). An excitable element is defined by its response to a perturbation: whereas a small distur- bance causes merely an equally small response, a perturbation above a certain threshold in amplitude excites a quiescent element that then decays back to quiescence during a refractory period in which it is unresponsive to further Address correspondence to Julyan H. E. Cartwright, Instituto Andaluz de Ciencias de la Tierra, CSIC–Universidad de Granada, Campus Fuentenueva, Granada 18071, Spain. E-mail: julyan.cartwright@csic.es Cybernetics and Systems: An International Journal, 41:281–286 Copyright # 2010 Taylor & Francis Group, LLC ISSN: 0196-9722 print=1087-6553 online DOI: 10.1080/01969721003778527 281 Downloaded By: [Cartwright, Julyan H. E.] At: 14:37 26 May 2010