Modelling the evolution of human trail systems

Many human social phenomena, such as cooperation(1-3), the growth of settlements(4), traffic dynamics(5-7) and pedestrian movement(7-10), appear to be accessible to mathematical descriptions that invoke self-organization(11,12). Here we develop a model of pedestrian motion to explore the evolution of trails in urban green spaces such as parks. Our aim is to address such questions as what the topological structures of these trail systems are(13), and whether optimal path systems can be predicted for urban planning. We use an 'active walker' model(14-19) that takes into account pedestrian motion and orientation and the concomitant feedbacks with the surrounding environment. Such models have previously been applied to the study of complex structure formation in physical(14-16), chemical(17) and biological(18,19) systems. We find that our model is able to reproduce many of the observed large-scale spatial features of trail systems.