Modelling the evolution of human trail systems

Many human social phenomena, such as cooperation1,2,3, the growth of settlements4, traffic dynamics5,6,7 and pedestrian movement7,8,9,10, appear to be accessible to mathematical descriptions that invoke self-organization11,12. 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 are13, and whether optimal path systems can be predicted for urban planning. We use an ‘active walker’ model14,15,16,17,18,19 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 physical14,15,16, chemical17 and biological18,19 systems. We find that our model is able to reproduce many of the observed large-scale spatial features of trail systems.