  Many human social phenomena, such as cooperation, the growth of settlements,
traffic dynamics and pedestrian movement, appear to be accessible to
mathematical descriptions that invoke self-organization. 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, and whether optimal path
systems can be predicted for urban planning. We use an `active walker' model
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 chemical and
biological systems. We find that our model is able to reporduce many of the
observed large-scale spatial features of trail systems.
