Many human social phenomena, suchh as cooperation [1][2][3], the growth of settlements [4], traffic dynamics [5][6][7] and pedestrian movement [7][8][9][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][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 physical [14][15][16], chemical [17] and biological [18,19] systems. We find that our model is able to reporduce many of the observed large-scale spatial features of trail systems.
Active walker models have recently proved their great value for describing the formation of clusters, periodic patterns, and spiral waves as well as the development of rivers, dielectric breakdown patterns, and many other structures.It is shown that they also allow to simulate the formation of trail systems by pedestrians and ants, yielding a better understanding of human and ani- Whereas pedestrians leave footprints on the ground, ants produce chemical markings for their orientation. Nevertheless, it is more important that pedestrians steer towards a certain destination, while ants usually find their food sources by chance, i.e. they reach their destination in a stochastic way. As a consequence, the typical structure of the evolving trail systems depends on the respective species. Some ant species produce a dendritic trail system, whereas pedestrians generate a minimal detour system. The trail formation model can be used as a tool for the optimization of pedestrian facilities: It allows urban planners to design convenient way systems which actually meet the route choice habits of pedestrians. Typeset using REVT E XHelbing/Schweitzer/Keltsch/Molnár: Active Walker Model for Trail Formation 3
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