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.

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Figure 1: Between the straight, paved ways on the university campus in Stuttgart-Vaihingen a trail system has evolved (centre of the picture).
Figure 2: The structure of the emerging trail system (yellow to blue) depends essentially on the attractiveness parameter κ.
Figure 3: The places and walking directions of pedestrians are represented here by arrows.
Figure 4: When pedestrians leave footprints on the ground, trails will develop, and only parts of the ground are used for walking (in contrast to pa.


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We thank F. Schweitzer for discussions, and W. Weidlich and M. Treiber for reviews of the manuscript.

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Correspondence to Dirk Helbing.

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Helbing, D., Keltsch, J. & Molnár, P. Modelling the evolution of human trail systems. Nature 388, 47–50 (1997).

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