A Better Way to Keep Us Off the Grass

Wednesday, October 01, 1997
RELATED TAGS: MATH
Like pedestrians everywhere, students at the University of Stuttgart in Germany take shortcuts, cutting across carefully tended lawns despite the BETRETEN DES RASENS VERBOTEN! signs. Dirk Helbing, a physicist at the university, has made a careful study of this universal tendency to trample. What he has found may help planners design paths that pedestrians will actually use.

Klaus Humpert, a university colleague of Helbing’s, began the study by obliterating the informal footpaths that crisscrossed the grassy areas of the campus. He regrew grass on the trails and watched what happened. Pedestrians soon trod new paths into the sod--no surprise. Yet, in a sense, the paths weren’t new at all--they formed in almost exactly the same locations as the old trails. That should be no surprise either, says Helbing. Human trails are self-organizing systems: they spontaneously develop into complex but predictable patterns.

To show how trails develop and evolve, Helbing created a computer model in which the actions of simulated pedestrians modified the environment experienced by subsequent walkers, and thus altered their behavior. In his model, the first cyber-pedestrian walks across a lawn to a particular destination rather than taking a more indirect paved path. Just as with real pedestrians, other walkers are more likely to follow in the footsteps of the first, although some deviations occur because Helbing programmed different destinations for the model’s walkers.

He also tried, in his model, to balance the urge to take a shortcut with the convenience of following an existing path. If you build a new path, you would have to trample some vegetation, says Helbing. This takes some time, and maybe your trousers would get dirty.

Over time, as Helbing’s programmed pedestrians balanced comfortable walking with taking the most direct route, the various trails began to bundle together, and the straight, direct paths began to curve. Trails have an attraction effect, Helbing says. If they are close enough, you will take an existing path, but if they are too far away, you will still build a new path. In the end, you will have a continuous shortening of the trail system, until we get some sort of optimum solution.

The exact shape of a trail system depends on a variety of factors, including the number of pedestrians that use it and the popularity of the destinations. Terrain affects the system, too, although Helbing has so far modeled only a flat, grassy area. His model may soon undergo a real- world test. He is now consulting with Munich city planners about the design of a public park.
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