However, because frequently used trails become more comfortable, the different routes begin to blend together in such a way that the overall length of the trail system decreases. The evolution of a path system in a square park. It provides a suitable compromise between minimal construction costs and maximal comfort. Moreover, it balances the relative detours of all walkers. Self-organization is evident in a wide variety of human social phenomena, from the evolution of cooperation to the development of traffic patterns and the growth of settlements.
Mathematical models help elucidate the factors that influence such processes.
These models naturally extend to problems where the goal is to optimize, or design 'best' paths, as is characteristic of many planning problems where the task is to design high-quality urban environments. The next MathLand article will appear on September 8. Copyright 1997 by Ivars Peterson. Predicting where we walk. Helbing, Dirk, Joachim Keltsch, and Peter Molnar.