Such collective pathbreaking is an example of a human social phenomenon that involves some form of self-organization. Recently, a team of researchers developed a mathematical model of pedestrian motion to explore the evolution of trails in urban green spaces. The paths pedestrians forge can be quite complex. In other words, the trails generated by walkers don't always reflect the most direct routes between entry and exit points.
Several factors come into play.
People usually want to take the most direct route, but they also prefer to walk on worn, existing trails rather than tramp over rougher terrain to blaze new ones. Moreover, the nearer a segment of an existing trail is to a walker, the greater its attraction. Helbing and his colleagues built these assumptions about human behavior into a set of equations that describes how the routes taken by pedestrians would change as time passes. Because not every route is used by the same number of walkers, some paths typically start to become more pronounced than others. If attractiveness is low, a direct-route system develops.