  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
animal behavior. A comparison with empirical material shows a good agreement
between model and reality.
  Our trail formation model includes an equation of motion, an equation for
environmental changes, and an orientation relation. It contains some model
functions, which are specified according to the characteristics of the
considered animals or pedestrians. Not only the kind of environmental changes
differs: 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.
