Although pedestrians have individual preferences, aims, and destinations, t
he dynamics of pedestrian crowds is surprisingly predictable. Pedestrians c
an move freely only at small pedestrian densities. Otherwise their motion i
s affected by repulsive interactions with other pedestrians, giving rise to
self-organization phenomena. Examples of the resulting patterns of motion
are separate lanes of uniform walking direction in crowds of oppositely mov
ing pedestrians or oscillations of the passing direction at bottlenecks. If
pedestrians leave footprints on deformable ground (for example, in green s
paces such as public parks) this additionally causes attractive interaction
s which are mediated by modifications of their environment. In such cases,
systems of pedestrian trails will evolve over time. The corresponding compu
ter simulations are a valuable tool for developing optimized pedestrian fac
ilities and way systems.