Hump pattern generation on ski slopes

Human activities may lead to pattern formation. Well known examples are human trail systems and the rather regular hump patterns on ski slopes. While the mathematical modelling has been advanced to a state of high sophistication with respect to trails, no attempt appears to have been made so far to model these fascinating arrays of humps. Here such a model is presented where skiers generate the humps and where the tracks of the skiers are modified by the humps in a nonlinear process. The model reproduces many of the observed features of hump fields. In particular, rather regular patterns can be generated. Regular patterns do not occur in a linear version of the model. The basic mechanism of hump pattern generation in the model is elucidated.