  Understanding the mechanisms behind human mobility patterns is crucial to
improve our ability to optimize and predict traffic flows. Two representative
mobility models, i.e., radiation and gravity models, have been extensively
compared to each other against various empirical data sets, while their
fundamental relation is far from being fully understood. In order to study such
a relation, we first model the heterogeneous population landscape by generating
a fractal geometry of sites and then by assigning to each site a population
independently drawn from a power-law distribution. Then the radiation model on
this population landscape, which we call the radiation-on-landscape (RoL)
model, is compared to the gravity model to derive the distance exponent in the
gravity model in terms of the properties of the population landscape, which is
confirmed by the numerical simulations. Consequently, we provide a possible
explanation for the origin of the distance exponent in terms of the properties
of the heterogeneous population landscape, enabling us to better understand
mobility patterns constrained by the travel distance.
