  Scaling mobility patterns have been widely observed for animals. In this
paper, we propose a deterministic walk model to understand the scaling mobility
patterns, where walkers take the least-action walks on a lattice landscape and
prey. Scaling laws in the displacement distribution emerge when the amount of
prey resource approaches the critical point. Around the critical point, our
model generates ordered collective movements of walkers with a quasi-periodic
synchronization of walkers' directions. These results indicate that the
co-evolution of walkers' least-action behavior and the landscape could be a
potential origin of not only the individual scaling mobility patterns, but also
the flocks of animals. Our findings provide a bridge to connect the individual
scaling mobility patterns and the ordered collective movements.
