  We model and study the patterns created through the interaction of
collectively moving self-propelled particles (SPPs) and elastically tethered
obstacles. Simulations of an individual-based model reveal at least three
distinct large-scale patterns: travelling bands, trails and moving clusters.
This motivates the derivation of a macroscopic partial differential equations
model for the interactions between the self-propelled particles and the
obstacles, for which we assume large tether stiffness. The result is a coupled
system of non-linear, non-local partial differential equations. Linear
stability analysis shows that patterning is expected if the interactions are
strong enough and allows for the predictions of pattern size from model
parameters. The macroscopic equations reveal that the obstacle interactions
induce short-ranged SPP aggregation, irrespective of whether obstacles and SPPs
are attractive or repulsive.
