  We stir vortices into a trapped quasi two-dimensional atomic Bose-Einstein
condensate by moving three laser stirrers. We apply stirring protocols
introduced by Boyland et. al. (2000) that efficiently build in topological
chaos in classical fluids and are classified as Pseudo-Anosov stirring
protocols. These are compared to their inefficient mixing counterparts,
finite-order stirring protocols. We investigate if inefficient stirring
protocols result in a more clustered distribution of vortices. The efficiency
with which vortices are 'mixed' or distributed in a condensate is important for
investigating dynamics of continuously forced quantum turbulence and the
existence of the inverse cascade in turbulent two-dimensional superfluids.
