  Strongly interacting systems of dipolar bosons in three dimensions confined
by harmonic traps are analyzed using the exact Path Integral Ground State Monte
Carlo method. By adding a repulsive two-body potential, we find a narrow window
of interaction parameters leading to stable ground- state configurations of
droplets in a crystalline arrangement. We find that this effect is entirely due
to the interaction present in the Hamiltonian without resorting to additional
stabilizing mechanisms or specific three-body forces. We analyze the number of
droplets formed in terms of the Hamiltonian parameters, relate them to the
corresponding s-wave scattering length, and discuss a simple scaling model for
the density profiles. Our results are in qualitative agreement with recent
experiments showing a quantum Rosensweig instability in trapped Dy atoms.
