  Strong, long-range interactions present a unique challenge for the
theoretical investigation of quantum many-body lattice models, due to the
generation of large numbers of competing states at low energy. Here, we
investigate a class of extended bosonic Hubbard models with off-site terms
interpolating between short and infinite range, thus allowing for an exact
numerical solution for all interaction strengths. We predict a novel type of
stripe crystal at strong coupling. Most interestingly, for intermediate
interaction strengths we demonstrate that the stripes can turn superfluid, thus
leading to a self-assembled array of quasi-one-dimensional superfluids. These
bosonic superstripes turn into an isotropic supersolid with decreasing the
interaction strength. The mechanism for stripe formation is based on cluster
self-assembling in the corresponding classical ground state, reminiscent of
classical soft-matter models of polymers, different from recently proposed
mechanisms for cold gases of alkali or dipolar magnetic atoms.
