Swarming is a unique manifestation of dynamic self-assembly (DySA) 1-3 in which self-propelling objects not only organize into dissipative structures but also perform collective motions. While swarms are ubiquitous in biological systems (bacteria 4,5 , fish 6 , ants 7,8 , etc.), the examples of artificial collective movers are largely limited to complex robotics systems 9,10. The chief difficulty in making simple components swarm is to engineer interactions that would propel these components while maintaining them at a distance from and in proper orientation with respect to one another. Here, we describe a hydrodynamic system in which swarming is mediated by asymmetric convection "rolls" around small, millimeter-sized gel particles floating at a water/air interface and emitting surface active chemicals. Remarkably, for thin water layers, these convective flows give rise to interparticle attractions that bring the particles close to-but not into contact-with one another. In collections of identical particles, this previously undescribed hydrodynamic interaction leads to the formation of high-symmetry, open-lattice, stationary structures. In contrast, particles of different shapes assemble into lower-symmetry, dynamic formations