Millimeter-sized gel particles loaded with camphor and floating at the interface between water and air generate convective flows around them. These flows give rise to repulsive interparticle interactions, and mediate dynamic self-assembly of nonequilibrium particle formations. When the numbers of particles, N, are small, particle motions are uncorrelated. When, however, N exceeds a threshold value, particles organize into ordered lattices. The nature of hydrodynamic forces underlying these effects and the dynamics of the self-assembling system are modeled numerically using Navier-Stokes equations as well as analytically using scaling arguments.