We consider the pattern-formation dynamics of a two-dimensional (2D) nonlinear evolution equation that includes the effects of instability, dissipation, and dispersion. We construct 2D stationary solitary pulse solutions of this equation, and we develop a coherent structures theory that describes the weak interaction of these pulses. We show that in the strongly dispersive case, 2D pulses organize themselves into V shapes. Our theoretical findings are in good agreement with time-dependent computations of the fully nonlinear system.