In this Letter, we use a nonequilibrium statistical theory, the stochastic structural stability theory (SSST), to show that an extended version of this theory can make predictions for the formation of nonzonal as well as zonal structures (lattice and stripe patterns) in forced homogeneous turbulence on a barotropic β plane. Comparison of the theory with nonlinear simulations demonstrates that SSST predicts the parameter values for the emergence of coherent structures and their characteristics (scale, amplitude, phase speed) as they emerge and at finite amplitude. It is shown that nonzonal structures (lattice states or zonons) emerge at lower energy input rates of the stirring compared to zonal flows (stripe states) and their emergence affects the dynamics of jet formation.