Recent years have witnessed considerable interest in simulating the dynamics of complex many-body systems by well-controlled cold atom model systems. Among others, magnetic ordering phenomena and supersolids draw a lot of attention. I will discuss an unconventional approach to light mediated atomic interactions using diffraction of light. Diffractive propagation of periodically modulated light fields leads to an exchange between phase and amplitude modulated planes (Talbot effect) which can be used to couple atomic degrees of freedom. In a feedback scheme this can lead to the spontaneous formation of coupled lattices in the light field and the atomic degrees of freedom. In the experiment a cold cloud of Rb atoms placed near a retro-reflecting mirror is driven by a detuned pump laser. Via optomechanical nonlinearities, the spontaneous emergence of density patterns is obtained and a possible extension to supersolids is discussed.  Via optical pumping nonlinearities magnetic ordering of anti-ferromagnetic and ferromagnetic structures is obtained and a connection to the transverse (quantum) Ising model exploited. Finally, novel spontaneous structures in quantum coherences are demonstrated, which corresponding to rotations of magnetic quadrupole structures.