This Thesis reports on a realization of self-organized magnetization patterns in a cloud of cold atoms driven far from equilibrium by a pump laser beam. The experiments are performed in the single mirror feedback configuration, where transverse ordering occurs due to amplification of fluctuations in the atomic medium at critical lengthscales via the optical non-linearity and the Talbot effect. For a linearly polarized pump beam a generation of modulated light with orthogonal polarization is seen to occur, signaling the presence of a polarization instability. Imaging of the refractive index modulations at the end of the cloud reveals complementary regions of the two orthogonal circularly polarized components of the imaged light, which is related to the ordering of atomic spins. A detailed investigation of dependence of pattern properties on the direction and strength of the applied B-fields is presented. In addition to this, a theoretical model describing the dynamics and coupling of atomic magnetic moments and the laser light in the relevant parameter regime is developed and shown to provide good agreement with results of the experiment. Non-equilibrium self-organization of atomic degrees of freedom in cold gases can in some cases be mapped onto phase transitions in condensed matter systems. In this respect, the single mirror feedback configuration is particularly interesting as it provides a simple arrangement where ordering breaks the continuous translational and rotational symmetries of the initial system.