Although coherent light is usually required for the self-organization of regular spatial patterns from optical beams, we show that peculiar light-matter interaction can break this evidence. In the traditional method of recording laser-induced periodic surface structures, a light intensity distribution is produced at the surface of a polymer film by an interference between two coherent optical beams. We report on the self-organization followed by propagation of a surface relief pattern. It is induced in a polymer film by using a low-power and small-size coherent beam assisted by a high-power and large-size incoherent and unpolarized beam. We demonstrate that we can obtain large size and well-organized patterns starting from a dissipative interaction. Our experiments open new directions to improving optical processing systems.