ABSTRACT
In 1952, Turing established the theoretical possibility that stationary spatial patterns could organize in an initially homogeneous reaction-diffusion system. That pioneering work has generated many theoretical studies on the role of diffusion in the stability of steady states. Turing instability to steady cellular patterns requires the diffusion coefficients of the different chemical species to be significantly different, which can occur in activator-inhibitor competition. Pattern formation in optics is a different process from pattern formation in chemistry. If the material medium is rather 'broadband', in frequency as well as in wavenumber, it just provides a flat gain and patterns are shaped by the boundary conditions applied to the wave equation. The oscillator yields field patterns varying in time. Since the proposal of Schawlow and Townes, coherent optical oscillators have been considered as discrete physical systems where only one mode, or a few at most, can survive.
