A microgravity protein crystallization experiment is described in which the existence of a supersaturation wave traveling across a diffusion-reaction system is experimentally demonstrated for the first time. The self-organized dynamics of the experimental setup were used to implement a crystallization technique able to search automatically through the crystallization parameter space for optimum nucleation and growth conditions. The crystals obtained by this automatic optimization produced the highest quality X-ray diffraction data ever collected from the model protein used in the experiment.