We present results of experiments of diffraction by an amplitude screen, made of randomly distributed circular holes. By careful selection of the experimental parameters we obtain an intensity pattern strongly connected to the Voronoi diagram (VD) generated by the centers of the apertures. With the help of simulations we give a description of the observed phenomenon and elucidate the optimal parameters for its observation. Finally, we also suggest how it can be used for a fast, all-optical generation of VDs.