The motivation for this work was to qualitatively describe the distribution of Au nanoparticles on the surface of a semiconductor. We discuss suitable mathematical characteristics which allow the uniform distribution to be distinguished from the distribution a ected by any physical phenomenon, i.e. by the repulsive force between electrically charged particles or by the influence of properties of the surface. We identify Voronoi decomposition and a statistical analysis of Voronoi cell properties as a suitable tool for this purpose.