We have analyzed the fine structure revealed by scanning tunneling microscopy for a flat (within 0.8 Å) fivefold surface of i-Al-Pd-Mn. Even though features in the image appear to be arranged randomly, self-similar features are separated by distinct distances. The distribution of such distances is compatible with the separations between pseudo-Mackay icosahedra tangent to the topmost layer, and with separations between other cluster-based units. We propose that the fine structure is due to electronic structure imposed by the clusters.