The results of studies of samples containing ZnSe quantum dots with a density corresponding to or considerably higher than the exciton percolation threshold, at which quantum dots form conglomerates, are reported. Excitonic emission from a percolation cluster of bound quantum dots as a fractal object is observed for the first time. Analysis of the structure of the photoluminescence spectra shows that the spectra are determined by the contribution of exciton states that belong to different structural elements of the perco lation cluster, specifically, to the skeleton (backbone), dangling (dead) ends, and internal hollow spaces. A qualitative model is proposed to interpret the dependence of the exciton energy in these structural elements on the concentration of quantum dots in the material.