Binary and ternary quasicrystals have been successfully separated by means of quantum structural diagrams in the light of new experimental data, and new potential candidates for the quasicrystalline state are presented. A general and simple classification of alloy systems, consistent with the experimental data, is proposed, which allows predictions of any type of binary and ternary quasicrystals. Quantum coordinates are analyzed and interpreted, and suggestions are given for an improvement of the present method.