Quantum diagrams and the prediction of new ternary quasicrystals

We use the quantum-diagram technique to identify the chemical factors which favor quasicrystal formation. Expressed diagrammatically, these factors provide severe constraints on compositions at which quasicrystals or high-order rational approximants are likely to form. We outline several computerized search strategies which utilize the diagrammatic conditions to identify compositions for experimental investigation, and give examples of typical results.