We consider a "cluster picture" to explain the structure and formation of quasicrystals. Quasicrystal ordering is attributed to a small set of low-energy atomic clusters which determine the state of minimum free energy. The nature of the ground state as T→0, depending upon the clusters and cluster energies, ranges from energetically stable and unique (as in Penrose tilings), to entropically stable and degenerate (as in random tilings).
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Jeong et al. (1994) studied this question.
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