Abstract
Entropically stabilized quasicrystals are usually modeled as equilibrium ensembles of random tilings. In several models, such as the two-dimensional square-triangle tiling studied here, the corresponding kinetics may be very slow because a large number of tiles must be rearranged at each step through the ensemble. Here we consider a simple growth model that generates a single element of the square-triangle tiling ensemble. Even though tile rearrangements occur only at the growth surface, in the limit of slow growth one obtains a structure that is representative of the equilibrium ensemble.
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