Random cluster covering model

The unit-cluster approach describing quasicrystalline structures by a single unit with possible ‘fat’ overlaps has mainly been worked out for the ideal case of perfect order. A general concept for corresponding random covering ensembles is still missing. As a natural framework, we introduce an ‘overlap-version’ of the well-known random tiling model in terms of relaxed cluster matching rules. We illustrate our method by a relaxed decagon determining a covering ensemble with positive configurational entropy. We characterize this coverings using equivalent underlying Penrose-type tilings, which form Hexagon-Boat-Star (HBS)-supertilings. Given an HBS-supertiling, we describe the effect of so-called bow-tie flips on corresponding decagon coverings.