A two dimensional aperiodic dense tiling

Using the modified Voronoï construction of Olamy and Alexander for the acceptance domain in perpendicular space of an aperiodic crystal, it is possible to build in a systematic way a dense aperiodic tiling, i.e. made of circles (in d = 2) or of sphere (in d = 3) which are in contact. We compare the results of this method (density and inflation properties) employed for a d = 2 tiling to those of Henley's method. We reach a higher density. Furthermore, our tiling shows quite clearly a very dense « backbone » surrounded by a « sea » of less well packed circles. We believe that this « frustration » effect is typical of locally disordered systems. Localized phason strains and other local excitations primarily affect the « sea », and might be related to typical anomalous transport properties of disordered systems, either in the supercooled state (phasons) or at low temperatures where two-level systems are acting (phasons and other local excitations).