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In this study, we analyze periodic crystal lattices characterized by spatial Hausdorff dimensions. We demonstrate the emergence of quasiperiodic wave functions for a very large unit cell where the crystals may correspond to quasicrystals. A number of additional features related to doping and the statistical physics of electrons and holes in semiconductors are observed. In particular, we demonstrate that the intrinsic carrier concentrations are improved for silicon and gallium arsenide. Additional properties are also identified and analyzed.