DECEPTIONS IN QUASI-CRYSTAL GROWTH

We discuss a new general phenomenon pertaining to tiling models of qua sicrystal growth. It is known that with Penrose tiles no (deterministi c) local matching rules exist which guarantee defect-free tiling for r egions of arbitrary large size. We prove that this property holds quit e generally: namely, that the emergence of defects in quasicrystal gro wth is unavoidable for all aperiodic tiling models in the plane with l ocal matching rules, and for many models in R(3) satisfying certain co nditions.