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We have seen how a plane can be covered by a periodic tiling of polygons or a periodic tessellation of animals and other such recognizable forms, but can a plane be covered with no gaps and no overlaps without being periodic? Sir Roger Penrose sought to answer this question, and he succeeded. Penrose, a math professor at the Oxford University in England, began exploring tilings as a student at Cambridge University. After tiring of periodic coverings, he searched for aperiodic or quasiperiodic tilings. Through years of experimentation and reams of paper, Penrose finally found a solution--a quasiperiodic tiling of the plane with only 2 figures. All of this may seem like a joke, to dedicate years of research to pretty pictures, but an application was found by a French company, in the quasiperiodic crystal coating on frying pans! A penrose tiling is an example of quasiperiodic tilings of the plane. A tiling of a plane is a way in which the entire space of the plane can be covered with a few shapes repeatedly in such a way that the shapes do not overlap. A periodic tiling is one in which the pattern of shapes repeats. For such a tiling to be quasiperiodic, it is not periodic, but identical copies of small sections of the tiling can be found elsewhere on the plane.
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