The Empire Problem in Penrose Tilings
نویسندگان
چکیده
Nonperiodic tilings of the plane exhibit no translational symmetry. Penrose tilings are a remarkable class of nonperiodic tilings for which the set of prototiles consists of just two shapes. The pentagrid method, introduced by N.G. de Bruijn, allows us to generate Penrose tilings by taking a slice of the integer lattice in five-dimensional space. The empire problem asks: Given a subset of a Penrose tiling, what tiles appear in all tilings that include that subset? We present a new approach to the empire problem that uses the pentagrid method to identify elements of the empire.
منابع مشابه
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