Dissection Methods for Aperiodic Tilings: From Medieval Islamic Architecture to Quasicrystals
Tiling Theory studies how one might cover the plane with various shapes. Aperiodic tilings are nonperiodic patterns that cannot be rearranged to form periodic tilings. Examples of this aperiodic symmetry are found in a variety of places from medieval Islamic architecture to 20th Century Penrose tile...
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2014
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| Online Access: | http://hdl.handle.net/20.500.12458/247 |
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| Summary: | Tiling Theory studies how one might cover the plane with various shapes. Aperiodic tilings are nonperiodic patterns that cannot be rearranged to form periodic tilings. Examples of this aperiodic symmetry are found in a variety of places from medieval Islamic architecture to 20th Century Penrose tilesand also characterize newly discovered quasicrystals. Construction techniques, other than the usual methods for producing periodic tilings, are required to successfully generate these aperiodic patterns. Historic manuscripts like the Topkapi Scrollprovide insight into how these intricate designs might have been produced in the past. This paper focuses on the discoveries of aperiodic symmetry with a brief historical perspective and examines the mathematics of dissection and iterative techniques for generating some well-known patterns. |
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