Non-Repetitive Tilings

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Non-Repetitive Tilings
In 1906 Axel Thue showed how to construct an infinite non-repetitive (or squarefree) word on an alphabet of size 3. Since then this result has been rediscovered many times and extended in many ways. We present a two-dimensional version of this result. We show how to construct a rectangular tiling of the plane using 5 symbols which has the property that lines of tiles which are horizontal, vertical or have slope +1 or -1 contain no repetitions. As part of the construction we introduce a new type of word, one that is non-repetitive up to mod k, which is of interest in itself. We also indicate how our results might be extended to higher dimensions.
James D. Currie, Jamie Simpson
Added 17 Dec 2010
Updated 17 Dec 2010
Type Journal
Year 2002
Authors James D. Currie, Jamie Simpson
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