Aperiodic tiles
نویسندگان
چکیده
منابع مشابه
An aperiodic tiles machine
The results we introduce in this work lead to get an algorithm which produces aperiodic sets of tiles using Voronoi diagrams. This algorithm runs in optimal worst-case time O(n log n). Since a wide range of new examples can be obtained, it could shed some new light on non-periodic tilings. These examples are locally isomorphic and exhibit the 5-fold symmetry which appears in Penrose tilings and...
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A new aperiodic tile set containing 11 Wang tiles on 4 colors is presented. This tile set is minimal in the sense that no Wang set with less than 11 tiles is aperiodic, and no Wang set with less than 4 colors is aperiodic. Wang tiles are square tiles with colored edges. A tiling of the plane by Wang tiles consists in putting a Wang tile in each cell of the grid Z so that contiguous edges share ...
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A finite subset A of integers tiles the discrete line Z if the integers can be written as a disjoint union of translates of A. In some cases, necessary and sufficient conditions for A to tile the integers are known. We extend this result to a large class of nonperiodic tilings and give a new formulation of the Coven-Meyerowitz reciprocity conjecture which is equivalent to the Flugede conjecture...
متن کاملA Small Aperiodic Set of Tiles
We give a simple set of two tiles that can only tile aperiodically | that is no tiling with these tiles is invariant under any in nite cyclic group of isometries. Although general constructions for producing aperiodic sets of tiles are nally appearing, simple aperiodic sets are fairly rare. This set is among the smallest sets ever found. A tiling is non-periodic if there is no in nite cyclic gr...
متن کاملA Note on Aperiodic Ammann Tiles
We present a variant of Ammann tiles consisting of two similar rectilinear hexagons with edge subdivision, which can tile the plane but only in non periodic ways. A special matching rule, ghost marking, plays a key role in the proof. We shall show that the set of tiles in Figure 1 is aperiodic, that is, it tiles the plane but only in non periodic way.
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1992
ISSN: 0179-5376,1432-0444
DOI: 10.1007/bf02293033