منابع مشابه
An aperiodic set of 11 Wang tiles
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 ...
متن کاملAn aperiodic set of 13 Wang tiles
A new aperiodic tile set containing only 13 tiles over 5 colors is presented. Its construction is based on a technique recently developed by J. Kari. The tilings simulate behavior of sequential machines that multiply real numbers in balanced representations by real constants.
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 کاملAn Aperiodic Set of Wang Cubes
We introduce Wang cubes with colored faces that are a generalization of Wang tiles with colored edges. We show that there exists an aperiodic set of 21 Wang cubes, that is, a set for which there exists a tiling of the whole space with matching unit cubes but there exists no periodic tiling. We use the aperiodic set of 13 Wang tiles recently obtained by the rst author using the new method develo...
متن کاملA Strongly Aperiodic Set of Tiles in the Hyperbolic Plane
We construct the first known example of a strongly aperiodic set of tiles in the hyperbolic plane. Such a set of tiles does admit a tiling, but admits no tiling with an infinite cyclic symmetry. This can also be regarded as a “regular production system” [5] that does admit bi-infinite orbits, but admits no periodic orbits.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1996
ISSN: 0012-365X
DOI: 10.1016/0012-365x(95)00120-l