list of aperiodic sets of tiles

    List of aperiodic sets of tiles GudangMovies21 Rebahinxxi LK21

    In geometry, a tiling is a partition of the plane (or any other geometric setting) into closed sets (called tiles), without gaps or overlaps (other than the boundaries of the tiles). A tiling is considered periodic if there exist translations in two independent directions which map the tiling onto itself. Such a tiling is composed of a single fundamental unit or primitive cell which repeats endlessly and regularly in two independent directions. An example of such a tiling is shown in the adjacent diagram (see the image description for more information). A tiling that cannot be constructed from a single primitive cell is called nonperiodic. If a given set of tiles allows only nonperiodic tilings, then this set of tiles is called aperiodic. The tilings obtained from an aperiodic set of tiles are often called aperiodic tilings, though strictly speaking it is the tiles themselves that are aperiodic. (The tiling itself is said to be "nonperiodic".)
    The first table explains the abbreviations used in the second table. The second table contains all known aperiodic sets of tiles and gives some additional basic information about each set. This list of tiles is still incomplete.


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    External links


    Stephens P. W., Goldman A. I. The Structure of Quasicrystals
    Levine D., Steinhardt P. J. Quasicrystals I Definition and structure
    Tilings Encyclopedia

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List of aperiodic sets of tiles - Wikipedia

48 rows · The first table explains the abbreviations used in the second table. The second table contains all known aperiodic sets of tiles and gives some additional basic information about each set. This list of tiles is still incomplete.

Aperiodic set of prototiles - Wikipedia

A set of prototiles is aperiodic if copies of the prototiles can be assembled to create tilings, such that all possible tessellation patterns are non-periodic. The aperiodicity referred to is a property of the particular set of prototiles; the various resulting tilings themselves are just non-periodic. A given set of tiles, in the Euclidean plane or some other geometric setting, ad…

List of aperiodic sets of tiles - Infogalactic: the planetary …

The second table contains all known aperiodic sets of tiles and gives some additional basic information about each set. This list of tiles is still incomplete. Contents

Lots of aperiodic sets of tiles - ScienceDirect

Nov 1, 2018 · Through readily generalized, robust techniques for controlling hierarchical structure, we increase the catalogue of explicit constructions of aperiodic sets of tiles hundreds-fold, in …

Lots of aperiodic sets of tiles - University of Arkansas

An aperiodic set of tiles is one that may be used to tile the plane, but only non- periodically — a form of complex global geometric structure arising through locally checkable, constant-time …

Aperiodic Tiling | by tjipke hibma.

The above and many other substitution tilings are depicted in the aperiodic tilings encyclopedia by E.O.Harriss and D. Frettlöh. Other useful links are the wikipedia page on aperiodic tilings and a list of aperiodic sets of tiles.

“Lots” of Aperiodic Sets of Tiles – Chaim Goodman …

Lots of Aperiodic Sets of Tiles gives intructions for producing more than 25,380 different aperiodic sets of tiles, taken in lots, from a base set of 211 tiles. These tiles allow different hierarchical structures, that are each restrictions from a …

Aperiodic Tiling -- from Wolfram MathWorld

An aperiodic tiling is a non-periodic tiling in which arbitrarily large periodic patches do not occur. A set of tiles is said to be aperiodic if they can form only non-periodic tilings. The most widely known examples of aperiodic tilings are those …

About: List of aperiodic sets of tiles - DBpedia Association

If a given set of tiles allows only nonperiodic tilings, then this set of tiles is called aperiodic. The tilings obtained from an aperiodic set of tiles are often called aperiodic tilings, though strictly …

APERIODIC TILINGS - Cornell University

One well-known set of six aperiodic prototiles was discovered by Robinson in 1971. But the most famous example of aperiodic tilings are known as Penrose tilings, discovered by Roger Penrose in the 1970s, and have only two …