Aperiodic tiling (nonfiction): Difference between revisions
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An aperiodic tiling is a non-periodic tiling with the additional property that it does not contain arbitrarily large periodic regions or patches. A set of tile-types (or prototiles) is aperiodic if copies of these tiles can form only non-periodic tilings. | An '''aperiodic tiling''' is a non-periodic [[Tessellation (nonfiction)|tiling]] with the additional property that it does not contain arbitrarily large periodic regions or patches. A set of tile-types (or [[Prototiles (nonfiction)|prototiles]]) is [[Aperiodic set of prototiles (nonfiction)|aperiodic]] if copies of these tiles can form only non-periodic tilings. | ||
The Penrose tilings are a well-known example of aperiodic tilings. | The Penrose tilings are a well-known example of aperiodic tilings. | ||
Aperiodic tilings serve as mathematical models for quasicrystals, physical solids that were discovered in 1982 by Dan Shechtman | In March 2023, four researchers, [[Chaim Goodman-Strauss (nonfiction)|Chaim Goodman-Strauss]], [[David Smith (nonfiction)|David Smith]], [[Joseph Samuel Myers (nonfiction)|Joseph Samuel Myers]], and [[Craig S. Kaplan (nonfiction)|Craig S. Kaplan]], announced the discovery of an aperiodic monotile. | ||
Aperiodic tilings serve as mathematical models for [[Quasicrystal (nonfiction)|quasicrystals]], physical solids that were discovered in 1982 by [[Dan Shechtman (nonfiction)|Dan Shechtman]] who subsequently won the Nobel prize in 2011. However, the specific local structure of these materials is still poorly understood. | |||
Several methods for constructing aperiodic tilings are known. | Several methods for constructing aperiodic tilings are known. | ||
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== Nonfiction cross-reference == | == Nonfiction cross-reference == | ||
* [[Aperiodic set of prototiles (nonfiction)]] | |||
* [[Gnomon Chronicles (nonfiction)]] | * [[Gnomon Chronicles (nonfiction)]] | ||
* [[Prototiles (nonfiction)]] | |||
* [[Quasicrystal (nonfiction)]] | |||
* [[Tessellation (nonfiction) | |||
== External links == | == External links == | ||
Revision as of 04:48, 22 March 2023
An aperiodic tiling is a non-periodic tiling with the additional property that it does not contain arbitrarily large periodic regions or patches. A set of tile-types (or prototiles) is aperiodic if copies of these tiles can form only non-periodic tilings.
The Penrose tilings are a well-known example of aperiodic tilings.
In March 2023, four researchers, Chaim Goodman-Strauss, David Smith, Joseph Samuel Myers, and Craig S. Kaplan, announced the discovery of an aperiodic monotile.
Aperiodic tilings serve as mathematical models for quasicrystals, physical solids that were discovered in 1982 by Dan Shechtman who subsequently won the Nobel prize in 2011. However, the specific local structure of these materials is still poorly understood.
Several methods for constructing aperiodic tilings are known.
In the News
Fiction cross-reference
Nonfiction cross-reference
- Aperiodic set of prototiles (nonfiction)
- Gnomon Chronicles (nonfiction)
- Prototiles (nonfiction)
- Quasicrystal (nonfiction)
- [[Tessellation (nonfiction)
External links
- Aperiodic tiling @ Wikipedia
- An aperiodic monotile @ Wikipedia