^{k}(T_{i})} is called a substitution tiling (for the tile substitution ( Q , σ ) {\displaystyle (Q,\sigma )} ). Pinwheel tiling Photographic mosaic Tübingen...

Penrose tiling is an example of an aperiodic tiling. Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and a tiling is...

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...

In geometry, an Ammann–Beenker tiling is a nonperiodic tiling which can be generated either by an aperiodic set of prototiles as done by Robert Ammann...

wallpaper groups. A tiling that lacks a repeating pattern is called "non-periodic". An aperiodic tiling uses a small set of tile shapes that cannot form...

chair tiling (or L tiling) is a nonperiodic substitution tiling created from L-tromino prototiles. These prototiles are examples of rep-tiles and so...

The Voderberg tiling is a mathematical spiral tiling, invented in 1936 by mathematician Heinz Voderberg [de] (1911–1945). Karl August Reinhardt asked the...

The Tübingen triangle is a form of substitution tiling. It is, apart from the Penrose rhomb tilings and their variations, a classical candidate to model...

of hyperbolic manifolds. Substitution tilings are a well-studied type of subdivision rule. A subdivision rule takes a tiling of the plane by polygons...

if a finite set of Wang tiles can tile the plane, then there also exists a periodic tiling, which, mathematically, is a tiling that is invariant under...

stills are much smaller. ASCII art Impressionist mosaics Micrography Substitution tiling Wikimedia logo mosaic Cartwright (2007) p.102 quote: Photographic...

problem asked for a single polyhedron tiling Euclidean 3-space, such that no tiling by it is isohedral (an anisohedral tile). The problem as stated was solved...

group. Joker substitution A joker may not be retrieved before the initial meld. A joker can be retrieved from a set by replacing it with a tile of the same...

periodic tiling. Figure 5 shows the first two stages of inflation of an order 4 set leading to a non-periodic tiling. Besides self-tiling tile sets, which...

shape necessarily forms the prototile for a tiling of the plane, in many cases an aperiodic tiling. A rep-tile dissection using different sizes of the original...

In geometry, a binary tiling (sometimes called a Böröczky tiling) is a tiling of the hyperbolic plane, resembling a quadtree over the Poincaré half-plane...

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...

cut-and-project method for constructing aperiodic tilings. Therefore, the vertices of the pinwheel tiling and Penrose tiling are not Danzer sets. A strengthened variation...

The Toynbee tiles, also called Toynbee plaques, are messages of unknown origin found embedded in asphalt of streets in about two dozen major cities in...

same authors demonstrated elsewhere that certain one-dimensional substitution tilings can either be hyperuniform or anti-hyperuniform. Cheney Lin, Steinhardt...

American mathematician who works in convex geometry, especially aperiodic tiling. He retired from the faculty of the University of Arkansas and currently...

Laves tilings are unique except for the square tiling (1 degree of freedom), barn pentagonal tiling (1 degree of freedom), and hexagonal tiling (2 degrees...

(which in turn depends on both the degree of substitution of the methoxy group and the molar substitution). That is, the higher the concentration of the...

mathematics, the Rauzy fractal is a fractal set associated with the Tribonacci substitution s ( 1 ) = 12 ,   s ( 2 ) = 13 ,   s ( 3 ) = 1 . {\displaystyle s(1)=12...

quaquaversal tiling is a nonperiodic tiling of Euclidean 3-space introduced by John Conway and Charles Radin. It is analogous to the pinwheel tiling in 2 dimensions...

Drawback on Beer exported from Great Britain; and to the Duty on Draining Tiles. (Repealed by Statute Law Revision Act 1861 (24 & 25 Vict. c. 101)) Duties...

Scrabble in different languages have differing letter distributions of the tiles, because the frequency of each letter of the alphabet is different for every...

and preserving of Pilchards and Scads; and for allowing certain Draining Tiles to be made free of Duty. (Repealed by Statute Law Revision Act 1861 (24...

anagram of another but for the substitution of a single letter. The term has its origin in competitive Scrabble, where a blank tile on a player's rack may be...

mah-JONG; also transliterated as mah jongg, mah-jongg, and mahjongg) is a tile-based game that was developed in the 19th century in China and has spread...