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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. [3] The tilings obtained from an aperiodic set of tiles are often called aperiodic tilings, though strictly speaking it is the tiles themselves that are ...
Robinson proves these tiles must form this structure inductively; in effect, the tiles must form blocks which themselves fit together as larger versions of the original tiles, and so on. This idea – of finding sets of tiles that can only admit hierarchical structures – has been used in the construction of most known aperiodic sets of tiles ...
Concrete paver blocks laid in a circular pattern Concrete paver blocks in a rectangular pattern. A paver is a paving stone, sett, tile, [1] brick [2] or brick-like piece of concrete commonly used as exterior flooring. They are generally placed on top of a foundation which is made of layers of compacted stone and sand.
An 1861 illustration of Marseilles tile. Another popular early interlocking tile pattern was the Marseilles design invented by the Martin Brothers in Marseilles, France as early as the 1860s. The Marseilles tile pattern is distinguished from other designs by its diagonal notches on its side rebate, as well as the teardrop-shaped end of its ...
The Socolar–Taylor tile was proposed in 2010 as a solution to the einstein problem, but this tile is not a connected set. In 1996, Petra Gummelt constructed a decorated decagonal tile and showed that when two kinds of overlaps between pairs of tiles are allowed, the tiles can cover the plane, but only non-periodically. [6]
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