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Smallest aperiodic set of Wang tiles. No image: Decagonal Sponge tile: 1: E 2: 2002 [58] [59] Porous tile consisting of non-overlapping point sets. No image: Goodman-Strauss strongly aperiodic tiles: 85: H 2: 2005 [60] No image: Goodman-Strauss strongly aperiodic tiles: 26: H 2: 2005 [61] Böröczky hyperbolic tile: 1: H n: 1974 [62] [63] [61 ...
Berger later reduced his set to 104, and Hans Läuchli subsequently found an aperiodic set requiring only 40 Wang tiles. [10] A smaller set, of six aperiodic tiles (based on Wang tiles), was discovered by Raphael M. Robinson in 1971. [11]
A portion of tiling by Ammann's aperiodic A5 set of tiles, decorated with finite, local matching rules which force infinite, global structure, that of Amman–Beenker tiling. 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 in the 1970s, or ...
In geometry, an Ammann A1 tiling is a tiling from the 6 piece prototile set shown on the right. They were found in 1977 by Robert Ammann. [1] Ammann was inspired by the Robinsion tilings, which were found by Robinson in 1971. The A1 tiles are one of five sets of tiles discovered by Ammann and described in Tilings and patterns. [2]
More letters followed, and Ammann became a correspondent with many of the professional researchers. He discovered several new aperiodic tilings, each among the simplest known examples of aperiodic sets of tiles. He also showed how to generate tilings using lines in the plane as guides for lines marked on the tiles, now called "Ammann bars".
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See List of aperiodic sets of tiles for examples. Pages in category "Aperiodic tilings" The following 19 pages are in this category, out of 19 total.
This first such set, used by Berger in his proof of undecidability, required 20,426 Wang tiles. Berger later reduced his set to 104, and Hans Läuchli subsequently found an aperiodic set requiring only 40 Wang tiles. [9] The set of 13 tiles given in the illustration on the right is an aperiodic set published by Karel Culik, II, in 1996.