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2. Penrose tiling - Wikipedia

   en.wikipedia.org/wiki/Penrose_tiling

   The pattern represented by every finite patch of tiles in a Penrose tiling occurs infinitely many times throughout the tiling. They are quasicrystals: implemented as a physical structure a Penrose tiling will produce diffraction patterns with Bragg peaks and five-fold symmetry, revealing the repeated patterns and fixed orientations of its tiles ...

3. Truchet tiles - Wikipedia

   en.wikipedia.org/wiki/Truchet_tiles

   In information visualization and graphic design, Truchet tiles are square tiles decorated with patterns that are not rotationally symmetric. When placed in a square tiling of the plane, they can form varied patterns, and the orientation of each tile can be used to visualize information associated with the tile's position within the tiling. [1]

4. Girih tiles - Wikipedia

   en.wikipedia.org/wiki/Girih_tiles

   There is no text, but there is a grid pattern and color-coding used to highlight symmetries and distinguish three-dimensional projections. Drawings such as shown on this scroll would have served as pattern-books for the artisans who fabricated the tiles, and the shapes of the girih tiles dictated how they could be combined into large patterns.

5. Aperiodic tiling - Wikipedia

   en.wikipedia.org/wiki/Aperiodic_tiling

   Any translation must be smaller than some size of square, and so cannot leave any such tiling invariant. A portion of tiling by the Robinson tiles. 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.

6. List of aperiodic sets of tiles - Wikipedia

   en.wikipedia.org/.../List_of_aperiodic_sets_of_tiles

   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 ...

7. Tessellation - Wikipedia

   en.wikipedia.org/wiki/Tessellation

   Truchet tiles are square tiles decorated with patterns so they do not have rotational symmetry; in 1704, Sébastien Truchet used a square tile split into two triangles of contrasting colours. These can tile the plane either periodically or randomly. [46] [47] An einstein tile is a single shape that forces aperiodic tiling. The first such tile ...