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  2. Pythagorean tiling - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_tiling

    A Pythagorean tiling Street Musicians at the Door, Jacob Ochtervelt, 1665.As observed by Nelsen [1] the floor tiles in this painting are set in the Pythagorean tiling. A Pythagorean tiling or two squares tessellation is a tiling of a Euclidean plane by squares of two different sizes, in which each square touches four squares of the other size on its four sides.

  3. 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 ...

  4. Tilings and patterns - Wikipedia

    en.wikipedia.org/wiki/Tilings_and_patterns

    The last five chapters survey a variety of advanced topics in tiling theory: colored patterns and tilings, polygonal tilings, aperiodic tilings, Wang tiles, and tilings with unusual kinds of tiles. Each chapter open with an introduction to the topic, this is followed by the detailed material of the chapter, much previously unpublished, which is ...

  5. 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 ...

  6. 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.

  7. Girih tiles - Wikipedia

    en.wikipedia.org/wiki/Girih_tiles

    The girih are piece-wise straight lines that cross the boundaries of the tiles at the center of an edge at 54° (3π/10 radians) to the edge. Two intersecting girih cross each edge of a tile. Most tiles have a unique pattern of girih inside the tile that are continuous and follow the symmetry of the tile.