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A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art , especially in textiles , tiles , and wallpaper .
The smallest wallpaper rectangle that can be tiled to form the whole pattern is known as the pattern repeat. Wallpaper printing techniques include surface printing , rotogravure , screen-printing , rotary printing press , and digital printing .
Examples of frieze patterns. In mathematics, a frieze or frieze pattern is a two-dimensional design that repeats in one direction. The term is derived from architecture and decorative arts, where such repeating patterns are often used. (See frieze.) Frieze patterns can be classified into seven types according to their symmetries.
Wallpaper group: A wallpaper group is a mathematical concept used to classify repetitive designs on two-dimensional surfaces, such as floors and walls, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art. The mathematical study of such patterns reveals that exactly 17 different types of ...
In Conway's Game of Life, a commonly occurring pattern called the glider is so named because it repeats its configuration of cells, shifted by a glide reflection, after two steps of the automaton. After four steps and two glide reflections, the pattern returns to its original orientation, shifted diagonally by one unit.
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 ...
The herringbone pattern has a symmetry of wallpaper group pgg, as long as the blocks are not of different color (i.e., considering the borders alone). Herringbone patterns can be found in wallpaper, mosaics, seating, cloth and clothing (herringbone cloth), shoe tread, security printing, herringbone gears, jewellery, sculpture, and elsewhere.
The original 1904 Droste cocoa tin, designed by Jan Misset (1861–1931) [a] The Droste effect (Dutch pronunciation:), known in art as an example of mise en abyme, is the effect of a picture recursively appearing within itself, in a place where a similar picture would realistically be expected to appear.