Quasiperiodic tiling
Encyclopedia
A quasiperiodic tiling is a tiling
of the plane that exhibits local periodicity under some transformations; we can slide or rotate it such that a finite number of tiles overlap perfectly, yet the entire tiling will not.
See
Tessellation
A tessellation or tiling of the plane is a pattern of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of parts of the plane or of other surfaces. Generalizations to higher dimensions are also possible. Tessellations frequently appeared in the art...
of the plane that exhibits local periodicity under some transformations; we can slide or rotate it such that a finite number of tiles overlap perfectly, yet the entire tiling will not.
See
- Aperiodic tilingAperiodic tilingAn aperiodic tiling is a tiling obtained from an aperiodic set of tiles. Properly speaking, aperiodicity is a property of particular sets of tiles; any given finite tiling is either periodic or non-periodic...
and Penrose tilingPenrose tilingA Penrose tiling is a non-periodic tiling generated by an aperiodic set of prototiles named after Sir Roger Penrose, who investigated these sets in the 1970s. The aperiodicity of the Penrose prototiles implies that a shifted copy of a Penrose tiling will never match the original...
for a mathematical viewpoint. - QuasicrystalQuasicrystalA quasiperiodic crystal, or, in short, quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry...
for a physics viewpoint.