A **Penrose tiling** is a non-periodic tiling generated by an aperiodic set of prototiles. Penrose tilings are named after mathematician and physicist 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. A Penrose tiling may be constructed so as to exhibit both reflection symmetry and fivefold rotational symmetry, as in the diagram at the right.

A Penrose tiling has many remarkable properties, most notably:

- It is non-periodic, which means that it lacks any translational symmetry.
- It is self-similar, so the same patterns occur at larger and larger scales. Thus, the tiling can be obtained through "inflation" (or "deflation") and any finite patch from the tiling occurs infinitely many times.
- It is a quasicrystal: implemented as a physical structure a Penrose tiling will produce Bragg diffraction and its diffractogram reveals both the fivefold symmetry and the underlying long range order.

Various methods to construct Penrose tilings have been discovered, including matching rules, substitutions, cut and project schemes and coverings.

Read more about Penrose Tiling: The Penrose Tilings

### Other articles related to "penrose tiling, tilings, penrose tilings, penrose, tiling":

Related Tilings and Topics -

... The aesthetic value of

**Penrose Tiling**s and Art... The aesthetic value of

**tilings**has long been appreciated, and remains a source of interest in them here the visual appearance (rather than the formal defining properties) of**Penrose tilings**... noted and Lu and Steinhardt have presented evidence that a**Penrose tiling**underlies some examples of medieval Islamic art ... Drop City artist Clark Richert used**Penrose**rhombs in artwork in 1970 ...Crystallographic Restriction Theorem - Dimensions 2 and 3 - Lattice Proof

... The existence of quasicrystals and

... The existence of quasicrystals and

**Penrose tilings**shows that the assumption of a linear translation is necessary ...**Penrose tilings**may have 5-fold rotational symmetry and a discrete lattice, and any local neighborhood of the**tiling**is repeated infinitely many times, but there is no linear ... A**Penrose tiling**of the whole (infinite) plane can only have exact 5-fold rotational symmetry (of the whole**tiling**) about a single point, however, whereas the 4-fold and 6-fold lattices ...Main Site Subjects

Related Subjects

Related Phrases

Related Words