Penrose tiling

The most famous of these are the Penrose tilings.

The front of the entrance is tiled in Penrose tiling.

These isosceles triangles can be used to produce Penrose tilings.

This is similar to a Penrose tiling, or the arrangement of atoms in a quasicrystal.

De Bruijn also worked on the theory of Penrose tilings.

One way to create quasi-periodic patterns is to create a Penrose tiling.

The game is based on Penrose tiling.

The three variants of the Penrose tiling are mutually locally derivable.

Many of these patterns are aperiodic penrose tilings.

Penrose tilings based on matched pairs of tiles like these are interesting not only to mathematicians but to commercial enterprises.

A Penrose tiling has many remarkable properties, most notably:

This shows that the Penrose tiling has a scaling self-similarity, and so can be thought of as a fractal.

This shows in particular that the number of distinct Penrose tilings (of any type) is uncountably infinite.

The rhombus Penrose tiling can be drawn using the following L-system:

In particular, the celebrated Penrose tiling is an example of an aperiodic substitution tiling.

Aperiodic tiling and Penrose tiling for a mathematical viewpoint.

Penrose tilings, which use two different quadrilaterals, are the best known example of tiles that forcibly create non-periodic patterns.

The existence of quasicrystals and Penrose tilings shows that the assumption of a linear translation is necessary.

Therefore a finite patch cannot differentiate between the uncountably many Penrose tilings, nor even determine which position within the tiling is being shown.

They are related and very similar to Penrose tilings, invented by Roger Penrose.

The quadrilaterals called the 'Kite' and 'Dart' can also be used to form a Penrose tiling.

The Penrose tilings, being non-periodic, have no translational symmetry - the pattern cannot be shifted to match itself over the entire plane.

A Penrose tiling features prominently in the painting Santa Fe Ribbon.

One property of a mathematical Penrose tiling scheme is that it incorporates fat and skinny rhombuses in exactly the ratio expressed by the golden mean.

A Penrose tiling is a non-periodic tiling generated by an aperiodic set of prototiles.