Pinwheel tiling

In geometry, pinwheel tilings are non-periodic tilings defined by Charles Radin and based on a construction due to John Conway.

can be divided in five isometric copies of its image by the dilation of factor

[1] The pinwheel tiling is obtained by repeatedly inflating

Radin found a collection of five prototiles, each of which is a marking of

[1] All of the vertices have rational coordinates, and tile orientations are uniformly distributed around the circle.

[2] Radin and Conway proposed a three-dimensional analogue which was dubbed the quaquaversal tiling.

in five isometric copies, following the Conway construction, and discarding the middle triangle (ad infinitum).

This "pinwheel fractal" has Hausdorff dimension

Federation Square, a building complex in Melbourne, Australia, features the pinwheel tiling.

The pinwheel tiling system was based on the single triangular element, composed of zinc, perforated zinc, sandstone or glass (known as a tile), which was joined to 4 other similar tiles on an aluminum frame, to form a "panel".

Five panels were affixed to a galvanized steel frame, forming a "mega-panel", which were then hoisted onto support frames for the facade.

The rotational positioning of the tiles gives the facades a more random, uncertain compositional quality, even though the process of its construction is based on pre-fabrication and repetition.

The same pinwheel tiling system is used in the development of the structural frame and glazing for the "Atrium" at Federation Square, although in this instance, the pin-wheel grid has been made "3-dimensional" to form a portal frame structure.