A rhombic Penrose tile. Strictly speaking, this is half a tile, because subdividing a full tile will result in half tiles protruding from the original tile. Subdividing half a tile however will produce half tiles that exactly cover the original tile. See subdivide.

There are two Penrose rhombs: A thick rhomb with an angle of 72°, and a thin rhomb with an angle of 36°.

The other half of a half tile.

Flips a tile: Keeps the same shape, but reverses the orientation. Note that flipping a tile in place will turn a legal configuration to an illegal configuration.

Convert the half tile to a polygon. Note that this should be rendered as an open polygon (i.e., don't use closePath).

A different graphical representation of a tile. The first-generation Penrose tiling (P1) uses four shapes: Pentagon, Star, Boat, and Diamond.

Note that like asPolygon, the resulting polygons are open, so don't use closePath.

Subdivide a Penrose tile into smaller tiles. While it's possible to generate a Penrose tiling iteratively by adding more tiles to the side, the possible configurations are non-local, i.e. adding a particular tile somewhere can prevent adding tiles (while following the tiling rules) somewhere else.

Constructing a Penrose tiling recursively via subdivision on the other hand is much easier, and guarantees to have a tiling that adheres to the tiling rules if you start with a correct tiling.

The golden ratio. It occurs quite frequently in Penrose tilings, e.g. the ratio between the long diagonal and the edge of a thick tile is phi.

36° is the base angle of Penrose tilings.

A thin tile with edge length 1 (two half tiles)

A thick tile with edge length 1 (two half tiles)

There are two star configurations, star1 and star2. Depending on the orientation of the thick tiles, the pattern grows differently.

There are two star configurations, star1 and star2. Depending on the orientation of the thick tiles, the pattern grows differently.

star2 is the base for decagonRose.

A basic Penrose fragment consisting of a star2 and some thin tiles around, forming a decagon.

Another Penrose fragment.