Aperiodic Colored Tilings

Each of the following tilings is given by a small, hand-coded PostScript program that exploits the self-similarity of these tilings.

Ammann-Beenker tiling made of squares and rhombi. This tiling is eightfold symmetric in the sense that the rotated tiling is locally indistinguishable from the original tiling.

Penrose tiling made of two kinds of rhombi. The Penrose tiling is ten-fold symmetric in the above sense. There is also a kite-and-dart version.

Penrose tiling with two-color symmetry. A rotation by 36 degrees exchanges the colors.

Shield tiling made of shields, squares and triangles. It is twelve-fold symmetric.

The wheel tiling, the Socolar tiling and the plate tiling are all locally equivalent to the shield tiling. All three have a two-color symmetry: the vertical mirror exchanges certain colors (again in the sense that the mirrored tiling with exchanged colors is locally indistinguishable from the original).

There is also a wheel tiling with more tiles.

Pinwheel tiling made of two triangles (left and right) in infinitely many orientations (in the infinite tiling). The colors are determined from the orientation of a tile. Two color scales are used for left and right triangles.

Square tiling with a limit-periodic coloring. This tiling is locally equivalent to the chair tiling.

Peano, a limit-periodic pattern due to Victor Ostromoukhov. The red and the yellow curve are locally indistinguishable from each other, and both fill the plane densely like a Peano curve. The yellow curve has a single connected component, whereas the red curve decays into three components, which are connected only at infinity.