Quasiperiodic Tilings

Description

Quasiperiodic rhombic tilings generated by the dual method. Several parameters, such as local rotational symmetry (5-fold to 20-fold), scaling factor and shift parameter options can be selected.

In order to obtain an N-fold symmetry, N grids of equidistantly spaced lines are overlayed, whereby the i-th grid (i=0..N-1) is rotated by 360/N*i degrees. The result is called a multigrid. A dual transformation then generates the rhombic tiles from the cross points in the multigrid. Criteria for distinguishing the tile types can be used for coloring the tiles. A shift of the individual grids with respect to the origin will result in different tilings. One may choose between special values of such grid shifts (symmetry types) or a random tiling. In the latter case each single grid may have a different shift, leading to a much wider variety of tilings.