© Steffen Weber, March 1999
Quasiperiodic rhombic tilings generated by the dual method. Several parameters, such as local rotational symmetry (5-fold to 22-fold), scaling factor and shift parameter can be specified. Random colouring is used for the tiling. For Fourier transforms of quasiperiodic tilings see Project 24.
scaling | Zooms tiling, results in a different number of tiles. If there are gaps you may increase the loop order to generate more tiles. |
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draw | Button for drawing/redrawing the tiling for the chosen symmetry |
loop order 1,2,3,.. | Loop order for generating the tiling. 2 should always be fine. The larger the value the more tiles are generated and the longer it takes. |
shift 1/n, ..., ... | Some shifting parameters for the dual grids, that actually produce the tiling. The result is a different arrangement of the tiles. |
This applet is based on my PC software
TILING. This program is based on the DUAL METHOD. 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. Then there is a dual transformation, which generates the rhombic tiles from the crosspoints of the multigrid. Criteria for distinguishing the tile types can be used for a colouring of the tiles. A shift of the individual grids with respect to the origin will result in different tilings. You may choose between two special values of such grid shift or a random. In the latter case each single grid may have a different shift, leading to a much wider variety of tilings. CREDITS: The used dual method algorithm is based on a FORTRAN algorithm by Dr.Akiji Yamamoto. |