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Abstract
A dodecagonal quasiperiodic tiling is generated by a substitution rule (SR) for four kinds of tiles, namely, a triangle, a square, a trigonal hexagon and a dodecagon. The scaling factor of the SR is equal to . The same tiling (exactly, quasilattice) is obtained with the projection method from a four-dimensional dodecagonal lattice and the relevant window has a fractal boundary. A set equation for the window is presented. It is emphasized that investigating quasiperiodic tilings of this type is a less explored but rich field in the crystallography of quasicrystals.
Notes
Note
If the second term of the bracket of the set map (Equation2(2) ) is discarded, we obtain a simpler set map, which is an iterative function scheme. It was found recently that a large number of QLs with fractal windows are obtained on the basis of set maps of this type.