FRACTALLY SHAPED ACCEPTANCE DOMAINS OF QUASI-PERIODIC SQUARE TRIANGLE TILINGS WITH DODECAGONAL SYMMETRY

We generate a quasiperiodic, dodecagonally symmetric tiling of the plane by squares and equilateral triangles embedded in a higher-dimensional periodic structure. Starting from a 4D lattice frequently used for the embedding of dodecagonal structures, we iteratively construct an acceptance domain (AD) for a quasiperiodic dodecagonal point set which proves to be the vertex set of a square-triangle tiling. It turns out that our procedure leads to fractally bounded ADs but leaves enough freedom to generate several different local isomorphism classes.