As discussed in the previous post “Quasiperiodic designs from superposition of waves” we get a quasiperiodic structure with eight-fold rotational symmetry using eight waves (n=8). Surprisingly, cosine waves of the same sign or alternating signs give us essentially the same result as the pattern only changes place. We have eight-fold rotational symmetry of the usual kind together with its two-color version. As before I use white for values of f above zero and black for values below zero:
Here, we see often the same distance between the white and black spots. They correspond to the corners of squares, rhombs and octagons. How does this fit to the Ammann-Beenker tiling ?
Using twelve waves (n=12) we get different results for cosine waves of the same sign or for alternating signs:
Can we find here some features of the Stampfli tiling ? Clearly, some spots indicate triangular, square and rhombic shapes.