The images were generated with my Java applet JFourier3.
click at image to see a larger image in a new window

n-fold	shift = 1/ n	shift = (n-1)/(2n)	shift = random
5-fold
7-fold
8-fold
9-fold
10-fold
11-fold
12-fold
	regular	superstructure	random tiling

The shift refers to a shift of the dual grids, which generate the tilings. Generally the tilings with a shift=(n-1)/(2n) form some kind of superstructures, due to the existence of small periodic tile clusters. (eg. four tiles packed periodically). The Fourier transforms are calculated using the "atoms" at the vertices of a tiling as point scatterers. Note that the random tilings give a similar Fourier transform (diffraction pattern) as the more symmetrical patterns. This is due to the long-range orientational order of the tiles, which means that they only occur in a few possible orientations.