Fig. 3

Projection windows and Fourier transforms. a Windows of the k = 3, 6, 9, and 12 type IA tilings with 324391, 123392, 1212652, and 7195910 points, respectively (top row), and type IB tilings with 95659, 11041, and 32767 points, respectively; the windows are obtained based on third-generation tilings except for the k = 3 tiling (fifth generation) and k = 12 type IB tiling (second generation). b Transforms of these tilings with spots normalized relative to the central peak; shown are all spots with intensities I(q^∥) > 0.0045