Quasicrystal Diffraction Patterns

Simulated patterns for 5,6,7, &11 plane waves :

This is a diffraction pattern of a real 3D quasicrystal. For a 3D crystal, the diffraction pattern is also three dimensional. All of the rendered images here are for 2D quasicrystals with 2D diffraction patterns.

Here is the spatial domain of a quasicrystal formed by 8 plane waves, spaced at even rotations, in a plane. This coloring was achieved by squaring the sum of all 8 waves at each point, then normalizing the whole image, then inverting the colors.

Here is a 5-fold 2D quasicrystal spatial domain. This pattern is related to Penrose tiling, I believe.

Here is a 7-fold 2D quasicrystal spatial domain

Edit : comments have indicated that systems of overlapping plane waves might not exactly be a quasicrystal, since they don't exactly have well defined lattice "points". So, I thresholded 5 summed plane waves to generate the following point distribution. The Fourier transform of this lattice looks more like what one might expect for a crystal.

&FT:

This is a diffraction pattern of a real 3D quasicrystal. For a 3D crystal, the diffraction pattern is also three dimensional. All of the rendered images here are for 2D quasicrystals with 2D diffraction patterns.

Here is the spatial domain of a quasicrystal formed by 8 plane waves, spaced at even rotations, in a plane. This coloring was achieved by squaring the sum of all 8 waves at each point, then normalizing the whole image, then inverting the colors.

Here is a 5-fold 2D quasicrystal spatial domain. This pattern is related to Penrose tiling, I believe.

Here is a 7-fold 2D quasicrystal spatial domain

Edit : comments have indicated that systems of overlapping plane waves might not exactly be a quasicrystal, since they don't exactly have well defined lattice "points". So, I thresholded 5 summed plane waves to generate the following point distribution. The Fourier transform of this lattice looks more like what one might expect for a crystal.

&FT: