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This shows the angular dependence of the Moire pattern of 2 graphene layers with the bottom-layer fixed. The relative angle between the two layers' lattices is shown in the top left. The point of rotation of the top layer is the empty site of the central honeycomb. Other patterns can be formed by rotating around other high (or low!) symmetry points.
The the individual sublayers of each frame were generated using a small Python package I wrote for myself for the creation of vector graphics using Cairo (cairocffi more specifically). My Python package was inspired in no small part by Gizeh by Zulko. He has a a lot of other neat packages avaialble on GitHub for people interested in generating graphics programmatically. The individual frames were parsed into an AVI using FFmpeg.
Cairo: cairographics.org/
Cairocffi: github.com/Sim... & pypi.python.or...
Gizeh: github.com/Zul...
FFmpeg: www.ffmpeg.org/