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Something I find interesting is that, although on the surface this seems like a way to deal with rotations in general, it only works for certain angles. For instance, with a 45 degree rotation, you have to scale the image, too, and the resulting tile contains two of the original image.

Topologically, an underlying problem is that there is not a continuous family of rotations for a torus (the topological space corresponding to two independent periodic dimensions).




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