[vez-]

This video gives a very concrete example of a non-repeating pattern (Penrose tiling) https://www.youtube.com/watch?v=48sCx-wBs34

[function_seven]

I understand the non-repeating patterns. I just don't see how a regular 3D lattice can produce such a pattern. Unless the light source creating this shadow is a point-source rather than a parallel one?

I guess I'm just looking for confirmation on this thought: A parallel light shone through a repeating 3D lattice will always produce a repeating 2D lattice.

[yazanobeidi]

Try projecting it on a surface with curvature. The projected grid spacing will be irregular and follow the curvature.