A Pen (a medieval quill in this case) and a Rose tile to make an enormous bouquet of Penrose Tiles.

This tessellation is based on the Penrose tiling which was published by Roger Penrose in 1975. The tiling is really interesting in that it is aperiodic when the tiles are marked or notched in a particular way. While aperiodic, some versions of the tiling have 5-fold symmetry, which is a version I have used to make this design.

What is aperiodic? The tiling lacks translational symmetry – while you can pick up any few tiles and find some nearby in the same orientation, if you pick up a different group and move it the same distance and direction as the previous selection you will find it won’t cover the tiles below it exactly.

It is self-similar, meaning there are structures within it that appear at multiple scales – and this means you can produce it by the iterative substitution method. The substitution is exponential, so by continuing this process just a few times, you could cover the entire universe with Pen-Rose tiles – and it would still be aperiodic.