These aren't just random geometric patterns; each coaster is a unique slice of a fascinating mathematical world. They are generated from a family of non-periodic tilings, meaning they can cover an infinite plane without ever repeating the exact same overall structure.

The designs come directly from the research paper "A Family of Non-Periodic Tilings, Describable Using Elementary Tools and Exhibiting a New Kind of Structural Regularity" by Miki Imura (arXiv:2506.07638v1).

What makes them special is a unique property the author calls "modulo-staggered rotational symmetry."Instead of simple, repeating symmetry, these patterns have a hidden, complex order that gives them their beautiful and organic feel, sometimes appearing crystalline and other times like spiraling galaxies.

This set was created using a custom OpenSCAD generator that faithfully implements the mathematics from the paper. Each coaster in the set uses different parameters, but they all belong to the same "Modulo Krinkle" family.

 The colors I’ve chosen are ocean colors, but you can pick any colors you’d like when printing your own.