A Family of Non-Periodic Tilings, Describable Using Elementary Tools

[joshu]

https://arxiv.org/abs/2506.07638

[jameshart]

Someone needs to get this into the hands of a ceramic tile manufacturer or a manufacturer of pavers. These are some of the most immediately aesthetically useful tile shapes mathematics has produced since the hexagon.

[ThalesX → jameshart]

Ever since those Einstein tiles I've been dreaming about making a company that does these kind of fancy tiling.

[noqc → jameshart]

>aesthetically useful

[jameshart → noqc]

Yes?

Useful for making aesthetically pleasing things.

[0y]

"The pattern shown in Figure 5(b) was originally presented by Jan Sallmann-Räder in a social media post"

this seems to be said post: https://www.facebook.com/share/1DJu7tSjKq/

[joshu → 0y]

yeah, miki also posts in https://www.facebook.com/groups/tiling as well. i've been following this for a few weeks

[ahazred8ta → 0y]

Correct me if I'm wrong, some of these patterns don't seem to be nonperiodic. The tiling within the wedge-shaped regions is repetitive, and then the regions just fit together with an irregular boundary.

[birn559 → 0y]

Fun fact: last part of his name "Räder" is a German word that translate to "wheels" which I find weirdly fitting.

[joshu]

Full title: A Family of Non-Periodic Tilings, Describable Using Elementary Tools and Exhibiting a New Kind of Structural Regularity

This is Miki Imura’s spiral tesselation.

[tocs3]

So, how do these tiles differ from other non periodic tiling? I have looked at but not read the paper. It could be a little over my head.