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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.

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
Ever since those Einstein tiles I've been dreaming about making a company that does these kind of fancy tiling.
noqc
>aesthetically useful
jameshart
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/

birn559
Fun fact: last part of his name "Räder" is a German word that translate to "wheels" which I find weirdly fitting.
ahazred8ta
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.
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.