Mathematicians have been searching for this non-repeating pattern for 50 years

For the tiles in your bathroom, do you like repeating patterns? Otherwise, mathematicians today offer you the opportunity to tile the entire room in the same pattern.

It is made up of eight kites joined by their edges. With its 13 sides, this polygon vaguely resembles a hat. But you can imagine that didn’t catch the attention of researchers. No, what is most exceptional about this form is that it can cover a surface without leaving space or overlapping and, above all, without repeating itself. The theory predicted the existence of such a shape, but no mathematician succeeded in implementing it.

In the 1970s, physicist Roger Penrose proposed an example of such tiling, which researchers call aperiodic. The famous Penrose tiling. But his purpose is based on two different forms. This time, it is actually an aperiodic monotileInternational team Gathered behind an ordinary mathematician. Most searched for “Einstein”. No relation to the famous tongue-twisting physicist. But with German meaning “Ein Stein”, ” a stone “.

Einstein hats in your bathroom?

Mathematicians have been searching for such a pattern for half a century. Some concluded that it was not. Or at least by imagining a more complex form. During this time “hat” Seems disarmingly simple.

To prove the exceptional nature of this fun pattern, the researchers relied on powerful computers. But also in the strength of the human spirit. First clue found: Truth “hats” The query divides itself into groups – called metatiles – and then into larger groups – supertiles – and so on. This is what mathematicians observe in all aperiodic tilings. But the final proof came from serious wrecks “hat”.

This work naturally excites researchers at a theoretical level. But they could find practical applications in the field of semi-crystals found in Terminator-type robots to Kleenex. If you feel like it, it might be time to give your bathroom a crazy look and update its tiles…