The resulting aperiodic layer could even exhibit novel physical properties. Is it possible to tile a surface with a single shape in such a way that the pattern never repeats itself? In 2022 ...

But what about an aperiodic tiling, a tiling that does not repeat itself? That might look something like a stained glass window in a church, which has artwork of flowers or angels or saints ...

"Our study highlights the effectiveness of aperiodic approximants in inducing modulations within self-assembled soft-matter systems employing the P31m plane group. Specifically, we utilized the rows ...

finding that the ideal arrangement for the particles is a metallic-mean tiling, consisting of up and down triangles. "Our study highlights the effectiveness of aperiodic approximants in inducing ...

If you’ve seen one small patch, you’ve seen it all. In the 1960s, mathematicians began to study “aperiodic” tile sets with far richer behavior. Perhaps the most famous is a pair of diamond ...

Previously, mathematicians needed more than one shape to cover an infinite plane in this nonrepeating way, known as an aperiodic tiling. Some earlier aperiodic tilings have connections to real ...

Such tile sets are called aperiodic. Although Berger and others were able to bring down the size of these aperiodic sets significantly, in the mid-1970s Roger Penrose captured the world’s attention by ...

Unless you’re renovating a bathroom, you may not think a lot about tiles. But mathematicians do. One of their long-standing quests has been to design a tile shape that can cover a plane of ...