Then, in 2023, Kaplan and collaborators stunned the mathematics world when they found the elusive einstein tile — a single shape that can fill a floor only with a never-repeating pattern ...

With a periodic pattern, it’s possible to shift the tiles over and have them match up perfectly with their previous arrangement. An infinite checkerboard, for example, looks just the same if you ...

A new 13-sided shape is the first example ... pattern. They call it "the einstein." For decades, mathematicians wondered if it was possible to find a single special shape that could perfectly tile ...

You may like When was math invented ... overlapping quasicrystalline tiles. Quasicrystalline patterns never repeat, but are completely symmetrical. A dizzying example is on display at its medieval ...

These patterns ... additional tile shapes that make non-repeating patterns, as shown in the video above. This new finding could lead to materials science investigations—for example, shapes ...

Researchers report that 15th-century buildings in Iran feature tiles arranged ... The researchers note that the pattern is equivalent to the most famous example of a quasicrystal, discovered ...

After 60 years of searching, mathematicians might have finally found a true single ‘aperiodic’ tile ... pattern. Periodic tilings have translational symmetry: a honeycomb pattern, for example ...