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 ...

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 ...

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 ...

The fundamental research, published in the journal Nature Chemistry, has shown that they can prompt the 'tiles' to form a range of random patterns by adjusting the conditions in which the ...