Einstein, meet “vampire einstein.” It’s been just months since researchers reported the first “einstein” — a single tile that can cover an infinite plane, but only with a pattern that ...

This week, mathematicians announced the discovery of a single tile shape that produces aperiodic patterns. It’s the latest advance in a field that stretches back decades.

It’s this kind of beauty that a retired print technician was seeking when he recently discovered the first “aperiodic monotile”— a single tile that fills up the plane in a non-repeating pattern. To ...

After half a century, mathematicians succeed in finding an ‘einstein,’ a shape that forms a tiled pattern that never repeats.

geometry Hobbyist Finds Math’s Elusive ‘Einstein’ Tile The surprisingly simple tile is the first single, connected tile that can fill the entire plane in a pattern that never repeats — and can’t be ...

Copies of these two tiles can form infinitely many different patterns that go on forever, called Penrose tilings. Yet no matter how you arrange the tiles, you’ll never get a periodic repeating ...

The swirling Arabesque ceramic tiles used in medieval Islamic mosaics and architecture were produced using geometry not understood in the West until the 1970s.

A new 13-sided shape is the first example of an elusive "einstein" — a single shape that can be tiled infinitely without repeating a pattern.

Islamic tiling patterns were put together not with a compass and ruler, as previously assumed, but by tessellating a small number of different tiles with complex shapes, say Peter J. Lu of Harvard ...