The original version of this story appeared in Quanta Magazine. If you want to tile a bathroom floor, square tiles are the simplest option—they fit together without any gaps in a grid pattern that can ...

Infinitely many copies of a 13-sided shape can be arranged with no overlaps or gaps in a pattern that never repeats. David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss (CC BY ...

Is it possible to tile a surface with a single shape in such a way that the pattern never repeats itself? In 2022, a mathematical solution to this 'Einstein problem' was discovered for the first time.

Mathematicians have discovered a single shape that can be used to cover a surface completely without ever creating a repeating pattern. The long-sought shape is surprisingly simple but has taken ...

Nature follows mathematical rules and creates repeating patterns across completely different organisms and environments.