In the 1970s, mathematician Roger Penrose discovered that two shapes could form a non-repeating tiling pattern together, prompting hopes that a single shape may be found to do this one day.

What is unique about this geometrical figure is that it can tile a plane without creating a repeating pattern. The hat can tile a surface without creating transitional symmetry. In other words ...

A quartet of mathematicians from Yorkshire University, the University of Cambridge, the University of Waterloo and the University of Arkansas has discovered a 2D geometric shape that does not ...

Previously, mathematicians knew of sets of tiles that could tile the plane only with non-repeating patterns. But until this year, they didn’t know of a single tile that would do it. After ...

Researchers have now also found a chemical solution: a molecule that arranges itself into complex, non-repeating patterns on a surface. The resulting aperiodic layer could even exhibit novel ...

The geometric ... regular but non-repetitive patterns of Penrose tiling – a concept developed in the West only in the 1970s. Simple periodic patterns can be generated easily by repeating a ...

A tiling is “periodic” if copies of a single shape fit together in a pattern that repeats itself ... The ultimate solution, a non­repeating sequence of numbers, can then be translated back ...