When people tile their floors, they tend to use simple geometric shapes that lend themselves to repeating ... want patterns that do not repeat but that represents a challenge if the same types ...

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.

A mathematician would look at your game and ask, “Can you determine whether you will hit a dead end just by looking at the types of ... without the color pattern ever repeating itself.

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 ...

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 ...