Mathematicians Solve Decades-Long Quest for Infinite Tiling Pattern.
Mathematicians may have discovered the first truly single aperiodic tile, a shape that can cover an infinite surface without repeating itself. Aperiodic tilings cannot be shifted in any direction to create a repeating pattern. The first aperiodic tilings were discovered in the 1960s, and they involved 20,426 tile types. Roger Penrose discovered the first aperiodic tiling made of only two tile types that were not merely mirror images of each other.