Two shapes can tile a floor forever without the pattern ever repeating
Most tiling patterns — bathroom floors, brick walls — eventually repeat in a grid. In the 1970s, physicist Roger Penrose found a set of just two tile shapes, nicknamed 'kites' and 'darts,' that can cover an infinite plane edge to edge with no gaps or overlaps, yet whose pattern never exactly repeats no matter how far it's extended. Why should two simple shapes make repetition impossible?
Reveal the answer
The kite-and-dart pair can only fit together following forced local matching rules, marked by coloured arcs on the tiles, and those rules mathematically prohibit any translational symmetry — shift the whole pattern in any direction and it will eventually mismatch. Penrose tilings later turned out to describe the atomic structure of real 'quasicrystals,' a discovery that won Dan Shechtman the 2011 Nobel Prize in Chemistry after being initially dismissed as impossible.