A never-repeating pattern: This pattern never settles into a repeating rhythm. Part of Fivefold, our family of never-repeating patterns built on the number five.

Take a diamond and cut it along a line set by the golden ratio: the two pieces are a kite and a dart. Roger Penrose showed that, with a simple rule about which edges may meet, these two shapes cover the plane forever, without repeating as a whole.

In some places you can see stars: five darts pointing inward, and in others, suns: five kites in a ring. Through the pattern, these two shapes keep returning in new arrangements, but with a rhythm: the kites outnumber darts by the golden ratio.

Never-repeating tilings are important puzzles in computation, too: no computer program can always tell whether a given set of tiles will cover an endless floor; a geometric version of the halting problem.

Even simple rules can result in extraordinary complexity: Some tiles can fit together to cover a floor forever, but only if the pattern never repeats. This pattern is one beautiful example.