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.

This pattern begins with five sets of parallel lines, each running in a different direction like five striped sheets over top of one another.

In 1981, Dutch mathematician Nicolaas de Bruijn showed how to turn this grid into a never-repeating tiling. Let the crossings act as instructions so that each one becomes a diamond. The diamonds can connect to cover the plane without gaps or a repeating pattern.

Sometimes the lines cross to make a pentagon surrounded by a ring, and at other places you'll see a star. All of this variety grows from the same five sets of straight lines, yet the pattern as a whole never repeats.

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.