Ribbon Weaver Tumbler — Blue Grey

Five sets of parallel lines, one hidden tiling.

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.

Who it’s for

De Bruijn’s method is how physicists model quasicrystals: a slice through a higher-dimensional lattice, projected down. Made for physicists, chemists, materials scientists, crystallographers and designers.

For long workdays, lazy weekend mornings and every walk in between.

The Tumbler

• 20 oz double-walled stainless steel, keeping drinks hot or cold for longer. About 18 cm (7 in) tall.
• Clear slide lid; fits most car cup holders.
• Printed all the way around.
• Hand wash only.

Every Zenzicube design is grown from a real piece of mathematics. Find more in the Mathematical Menagerie.