Copies of these two tiles can form infinitely many different patterns that go on forever, called Penrose tilings. Yet no matter how you arrange the tiles, you’ll never get a periodic repeating ...

When humans cover a space using tiles of the same shape without overlap or gaps—a geometrical process called tiling—we will usually opt for a shape with sharp corners and straight lines, like squares ...

In the 1970s, mathematician Roger Penrose discovered that two shapes could form a non-repeating tiling pattern together, prompting hopes that a single shape may be found to do this one day.

Pinecones, spiral nautilus shells, and ice crystals all have self-repeating patterns as well. But among recursive patterns that appear in living beings, Romanesco broccoli is a fractal par ...

In some art from the Islamic world, you will find repeating patterns of flowers and plants. ... Spot the geometric patterns on this traditional decorative copper plate. Image caption, ...