Tiling and Tessellations

Tessellations are patterns of shapes that fit together perfectly without any gaps or overlaps.

Penrose Tilings: Unlike traditional periodic tilings (like a checkerboard), Penrose tilings are aperiodic, meaning they never repeat. They use just a few simple shapes (like kites and darts) to create intricate and beautiful patterns with a hidden order.

Escher's Art: The artist M.C. Escher was a master of using tessellations to create impossible and mind-bending art, often incorporating animals and other figures. His work beautifully blurs the line between mathematics and art.