aperiodic tiling

Aperiodic tiling involves covering a surface completely with shapes that do not repeat in a regular pattern. Unlike traditional tiling, which forms repeating patterns like squares or hexagons, aperiodic tilings create intricate designs that lack translational symmetry, meaning you can't shift the pattern to make it align with itself. These tilings can produce visually fascinating and complex structures, illustrating how non-repeating arrangements can fill space perfectly. They are important in understanding quasicrystals and have applications in design, art, and materials science. Ultimately, aperiodic tiling combines mathematical rules with artistic complexity to produce patterns that are both orderly and non-repeating.