Penrose Tiling

Penrose tiling is a type of non-repeating pattern formed by fitting together a few specific shapes, typically two types of tiles, in a way that covers a surface without gaps or overlaps. Unlike regular tilings like squares or triangles, Penrose tiling never repeats exactly, creating an aperiodic pattern that exhibits long-range order. This unique property makes it valuable in understanding quasicrystals—materials with an ordered structure but no repeating unit. Penrose tilings demonstrate how complex, non-repeating patterns can arise from simple rules, blending aesthetics with mathematical precision.