Aperiodic tiling refers to a way of covering a surface with tiles that do not repeat in a regular pattern. Unlike traditional tiling, where patterns can be extended infinitely, aperiodic tiling creates a non-repeating arrangement. This concept is often illustrated using specific shapes, such as the Penrose tiles, which can fit together in various ways without forming a periodic pattern. The study of aperiodic tiling has implications in mathematics, art, and even materials science. It challenges our understanding of symmetry and order, leading to discoveries in quasicrystals, which are materials that exhibit aperiodic structures. Aperiodic tiling showcases the beauty of complexity in seemingly simple arrangements.