Penrose Tiling is a unique way of arranging shapes to cover a surface without repeating patterns. It uses two types of shapes, usually rhombuses, that fit together in a specific way. This creates a beautiful, non-repeating design that can extend infinitely in all directions. The concept was discovered by mathematician Roger Penrose in the 1970s. Unlike traditional tiling, which can repeat, Penrose Tiling showcases a form of quasicrystal structure. This means it has an ordered pattern but lacks periodicity, making it a fascinating subject in both mathematics and art.