Penrose tiles are a set of specially designed shapes that can cover a flat surface infinitely without ever repeating the same pattern. Unlike regular tiles, which create predictable, repeating designs, Penrose tiles form non-repeating, aperiodic patterns. Discovered by mathematician Roger Penrose in the 1970s, these tiles have become important in mathematics and physics for studying symmetry, order, and complexity. Their unique properties have inspired applications in art, architecture, and even the study of quasicrystals in materials science.