Penrose tiles are a set of shapes that can cover a surface without repeating patterns. They were discovered by mathematician Roger Penrose in the 1970s. These tiles come in various forms, but the most common are the kite and dart shapes. When arranged correctly, they create beautiful, non-periodic patterns that never repeat. The unique property of Penrose tiles is that they can fill a plane completely while maintaining a specific arrangement. This means that no matter how far you extend the pattern, it will never look the same twice. This fascinating characteristic has implications in mathematics, art, and even quasicrystals in materials science.