Penrose tiles

Penrose tiles are a special set of shapes that can cover a flat surface without repeating patterns or any gaps, creating an aperiodic tiling. Typically, they consist of two different shapes, such as kites and darts or thick and thin rhombs, arranged in a way that results in a non-repeating, infinitely complex pattern. Discovered by mathematician Roger Penrose in the 1970s, these tiles illustrate how order and symmetry can exist without traditional periodicity, offering insights into quasicrystals and complex systems. Despite their intricate patterning, Penrose tiles follow specific matching rules to ensure the pattern remains non-repeating.