The Mandelbrot set is a complex mathematical structure that is defined using a simple iterative formula. It consists of points in the complex plane that do not escape to infinity when the formula is repeatedly applied. The boundary of the set displays intricate and beautiful patterns, which are self-similar at different scales. Discovered by mathematician Benoit Mandelbrot in the late 20th century, the set is often visualized using computer graphics, revealing stunning fractal shapes. The Mandelbrot set is significant in the study of chaos theory and complex dynamics, illustrating how simple rules can lead to complex behaviors.