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 is known for its intricate and beautiful patterns, which exhibit self-similarity at different scales. Discovered by mathematician Benoit Mandelbrot in the late 20th century, the set has become a popular subject in both mathematics and art. Its visual representations often feature vibrant colors and elaborate shapes, making it a fascinating example of how simple rules can lead to complex and stunning results.