A Mandelbrot set is a complex mathematical structure that emerges from a simple equation involving complex numbers. It is defined by iterating the equation z = z^2 + c , where z and c are complex numbers. The set consists of all values of c for which the sequence does not diverge to infinity. The boundary of the Mandelbrot set is famous for its intricate and infinitely detailed patterns, which exhibit self-similarity. This means that zooming into the boundary reveals smaller copies of the overall shape, showcasing the beauty of mathematics and its connection to fractal geometry.