Zoom into the Mandelbrot set, revealing the self-similarity of this fractal at different scales. Between the start and end of the zoom, the magnification increases by a factor of 10 to the 15 (one quadrillion). The Mandelbrot set is a two-dimensional boundary that displays the same level of complexity regardless of the scale at which it is viewed. The boundary lies between two outcomes of the application of a mathematical function on complex numbers. The set was popularised by the mathematician Benoit B Mandelbrot, after whom it is named.