Mandelbrot defined a new mapping of the complex plan (the Mandelbrot Set) by including all complex points that do not diverge to infinity when iteratively squared and added to the initial point: z_i+1 = z_i² + z₀. The boundary of the surface thus defined has the peculiar property of having a Hausdorff dimension of 2 while it has (it is a curve) a topological dimension of 1. Mandelbrot Set's complexity actually increases when zooming in!