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: zi+1 = zi2 + 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!
Click & drag a new square on the Mandelbrot set to zoom in.
Click [Reset] to zoom out to the initial coordinates.
