The Mandelbrot Set uses complex numbers on a two dimensional grid to solve an equation. For each point in the grid, the algorithm performs a relatively simple calculation over many iterations. In most cases, points on the grid either converge to infinity and are not part of the set (represented below in white) or converge to the number 2 and are part of the set (represented below in black). The interesting points are near border where they may or may not be part of the set. Colors are used to represent the degree of uncertainty and to create startling geometric patterns.