This applet draws the Mandelbrot set, i.e. the set of points [math]c\in\mathbb{C}[/math] of the complex plane for which the orbit of [math]z=0[/math] under the iteration map [math]f(z)=z^2+c[/math] is bounded, that is, it does not "escape to infinity". It can be shown that the Mandelbrot set corresponds to the set of points [math]c\in\mathbb{C}[/math] for which the corresponding Julia set is connected (i.e. it is not the union of disjoint open subsets).

Use the [i]Draw[/i] button to start rendering the set and the [i]Clear[/i] button to (stop and) clear the window.