The (coloured) Mandelbrot set
This applet draws the Mandelbrot set, i.e. the set of points of the complex plane for which the orbit of under the iteration map is bounded, that is, it does not "escape to infinity". It can be shown that the Mandelbrot set corresponds to the set of points for which the corresponding Julia set is connected (i.e. it is not the union of disjoint open subsets).
Use the Draw button to start rendering the set and the Clear button to (stop and) clear the window. WARNING The applet computes the colour of 102400 points using 20 levels of colour so it needs a long time to complete the task (about an hour on an Intel Core I7, 2 GHz), but the game is worth the candle. For a faster rendition without color look for my The Mandelbrot set.