Mandelbrot Escape Iterations

This Java applet and page is given to us through the generosity of Ivan Scott Fuller

How To Use - Click anywhere on the Mandelbrot set above. Click and drag for a more dynamic view.

The Mandelbrot set is the set of points in the complex plane that do not diverge after any number of iterations of the following formula:

x₀ = k
x_i+1 = (x_i)²+k

What this means is that, to find out if a point diverges or not you must put it into the equation and start iterating. When you put it in the equation, you find out what the next point in the iteration is. Then you put that point in and find out what the next point is, and so on. If the points you get get to be more than two units away from the origin, they will diverge to infinity. If not, they will not diverge and are thus in the set.

The black points in the picture represent points that are in the Mandelbrot Set - that is, they do not diverge.
The yellow dots you see represent the first few iterations for the point on which you have clicked. Have fun!

-Ivan Scott Fuller / David