This fractal is generated using the complex polynomial f(z) = z^4 - 1. The roots (zeros) of this polynomial are 1, -1, i and -i (where i is the square root of -1). In the complex plane these roots are located at (1, 0), (-1, 0), (0, 1) and (0, -1), respectively. The applet samples a point in the plane, iterates Newton's Method on f(z) using that point as the initial value, and colors the point based on which of the four roots the iterates converge to. Points that converge to (1, 0) are colored yellow, those that go to (-1, 0) are colored green, and so on. If the iterates of a point do not come within 0.1 of a root after the prescribed number of iterations, the point is left black.
The buttons on the left side of the applet allow you to zoom in and out on the picture. When you click on a button to zoom you must then click on the fractal. The point that you click on the fractal will become the center of the new picture. If you have not selected either "Zoom In" or "Zoom Out" clicking on the fractal will allow you to move the picture around without changing the scale. If you select "Reset" you must also click on the fractal to activate the command; where you click is unimportant as the applet will return the original picture, with (0, 0) in the center.
The buttons on the right side allow you to change the number of iterations the applet performs before checking to see if the iterates are within 0.1 of a root. As before, once you have selected a button click on the fractal where you want the center of the picture to be.