#
*Java Number Cruncher*

Program 16-3

## Newton's Fractal Image

This applet demonstrates how Newton's Method, when applied
to the complex plane, can generate a fractal image. The function
*f*(*z*) = *z*^3 - 1 has three roots in the
complex plane: 1, -0.5+0.87*i*, and -0.5-0.87*i*.
The applet plots each point in the plane as follows:

- Apply Newton's Method using that point as the starting point.
- Set the point's color (red, green, or blue) according to which root the algorithm converges to from that point.
- Set the color intensity of the point according to the number of iterations required to converge to the root.

The resulting graph is a fractal image.

## To run the demo:

- The initial fractal image is generated automatically.
- Use the mouse to drag a rectangle around an area of the image that you want to zoom into.