This program 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+0.87i, and -0.5-0.87i. The program 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.