COMPUTING II: PROJECT A (00/01)

Newton’s method may be used to find both real and complex roots of equations. In lecture 5 I discussed that for the equation z³=1 (where z is a complex number), the root that Newton’s method produces can be critically dependent on the initial guess used. In this project you will write a program to generate a graphical display of the results of Newton’s method when applied to finding the roots of z³=1.

The Newton’s method algorithm you will employ is identical to that used for real numbers (and which you used in lab. session 5 and coursework 5). However, you will of course need to modify the code so that it may be used with complex numbers and functions.

To generate a graphical display of the Newton's method solutions to z³=1 your program should:

1. choose an initial guess on the complex plane;
2. determine which of the three roots Newton’s method finds using this initial guess;
3. colour a pixel on the screen representing the initial guess red, blue or yellow depending on the value of the root.

You should examine regions of the graphical display you have created at various magnifications and modify the equation to generate different types of fractals.