CSCI 250

Project 3

For this project, you are to produce the image of a Julia set. We are going to iterate f(z) = z² + c where c is a constant that determines which Julia set we are producing. We take the output of the function and feed it back as input and see if the function values are bounded or not. The color chosen indicates the boundedness after iterating 1000 times. Black goes to infinity, green indicates bounded.

Now the value z is a complex number, so we need to use complex arithmetic. C++ has complex arithmetic in the library, but for practice, I want you to implement your own complex arithmetic class. It should include the four basic operations, +, -, *, and /. In case you forgot, a complex number has 2 parts, the real and the imaginary. Arithmetic is done as follows:

You should also have a default constructor and one that takes a real and converts it to a complex number, and one that takes two reals and creates a complex number, as well as I/O routines for complex numbers.

Your program should scan across the screen and for every pixel (x,y), should construct the corresponding complex number z = x+yi. You should iterate

where c is a predefined constant. I used 0.244325 – 0.0602826i. Do this for 1000 times or until the magnitude squared (x² + y²) is bigger than 4. If you get 1000 iterations, color it your favorite color: otherwise color it black. Do a glFlush() to get the image to the screen and enjoy!

Below is a sample I created:

Since the points were so small they didn’t show up, I drew a polygon for each point (glBegin(GL_POLYGONS)), going in counterclockwise order (x,y), (x+0.001, y), (x+0.001, y+0.001), (x, y+0.001). This made a “point” big enough to see.

Also, the default screen coordinates run from (-1, -1) to (1,1), so your loop should be restricted to that range.

Try different values of c and see how the shape changes.