If you really want to see how a fractal-generating program works then download the source and executable of Winmand as a zip file (50 k). This program was written by Robert Banting. It is about as simple as a Windows fractal generator can be. It allows you to zoom into the mandelbrot set. You can view the source of the program with notepad. If you have a C compiler you can compile and alter the program to see what happens when various parameters are changed, make it draw other fractals, and so forth. The source of the program contains a long comment in clear English that explains exactly how the fractal image is generated. If you want to just play with the program then you can do that without even looking at the source.
To see just the explanation, with the core part of the code, click here. Here is the output from the program (click to enlarge).