To create mandelbrot set we must simply iterate: z -> z * z + c, where z and c are complex numbers. For every pixel in the wanted region we calculate mapping to the coordinates on the complex plane and then assign this point to c. For every c we start iterating from z = 0. Iteration stops when |z| or number of iterations reaches the boundaries.

Coloring scheme is a huge field for improvisation. Generally speaking, the intensity is determined by how fast z goes to infinity (relative to the maximum iterations).
Parallel rendering is done by independently processing chunks of window area (I should say, that it's implemented "dirty" - through the global variables).

In this implementation, you can zoom-in by double clicking inside the window. And zoom is actually not infinite, due to the limitation of floating point calculations precision. So if you zoom in up to 10e+13 you'll see very discrete image, something like this:

Install OpenGL libraries and freeGlut:

sudo apt-get install mesa-utils
sudo apt-get install freeglut3-dev

Compile mandelbrot.cpp:

g++ -O2 -fno-stack-limit -x c++ mandelbrot.cpp -lglut -lGL -lpthread -o mandelbrot

Then you can specify arguments and run the code:

• maximum number of iterations (250 by default);
• number of threads (4 by default);
• scale factor in range 0..1.0 to use zoom-in (0.5 by default);

./mandelbrot 1000 10 0.5

If you need to change the window size, replace variable width inside the code with whatever you want.