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.