It was already time to change the animation for this blog, (the little thing at the right, now with a chess board), so I would do a very short description of the previous one here:
This animation is just a Pascal's Triangle (reflected in the four quadrants) with different colors for cells accordingly to their modules with some random number not prime that changes with every iteration. The triangle for the next iteration is drawn row by row, while the previous one is faded. Empty spaces are cells that are divisible by the selected random number.
If you feel more interested, you could check the section 2.3 of the book Chaos and Fractals (Springer) that gave me the inspiration for this. NOTE: I updated this animation to use canvas HTML5 but the old Flash source code is here