I'm going to guess the pink dots fade out due to the grey and pink being of the same intensity, also the B&W part of the eye causes fading if you dont move your gaze. Staring at the centre dot causes only the B&W part of the retina able to see the pink dots, and without colour the dots fade into the background due to being the same intensity.
The green dot appears because the picture moves in steps (12 steps in all), when one of the pink dots dissapears, your eye sees something has changed, and tries to estimate its colour from the surroundings. Just so happens on this pic it gives you a green dot.
Theres the biology, now prove me wrong