The trick is to focus slightly behind the image, then you see it as it really is, no optical illusion. Which, btw, is a good method to use when looking at something which is not clear, you look at the whole and not parts of it. You can use the same trick with a picture that is blown up out of focus or delibrately pixellated - you look at the whole image and not its structure, and you will see more that way.
If you focus on this image then your brain tries to add depth, and then attempts to fill in the gaps between the missing parts of the squished overlapping circles. Because the color sequence is alternating you process it as movement. At least, that is what I think.
I bet it wont work if the color sequence is the same in all the sets of circles.
