I dont know the exacts, but a magic eye is just a picture or random pixels that have a 3d image hidden inside it, when you look through the picture, i.e, focus your vision into the picture, as you would a mirror, you see a picture in 3d more or less. The 3d picture is made from a picture that looks like a grayscale heightmap, which in a sense it is, the color determines how far into the picture it appears when you see it in 3d, so black is in the distance, and white is close to the screen. It would be possible to generate this as an animation.
Its something I always wanted to attemp my self, I mite give it a go, I will see what I can find, its fairly strait forward to generate and if I remember correctly the method and examples of are fairly available onlnie.