The trick lies in starting with 2 identical copies of static and inverting the static in one of the images in the area you want to appear black. That way, when the copies are aligned the regular static is still just static, 50% gray, but in the other area the black pixels are aligned with the clear pixels and vice versa, so that part is dark.
Note that inverted static holds as much information as non-inverted static, that is, zero. Neither of the sheets of static contain an image of the cat. It's only by juxtaposing the two images that the information can be generated/retrieved.