Some time ago I found this picture and worked on it until I could generate similar animations on my own. It's tricky: the guy that disappears is gone not because it's divided in two parts and both are made into different guys; but because lots of little parts are made into different guys, so making a disappearing complete guy. That is: lots of different parts in different guys disappear in a very obvious way, and if you sum all of them, they complete a single guy (it's not easy to explain, but there is not a single disappearing guy, but a lot of tiny parts of different guys disappearing at once).
Try to make it work on paper to understand how it works. Notice that the upper half of the "paper" should be cut in two halves, and those two halves _have_ to be of a different size.
Not an optical illusion. Twelve guys really become thirteen. But they have to pay a price for that: they're somewhat shorter, their heads are slightly smashed in, etc. Basically the same as what happened when hunter-gatherers switched to agriculture: more people but less healthy.
edit: if you can't let this go either, save yourself a few minutes: http://tlrobinson.net/misc/illuuusions.png