Weaving Video After Effects

I guess it depends on how reusable and versatile you want it to be. As with most of this stuff, 90 % of the work indeed goes into creating custom mattes, displacment maps and so on. I could think of several ways to do it such as Card Dance, Shatter or conventional displacment maps along with matching custom mattes which could be created in a million ways, including the Mosaic effect, Venetian Blinds, other checkerboard-y stuff, but unless I were to actually sit down and spend the hours figuring out the details I can't offer any more concrete advice. This is definitely a lot more than just stacking a bunch of effects and you could end up with lots of pre-comps just for a single shot.

Mylenium

I think the checkerboard effect is probably what you're after, although you might also want to check out Card Wipe.