Let about half the tiles move around in one direction (in front of the
slide plane), and the rest the other direction (behind the slide
plane).
Make sure tiles that rotate into each other's location go the same way
around, so that they don't pass through each others, which looks ugly.
Avoid z-fighting by not letting the tile end up exactly on top of the
one it is replacing, in case that one has not started moving yet.
Change-Id: I232b0f815412d5d575b0dde4df2d337288e645bb
3042270bc5