These tiles have a remarkable property — by working together, the four can impersonate any one of their number (click to enlarge):

The larger versions could then perform the same trick, and so on. Here’s another set:

In this set, each of the six pieces is paved by some four of them:

By the fathomlessly imaginative Lee Sallows. There’s more in his article “More on Self-Tiling Tile Sets” in last month’s issue of Mathematics Magazine.