A "self-tiling set"

This one, found in the Futility Closet, consists of four tiles, each of which can be constructed by smaller versions of the same four tile shapes.  I then found this example at Wikipedia:

In geometry a self-replicating tiling is a tiling pattern in which several congruent tiles may be joined together to form a larger tile that is similar to the original. This is an aspect of the field of study known as tessellation. The "sphinx" hexiamond is the only known self-replicating pentagon. For example, four such concave pentagons can be joined together to make one with twice the dimensions.

Solomon W. Golomb coined the term rep-tiles for self-replicating tilings.