We consider tilings of the plane by a lattice of translates of some co
mpact set A such that the union of k suitably chosen tiles is similar
to A. Affine and metric equivalence of such 'k-reptiles' are defined.
We show that for every k greater than or equal to 2 there is a finite
number of equivalence classes for which A is homeomorphic to a disk. T
here are three affine types of tiles with two pieces, and seven types
with k = 3.