  We investigate the formation of bound states made of two interacting atoms
moving in a one dimensional (1D) quasi-periodic optical lattice. We derive the
quantum phase diagram for Anderson localization of both attractively and
repulsively bound pairs. We calculate the pair binding energy and show
analytically that its behavior as a function of the interaction strength
depends crucially on the nature -extended, multi-fractal, localized- of the
single-particle atomic states. Experimental implications of our results are
discussed.
