  We investigate the optimal arrangements of two planar sets of given volume
which are minimizing the $\ell_1$ double-bubble interaction functional. The
latter features a competition between the minimization of the $\ell_1$
perimeters of the two sets and the maximization of their $\ell_1$ interface. We
investigate the problem in its full generality for sets of finite perimeter, by
considering the whole range of possible interaction intensities and all
relative volumes of the two sets. The main result is the complete
classification of minimizers.
