Double crystals

The lowest-energy way to enclose and separate two planar regions of prescribed areas is found, where the energy is given by the l1 norm ('Manhattan metric'), in which horizontal and vertical directions use less energy than other directions, as in some crystals. With the assumption that interfaces carry a fraction lambda of the energy of exterior faces, it is proved that there are three possible types of energy-minimizing double crystals. The dependence of these three types of lambda as well as the ratio of the areas of the two regions is discussed, and some paths for further study are suggested.