Many of the pattern forming features of ferrofluids, lipid monolayers, type
-I superconductors, and magnetic bubbles can be understood by treating them
as dipolar (uniformly magnetized or polarized) domains. Here, we investiga
te the early stages of pattern formation in a system consisting of two quas
i-two-dimensional dipolar domains, We calculate the linearized interaction
energy for these domains and find that the lowest energy states are those f
or which each drop has an indentation directed toward the other. These theo
retically preferred states compare favorably with results of experiments pe
rformed with ferrofluids.