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In our more general setting, including gravity and a stabilization field, we find numerically that there exists more than one solution for the same Lagrangian in a large portion of the parameters space. In Fig. 6 we show two such solutions. Note that these solutions would be extremely difficult to discover by randomly guessing initial-boundary conditions. To be more methodical we follow the same procedure as before to find level-curves of the final- boundary conditions, shown in Fig. 7. Again, solutions to a particular action will be given by the intersection of the appropriate contours for the brane mass squared µ 2 and brane tension Σ$_{2}$. As can be seen, there are regions in which some contours intersect at more than one point, showing that multiple solutions for the same action are possible as expected. In 

