  Most known examples of doubly periodic minimal surfaces in $\mathbb{R}^3$
with parallel ends limit as a foliation of $\mathbb{R}^3$ by horizontal noded
planes, with the location of the nodes satisfying a set of balance equations.
Conversely, for each set of points providing a balanced configuration, there is
a corresponding three-parameter family of doubly periodic minimal surfaces. In
this note we derive a differential equation that is equivalent to the balance
equations for doubly periodic minimal surfaces. This allows for the generation
of many more solutions to the balance equations, enabling the construction of
increasingly complicated surfaces.
