Many plane-filling curves can be given in terms of L-systems. In this article, our starting point is Dekking's folding curves, which extend the Heighway fractal dragon construction. An interesting aspect of these curves is their generally fractal boundary. We show how to find the L-system for only the boundary. This gives a more direct way to obtain the boundary than first computing the whole plane-filling curve, and then extracting the boundary. The final section discusses the order of operations required to find the boundary with this method; sequences of the boundary length; and a new example of computation of the Hausdorff dimension of the boundary of one of the curves under consideration.