  For each integer n, an n-folding curve is obtained by folding n times a strip
of paper in two, possibly up or down, and unfolding it with right angles.
Generalizing the usual notion of infinite folding curve, we define complete
folding curves as the curves without endpoint which are unions of increasing
sequences of n-folding curves for n integer. We prove that there exists a
standard way to extend any complete folding curve into a covering of the plane
by disjoint such curves, which satisfies the local isomorphism property
introduced to investigate aperiodic tiling systems. This covering contains at
most six curves.
