Erik D. Demaine and Joseph S. B. Mitchell, “Reaching Folded States of a Rectangular Piece of Paper”, in Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG 2001), Waterloo, Ontario, Canada, August 13–15, 2001, pages 73–75.
We prove that any folded state of a rectangular piece of paper
(a continuous isometric non-self-intersecting mapping of the paper into space)
can be reached by a continuous folding process, starting from the unfolded
state, while at all times being a valid folding.
In our model, the paper cannot properly cross itself, but can touch itself,
as in a flat folding.