  Simple closed curves in the plane can be mapped to nontrivial knots under the
action of origami foldings that allow the paper to self-intersect. We show all
tame knot types may be produced in this manner, motivating the development of a
new knot invariant, the fold number, defined as the minimum number of creases
required to obtain an equivalent knot. We study this invariant, presenting a
bound on the fold number by the diagram stick number as well as a class of
torus knots with constant fold number. We also pursue a characterization of
those foldings which admit nontrivial knots, giving a proof that no "physically
realizable", or proper, foldings can admit nontrivial knots. A number of
questions are posed for further study.
