  It has been known since 1996 that deciding whether a collection of creases on
a piece of paper can be fully folded flat without causing self-intersection or
adding new creases is an NP-Hard problem (Bern and Hayes). In their proof, a
binary state was implemented as a pleat, with the state corresponding to the
pleat layering order; states then interact via pleat intersections. Building on
some of the machinery of their result, we will present a method for
constructing an origami NAND logic gate, leading to a theoretical origami
Universal Turing Machine.
