Good question, arbitraryaardvark. An origami work probably merits copyright protection under U.S. law as a work of sculpture, unless due to the constraints imposed by paper-folding (there are only so many ways to fold a heart) merger doctrine bars the claim. As for the folding sequence, it would arguably fall outside the scope of copyright on grounds that it constitutes a "procedure, process, system, [or] method of operation," per s. 102(b). (The *illustration* of the folding sequence would of course be protectable under copyright, but I take it you do not question that.)
I know that THIS guy didn't copyright it. But how do I know that nobody else, since 1923 or whenever, didn't do so? If I went to the Copyright Office, could they give me useful directions on researching 85 years of folded paper heart shapes?
I could have used it yesterday!