Houdini's most famous magical act was as an escape artist, but one of his other tricks, which some coauthors and I wrote about some time ago, involved origami-like constructions, in which a piece of paper was carefully folded, then cut along a single line, and unfolded to produce complex shapes. Erik Demaine has evidence that this problem dates back at least to early-18th-century Japan. In our paper (and others roughly contemporaneously by different sets of authors) we showed that any polygon can be cut in this way.

Anyway, now there's an open-source implementation called JOrigami, due to a Brazilian team of programmers involving Paulo Silveira, Rafael Cosentino, José Coelho, and Deise Aoki. Their web site has lots of pretty pictures of what look like quite difficult folding patterns...