Hi all, I've corresponded a bit with a cosmologist, Mark Neyrinck, who studies how galaxies and space-time evolve on the large scales of the universe, and he has noted some similarities between the rules of origami and how space-time evolves (spoiler alert: it folds). Recently he sent me a Mathematica simulation of an origami triangle twist in the 4th dimension, which I though was cool enough to share, so here it is:
http://skysrv.pha.jhu.edu/~neyrinck/TetCollapse/ This is a Wolfram Mathematica thing, so you'll need to download the CDF plug-in from the Wolfram website: http://www.wolfram.com/cdf-player/ To explain what you're looking at once the plug-in works: this is like adding a dimension to conventional origami. A flat sheet of paper is 2D, and if you fold it into a flat-foldable triangle twist, the result is also 2D, but some of the layers overlap in space. So here Mark has taken a 3D "piece of paper" -- I.e., a tetrahedron and folded it "flat" in 3D so it still looks 3D, but now some of the "layers" overlap. And that's what you're looking at. And just as a 2D flat sheet needs to move into 3D on the way to becoming a 2D flat-folded shape, this 3D tetrahedron would need to move into 4D on the way to become a flatly-folded 3D tetrahedral twist. (Since Mathematica doesn't yet have a plugin that renders in 4D, you don't get to see that part.) There's controls to play with dimensions and parameters. Enjoy! Oh, and Mark also suggests that if you're interested, check out their Origami6 submission, which they've posted on the Arxiv (as physicists tend to do with their papers): http://arxiv.org/abs/1408.2219 Regards, Robert
