# Math, Astrophysics, and Paperfolding: The Origami Cosmic Web

Math, Astrophysics, and Paperfolding: The Origami Cosmic Web[1]

At Johns Hopkins University, Mark Neyrinck leads students to create a representation of structures outlined by observed galaxies in the universe. They used large-format inkjet printer to print folding lines and galactic data onto glassine paper. (See image at left.)

For several years Mark Neyrinck has been studying the behavior of infant galaxies using a non-traditional approach: the science of folding. This article, recaps and examines how origami mathematics can be used to understand the Universe.

My [Mark Neyrinck] personal origami voyage began with a colloquium by Robert Lang at the Space Telescope Science Institute in Baltimore. I was working on a new geometrical method[2] of detecting structures that correspond to galaxies in computer models and I was astonished to see a connection to paper origami. I wondered: could origami mathematics be useful to understand the universe?

In Einstein’s theory of general relativity, gravity comes about through distortions of a four-dimensional spacetime “sheet”. But gravity also causes a different kind of sheet to distort and fold: the three-dimensional cosmological sheet of dark matter. It turns out that the way this dark matter folds up to form structures like our galaxy is not unlike origami.

A fresh sheet of origami paper has no folds. Similarly, at the Big Bang, when matter was nearly uniformly distributed in the universe, the cosmological sheet had no folds. But some locations had more matter than others. There, the sheet further bunched up, drawing matter from all around to form galaxies. Elsewhere, the sheet stretched out, forming voids between galaxies. The rich got richer, the poor got poorer.[3]

What do I mean by “folding” for the cosmological sheet? Usually, 2D origami paper folds up in 3D. The 3D cosmological sheet folds up in 6D! But thankfully, a lot of the process can be understood without thinking in 6D, which is impossible! Think of a 2D origami work that afterwards can be squashed into a book without further creasing; much of the structure can be understood with a 2D picture of it. Similarly, the cosmological sheet “folds flat” in 3D, and much of the structure can be understood in 3D.

This folding process is one reason that a galaxy is not just a pile of matter, unstructured and random. Instead, matter folds up to construct it, much like an origami twist fold. And just as pleats must stick out of a folded-up origami twist, filaments of matter must stick out of a galaxy after it forms.

For animations illustrating how 3D twist folds operate, see http://skysrv.pha.jhu.edu/~neyrinck/irrotet, and http://skysrv.pha.jhu.edu/~neyrinck/rotet.mov