The Origami Revolution

PBS Airdate: Feburary 15, 2017

NARRATOR: Origami: the ancient art of paper folding; it's been practiced for centuries, but now it's sparking a scientific revolution. The power of folding is shedding new light on our world and propelling a wave of innovation.

ERIK DEMAINE (Massachusetts Institute of Technology): Folding lets you take an object and completely change its shape from one thing to another, sort of like Transformers or The Terminator T-1000 robot. That's all science fiction, but origami offers a way to make that actual science.

NARRATOR: Nature itself is a relentless folder. Origami patterns can be found everywhere, including on the surface of the human brain. Even the proteins within our cells must be folded correctly to function.

A new appreciation of origami is emerging, as engineers and designers apply its patterns to explore space and reshape the world around us. By mastering the rules of folding, scientists are creating novel drugs, shape-shifting robots and materials with extraordinary properties.

Right now, on NOVA, The Origami Revolution: a tradition lasting centuries, changing slowly, until now.

In her studio, Tomoko Fuse invents a new kind of origami, adding a modern touch to the art of folding. As she transforms a single sheet of paper into a three-dimensional sculpture, one can glimpse an infinity of possibilities. A folded piece of paper can change in size and shape and become something totally unexpected.

As the power of folding is discovered, origami is becoming an invaluable tool for science. At NASA'S Jet Propulsion Laboratory, engineers are using an origami pattern to build a Star Shade. It will deploy in space, expanding to about half the size of a football field. The shade will block enough light so that a telescope can detect distant planets that would otherwise be too hard to see. It's one of many surprising applications of the origami revolution.

In Tokyo, an international conference on the latest trends in origami research is attracting both artists and scientists. On exhibit are the multitude of ways a sheet of paper can be folded into a three-dimensional object.

Traditional origami patterns, like the classic crane, have fewer than 30 steps, but modern patterns can have hundreds, posing complex geometry problems.

One researcher exploring this new field is mathematician and origami artist, Erik Demaine.

ERIK DEMAINE: Origami is challenging, from a mathematical perspective. It has this core underlying geometry of lines and points and folds. And there's really stringent constraints on what you can do with the material, which is folding, no stretching, no cutting. And it's kind of mind-blowing that this simple operation of folding lets you transform a boring square of paper into super-complicated, crazy, 3D shapes.

NARRATOR: Another artist and pioneer of the origami revolution is Robert Lang, who lives east of San Francisco. With degrees in physics and engineering, Lang's scientific training has helped him radically modernize paper folding.

He starts by transforming an image, in this instance of a black widow spider, into a simple skeleton. Then, he breaks with tradition and uses a computer program to create a crease pattern for folding it.

ROBERT J. LANG (Physicist and Artist): So, that's now a crease pattern for a spider, and it's got all the parts. You can see, roughly, the allocation, by these shapes, that each of these hexagons is outlining a leg. So, there's a leg, front leg, middle leg, middle leg, back leg, back leg, middle leg, middle leg, front leg. This will be the body, in the middle. There's actually more paper here than we need to make a body, but, since the body is large and bulbous, it'll be easy to hide. And so overall, that's the design.

NARRATOR: The digital crease pattern is sent to a laser cutter, which etches the design on an ultra-thin sheet of paper. The final stage of folding will be done in the time-honored way, by hand. Lang's early software could only generate patterns for stick figures with bodies and limbs, like bugs or people, but creating a mathematical tool for designing made it easier to tackle complex folds.

ROBERT LANG: I started origami, when I was about six, when I encountered some instructions in a book. Interestingly and coincidently enough, one of them was for a spider. I was hooked. And I think the thing that hooked me was the idea that all you needed was a sheet of paper and knowledge, nothing else. You didn't need extra parts that could wear out, just paper, and paper that was available anywhere. This spider shares something in common with most other origami figures, even going back to that very first figure I folded. This is still, after all this manipulation, an uncut square of paper.

NARRATOR: Lang's analytical approach allowed him to fold a truly credible origami spider. As he tackled increasingly complex shapes, mathematics was the tool that let him explore new designs.

ROBERT LANG: This new field of geometric, or abstract, origami relies upon some pretty advanced mathematical analysis. One of the leaders, perhaps the leader in that field, is Tomohiro Tachi, who is a professor at the University of Tokyo.

NARRATOR: Tomohiro Tachi is attempting to push computational design even further. He is writing a software program that will create crease patterns for any object, not just stick figures. He is collaborating on the math with Erik Demaine.

Their project began after Tachi folded a sheet of paper into a three-dimensional teapot, mastering its facets and curves.

It may seem simple, but it's not.

TOMOHIRO TACHI (University of Tokyo): So, this is a challenge to make this type of 3D structure. This is quite complex. But actually, at that time, I did not use a computer, so I just solved the geometry by my hand.

ERIK DEMAINE: And it's, like, kind of mind-blowing, because it doesn't look like any origami art that we've ever seen. It's, like, a whole new type of folding that gives you this crazy 3D form. And there's undercuts and reflex angles, convex angles. There's a lot going on in the teapot.

TOMOHIRO TACHI: Once I folded this one, I knew that it is possible to make almost anything.

NARRATOR: Inspired by the teapot, Tachi's software, called "Origamizer," converts a 3D model into a 2D crease pattern, which can then be folded into the desired shape. Gray spaces are where excess paper can be hidden.

Erik Demaine shows how it works.

ERIK DEMAINE: Our simple model is…we are going to fold just three squares out of a cube, a little corner of a cube. We're going to fold it using this crease pattern, which we've computed using Origamizer. So, let's do some folding.

Okay, the main idea is pretty simple. We are folding along these bisectors to bring two edges of the two squares together, so, something like this. So, there, the two squares are good. Getting all three at once, though, that is a little trickier. Yeah, so we made exactly what we wanted. I guess I had some extra material out here. I could just fold that away. That's not too bad.

NARRATOR: Origamizer can also compute the angles and folds needed to create curved surfaces, as seen in this doughnut.

ERIK DEMAINE: But it didn't always work. So, sometimes you'd give it a 3D model and it says, "I don't know how to fold it."

NARRATOR: To perfect the software, Tachi and Demaine are now working on a universal proof. The goal is to figure out the exact mathematical steps that can turn any 3D surface into a 2D crease pattern and tell you how to fold it.

TOMOHIRO TACHI: Erik and I will prove that any shape is foldable from a sheet of paper. So, we are very excited about that.

NARRATOR: If they succeed, Origamizer could be an invaluable design tool.

ERIK DEMAINE: As a geometer, when I look around in the world, I see geometry in everything. I think about decomposing everyday objects into geometric components. And Origamizer lets you take some complicated, real world thing, translate it into geometry, so then it could be represented on a computer, and then the mathematics can take over and say, "Okay, here's how you fold this geometry."

NARRATOR: Advances in the mathematics of origami are opening new possibilities. Folding is being applied to biology, physics and engineering. It's revealing a new way to control matter, one that resembles nature's strategy for building.

Long before humans existed, the natural world was folding. So how does it do it?

In the southwest of France, artist Vincent Floderer has been observing the folding patterns in nature.

VINCENT FLODERER (Origami Artist): On this bank, I can find folds of the most basic kind. For example, each blade of grass is built by parallel creasing. It has a single fold in the center, surrounded by parallel lines.

NARRATOR: Floderer has discovered an amazing way of folding paper: crumpling it. This means bending the rules of traditional origami.

VINCENT FLODERER: Origami means folded paper, and that is exactly what I do. Even though I'm just crumpling it up, it really is folding with a lot of creases. And the work can have hundreds, thousands or millions of folds, in some cases.

ERIK DEMAINE: Vincent's work is really amazing in the way that it combines geometry and art and physics. I mean, the end result looks kind of chaotic and random, but if you watch the process of how he makes them, it's actually extremely structured. Still not fully understood mathematically, but practically, he can make incredible, beautiful and very natural looking forms that sometimes you can't even distinguish from their real biological counterparts.

NARRATOR: But how does Floderer achieve such realism?

VINCENT FLODERER: For me, this is a sequence of rectangles. It looks strangely like a pinecone. But in reality, it is a pure geometric construction, which self-assembles itself. My crinkle technique is based on this self-assembly, which you can see also here.

This looks almost like a real sponge.

These patterns are flexible, they can vary, change, but they are, in principle, just a sequence of hexagons.

NARRATOR: Floderer's work captures the geometry he sees in nature, but why is nature such a relentless folder in the first place?

It's a question scientists are grappling with.

Mathematician and scientist L. Mahadevan is studying the origami-like folding that is all around us in nature. Today, he's taking a close look at the buds that grow on beech trees. The leaves are packed in a tiny space before they blossom. Only once they begin to grow, do the leaves start unfolding.

L. MAHADEVAN (Harvard University): Think about the leaf as a relatively thin surface, and now it is growing. And it is growing, potentially, in both directions. So, the thin sheet is growing faster than the bulk tissue. One possibility is for the thin sheet to just bend in the two directions, so, to form something, which looks like the surface of a balloon, for example, relatively smooth. But if the sheet does that, then it will have to pull on the substrate a lot, because it has to come out, and so, that is energetically very expensive.

And so, there's another potential solution. And the other potential solution is to have a much larger number of small bends. So, you can see now, that I will have bends in one direction and I'll have bends in the other direction, sharp bends. And in between the sharp bends, the sheet remains flat. And the consequence is this structure.

NARRATOR: This arrangement is called a Miura-ori fold. The beech tree masters this fold countless times every spring.

In general, plants fold when they need to squeeze a large surface into a tiny compartment, but it's not only plants. Animals and insects have also evolved to use the techniques of folding.

Consider the Thai horn beetle. An origami-like pattern allows its wings to unfurl for flight.

L. MAHADEVAN: I unfold it. Voila!

So, there is this rather large and very beautiful wing, and I'll just show you in reverse. The same thing when I fold it, it tucks away, and then it's packed. So, this is the way the wing was folded, and then it opened up, something like that; really beautiful.

NARRATOR: It seems evolution has favored origami-like folding patterns repeatedly. They are even present in the human body, including the surface of the brain.

Back in Mahadevan's lab, an experiment is underway to mimic the growth process of the brain. A model is made of gel, which has an inner core and an outer shell. When immersed in liquid, the outer shell expands faster. However, because it's held back by the inner core, the outer shell wrinkles and folds.

The experiment shows that the folding patterns found in the brain are created when different layers grow at different speeds. Folding allows the brain to increase its surface area and capacity inside the skull.

ERIK DEMAINE: It's kind of annoying, because nature does it so well. We have such a hard time doing folding, and nature does it all the time. It's our challenge to reproduce that in an engineered way, but we have sort of the shining example that it can be done.

NARRATOR: That challenge is being taken up by scientists like David Baker, whose work shows how folding is critical for life.

Folding is how D.N.A., the six-foot-long molecule of heredity, fits inside the nucleus of a cell. Unfolding D.N.A. starts a process that allows genes to produce proteins, the molecules that keep our bodies running. And how a protein folds into a specific shape determines how it will act—as a hormone, perhaps, or a disease-fighting antibody.

DAVID BAKER (University of Washington): Proteins mediate essentially all the important processes in your body, from digesting food, to managing the electric currents that are responsible for thought, to movement, to making molecules inside you. So, basically, everything that's going on at the molecular level in your body is being mediated by proteins.

NARRATOR: When a protein folds correctly, it fits like a key in a lock and starts a biological process in the cell. Misfolded proteins can't function and can trigger diseases.

Our bodies have about 100,000 proteins, built from 20 amino acids and strung together in a seemingly endless number of ways. They are often visualized as ribbons of color.

DAVID BAKER: But proteins don't stay as these long, straight chains of amino acids. Instead, they fold up into very elaborate, precise structures. And it's having those precise structures that is critical for how they function, so, this folding process is absolutely essential to life.

NARRATOR: Baker's lab is trying to solve one of the hardest problems in biology: predicting how strings of amino acids fold up into three-dimensional proteins. In some ways, it's similar to origami.

AARON CHEVALIER (University of Washington): So, here you have a piece of origami paper that's been folded and unfolded. And what you don't know from seeing these creases is what the final shape is going to be at the end. And so, this is what we'd call, in the protein engineering world, a structure prediction problem. We need to be able to predict this structure. And what you do is you have to be able to kind of simulate the folding of the protein, or, in this case, the origami paper, to see what shape it will come out at the end. So, in prediction world, this fold pattern or crease pattern, will result in this paper crane.

NARRATOR: To figure out a protein's shape, Baker takes its amino acid sequence and uses a computer program, called Rosetta, to search for all the ways that sequence can fold.

AARON CHEVALIER: It's really physics forces that are happening on these molecules that cause them to fold up. And the number of ways that you can fold a protein is in the millions or billions or trillions. The number's huge. But there's really only a few distinct correct answers, so, you have to try a lot of the different fold creases and sequences, until you come up with the correct solution.

NARRATOR: The goal is to find a protein's most stable or lowest energy state.

DAVID BAKER: Once they're in that lowest energy state, they stay there. That's the state they're stable in. So, if you take a protein, and you pull it apart using chemicals or force and then you let it go, it will go right back to its shape again.

NARRATOR: Determining a protein's structure requires enormous computing power, so Rosetta has a crowd-sourcing application that enlists the help of computers around the world. There is even a game, called Foldit, which challenges players worldwide to solve protein-folding puzzles.

So far, Baker's lab has identified the structure of about 600 of the 15,000 known protein families.

DAVID BAKER: The exciting thing, now, is that we can build new proteins in the same way that we build bridges or anything else in the modern world, from scratch, for exactly the purpose that we want.

NARRATOR: Novel proteins could generate new drugs to attack pathogens and fight diseases. One of Baker's first projects was to target a protein on the surface of the flu virus.

DAVID BAKER: There are a couple regions on the flu virus where, if you can attack it, it's got an Achilles' heel. You can prevent it from killing people and animals. And so we thought this would be a really good challenge. Could we design a protein which folded up in such a way that it had a shape that was complementary to that of the flu virus?

AARON CHEVALIER: Because the proteins would bind to the influenza virus in such a way as to inhibit it from invading cells, they would lock it down in an inactive state; just the act of binding. So, it was, basically, one protein coming and fitting in another protein in a very specific way.

NARRATOR: On the computer, they experiment with protein shapes that might bind to the flu virus and disable it. It's essentially like starting with a blank key, and carefully filing the right grooves so it will fit into the lock.

DAVID BAKER: So now, we know what shape we want to make. And at that point, it's just science fiction. What you have is an amino acid sequence on the computer, and you don't really know whether it actually does what you designed it to do. But the beauty of it is that we can very quickly actually produce that protein in the lab and see whether it works.

NARRATOR: Finding out involves a complicated series of steps. The amino acid sequences are put into bacteria, which mass produce the new proteins. Next, the novel proteins are mixed with the flu virus. Then, a special machine runs them through a sorter to identify which proteins bind most tightly to the virus. They are the ones that make it above the line.

DAVID BAKER: This was the big moment. And what we saw here is that there are quite a substantial number of them which are binding the flu, which is very exciting.

NARRATOR: Finally, the winner is selected and then built, one amino acid at a time, to make a new drug.

DAVID BAKER: This is a blowup of that three-dimensional structure of the virus. Each of these round things is an atom, to give you a sense of scale. So here's the flu virus. Here's the designed protein. And they fit together perfectly, like a lock and key.

NARRATOR: Mice were given the new protein, either before or just after being exposed to the flu virus.

DAVID BAKER: And they didn't get sick. Now, obviously, humans are very different from mice. But what we have now is a proof of concept that design proteins can be effective, at least in mice.

NARRATOR: It's unclear how our immune system will react to these novel proteins. But Baker's lab is moving ahead, developing proteins that target H.I.V., break down gluten in the stomach or deliver drugs to cancer cells. For Baker, protein origami is the future of drug development.

Across the world, the power of folding is inspiring medical research. In Japan, Kaori Kuribayashi is trying to make medical devices simpler and better. She's collaborating with a team of scientists to improve a surgical implant used to treat heart disease, the stent.

It's placed inside a clogged artery to keep blood flowing. To open the artery, the stent must be inserted in an inflatable balloon. Kuribayashi saw an easier, potentially safer solution.

KAORI KURIBAYASHI-SHIGETOMI (Hokkaido University): So, I used the origami technique to produce a new type of a stent graft, but instead of the normal tube, they have this pattern. Therefore, we can fold it very compactly, and then we can put inside a body to support weakened vessels.

NARRATOR: This way, no balloon is needed to widen the artery. The origami stent, made of a special metal, unfolds automatically when exposed to the body's heat. So, a small sheet of metal, folded in the right way, could one day save lives.

Besides medical research, origami designs are also being used in engineering, to design tiny drones and micro-robots. Building such miniaturized machines poses a unique set of challenges.

ROBERT WOOD (Harvard University): Early on, when we were thinking about how would we actually build these classes of robots, there's really no manufacturing methods which would be amenable to the types of scales that we're talking about. You know, things that are at the size of an insect or smaller in feature sizes? And folding turned out to be a fantastic method to create these small-scale devices.

NARRATOR: In the robotics lab at Harvard University, students first design larger robots, using sheets of cardboard or plastic and the principles of origami.

DANIEL AUKES (The Polytechnic School at Arizona State University): And so, origami is a great starting point to understand how something is going to move, how something's going to fold up, and then we get to break all the rules, because now we can start cutting; we can remove material; we can connect it in different ways.

NARRATOR: By combining folding and cutting, robots can pop up from flat sheets of material. Once the design is perfected, the scale of the robot is reduced.

It's an approach that simplifies construction.

ROBERT WOOD: If I think about an example of assembling a car, you know, however many thousands or tens of thousands of components go into that? Now, if I want to assemble something maybe not that complicated, but of similar complexity, down on the scale of an insect or even smaller, you're not going to be able to do the sort of nuts and bolts approach. You're not going to be able to hand-assemble hundreds or thousands of components together.

NARRATOR: Many of the micro-robots can unfold automatically. As the temperature rises, this sheet transforms to a three-dimensional object.

The components can be pre-cut and then fold up on their own, like this material, which can remember its shape.

ROBERT WOOD: In our case, we use folding as the self-assembly means. That allows you to do things faster, more precise. The faster really is actually very important, not just for obvious reasons, but if it takes you weeks to develop a single prototype, then you get very conservative in your designs. But, if we can go through prototypes in a matter of hours or even if it's a day, then we can build all sorts of crazy things and try all sorts of different designs and not worry about failure.

NARRATOR: The research has produced an array of micro-robots and drones with different abilities. Here, an electrical current heats the hinges and the device unfolds.

In the future, smart sensors will allow these machines to take on useful roles.

ROBERT WOOD: They're small, they're relatively cheap, and they're agile, so maybe they could be used in disaster sites and getting into, you know, collapsed buildings and trying to find survivors. That's certainly an exciting application.

NARRATOR: With an onboard power source, this flying drone could be used for surveillance, monitoring crops, weather or assessing areas hit by disasters.

To save energy, it can use electrostatic forces to rest on nearby surfaces.

ERIK DEMAINE: Traditionally, you think of building robots out of lots of really complicated, sophisticated 3D parts. And origami sort of simplifies this down to this common medium of, "What can we make out of a flat sheet of material?" And also, having everything connected into one big sheet, simplifies a lot of the problems of just holding the robot together, giving it structural integrity. And so this could change the way that we manufacture objects.

NARRATOR: As origami moves into industry, engineers are exploring the power of folding in terms of sheer strength.

In Germany, Yves Klett is creating innovative materials that are light and surprisingly strong.

YVES KLETT (University of Stuttgart): We were looking for new lightweight materials that could be used for construction, and we found these structures, which are inspired by origami. They are ideal for providing structural support in a sandwich-type construction, like this one. There are two surface layers, and in between, we have a an origami folded core. And this structure is tremendously stable. It's also very lightweight. It can withstand very high loads, so I can now no longer crush it. The core alone could not withstand the pressure, but in combination with the layers, it creates a powerful structure.

NARRATOR: To test its strength, Klett will see if his car can crush it. A section that weighs about an ounce can withstand the weight of one ton.

Klett is now testing origami designs using durable, high-tech materials like Kevlar paper, carbon fiber composites, as well as plastic and aluminum foils. He is hoping that origami engineering could give these materials new properties, useful for industry.

YVES KLETT: Here, we have a sandwich structure that can be used in the main section of an airplane. The hull has a radius of six feet, and this core integrates itself perfectly in the geometry. This way we get a structure that is very light but very stable. We can guarantee that there is no water accumulating in the hull, and there is space to integrate electric cables and air conditioning between the folds.

NARRATOR: Klett believes that origami-based structures could revolutionize aircraft design, by dramatically reducing the weight of an airplane. This would significantly cut down on fuel consumption.

He also hopes these new materials might one day provide an alternative to concrete or steel for green building.

But there is one issue that needs to be solved: machines can cut the lines of the crease pattern, but it's difficult for them to do complex folding. Until recently, Klett used a basic mold to speed up the process. To make production even faster, he is testing a new machine that completely automates the folding. It's an important step to applying origami design on an industrial scale.

RoboFold, a company in London, has come up with another solution. They've modified industry robots to do something previously too difficult—folding metal into curved structures. This technology can bend metal into extremely precise shapes, like the curved body of this model car.

ERIK DEMAINE: In the last few years, there's been a lot more excitement about the engineering and science applications of origami, that you can make practical structures that fundamentally change their shape: either going from a flat thing or very tightly folded thing and being able to deploy into a different size or completely change their structure, change from one shape to another, just by folding. Folding gives you a way to think about shape transformation.

NARRATOR: But how do you design practical products that can change their shape?

It's a challenge engineering students at Brigham Young University are grappling with, as they apply origami patterns to new inventions with real-world applications.

LARRY HOWELL (Brigham Young University): A lot of people, when they hear "origami" think, "I did origami when I was in second grade. Why are these engineers at this engineering lab doing research in origami?" But when you look at it from an engineering standpoint, there's a lot that we can learn, whether that's new levels of compactness, new types of motions. The complexity of all these things coming together give us the potential to create totally new products that were not possible before.

NARRATOR: Origami gets its motion from the bending of flexible parts instead of something more traditional like a hinge or bearing. Of course, it's a lot easier to see how this works with paper, which can change its shape with ease.

LARRY HOWELL: Paper's an amazing material, but, unfortunately, it's not really the material that we want to use for most engineering products. We need things that are more durable and suited to the applications that they will go in. So, that becomes a real challenge. How do we now get those same kinds of motions in other materials, without breaking?

NARRATOR: To that end, mathematicians and engineers have created a new field called "thick origami." Using conventional cuts, layers or hinges, rigid or dense material can be folded, a technique that uses origami to make something that can even stop bullets.

Starting with paper, students fold models using a classic Yoshimura pattern. It produces a shield that unfolds easily and quickly. In early prototypes, bolts or tape hold the panels together. Then it's time to make a barrier that's actually bullet-proof.

They start with Kevlar.

LARRY HOWELL: Kevlar comes as a fabric, and we need 12 layers of Kevlar to stop a barrage of bullets. But we also need it to be flexible enough that it can move, but stiff enough that it can stand on its own. So, we've added these panels of lightweight aluminum and plastic. But the panels aren't providing any ballistic protection. It's the Kevlar.

NARRATOR: The panels, glued to the Kevlar, form the pattern. It's the spaces between the panels that allow the barrier to fold. Layers of black, ballistic nylon protect the Kevlar from the elements.

The first shot comes from a 9-millimeter handgun. The force might pierce the barrier and knock it down, but it doesn't. Next comes a .357 Magnum, followed by a .44 Magnum, the most powerful handgun police encounter.

The barrier holds; only an assault rifle can pierce it, at least for now.

LARRY HOWELL: Our colleagues in Homeland Security tell us how valuable it would be to have a ballistic barrier that could deploy very quickly and could be a lot more usable than these large, cumbersome, heavy shields that they use now.

NARRATOR: Thick origami is also finding a place in outer space, as a solar array.

ROBERT LANG: Space is one of the places where origami has a great role to play, because you have this problem of something that needs to be small, when it goes up into space—it needs to fit inside a rocket—and then, once it gets to its destination in space, it needs to be larger. And so, when you have those two requirements, folding provides a very good solution for making the transition between those two states.

NARRATOR: In development is a revolutionary way to power NASA missions, based on an origami flasher pattern. A solar array wraps around a rocket during launch and opens in space.

LARRY HOWELL: So, this was quite a challenge, to go from a paper origami pattern to a solar array that would cover six lanes of traffic and provide more than twice the amount of power than all of the solar panels on the International Space Station, combined.

NARRATOR: Silicon solar panels will make up the array. They'll be glued to a flexible film called Kapton. To reduce the number of parts that could break in the harsh environment of space, electrical circuits will be printed directly on the film. 01:45:36

LARRY HOWELL: In the end, it's hard for someone outside to actually see the origami inside of it, but it's really there. It's just that our goal was to accomplish the final product, not necessarily to make the origami obvious.

NARRATOR: Can the principles of origami even help scientists understand the nature of the universe?

At Johns Hopkins University, astrophysicists are studying the distribution of matter in the cosmos. Mark Neyrinck believes an origami model can help represent that distribution.

We can only observe visible matter, shown here: the material that forms stars, planets and entire galaxies. But this is only part of our universe. There is also a mysterious substance called "dark matter" that's invisible. Astrophysicists have detected it only indirectly, but many believe that it forms the hidden skeleton of our universe.

MARK NEYRINCK (Johns Hopkins University): The dark matter started to accumulate up into clumps, almost immediately after the Big Bang. And we wouldn't have as much structure as we see in the universe today, if there hadn't been this dark matter. The normal matter started to form structures based on the groundwork, the skeleton that the dark matter laid down right away. So, the dark matter is really the basis of understanding the structures that we see today.

NARRATOR: According to Neyrinck, the unseen dark matter folds like origami. Gravity gathers and crumples together the dark matter sheet, in places where ordinary matter is drawn, to form galaxies and stars. Pleats in the sheet, called filaments, poke out from each galaxy, aligning its rotation with neighboring galaxies in a pattern similar to an origami twist fold.

MARK NEYRINCK: In a twist fold, you have a small polygon, so, let's say a triangle. So, here we have a triangle, and going from the unfolded to the folded state entails twisting that triangle.

Even though this is a dark matter structure, it creates regular matter toward that. So, the galaxy, here, would form here. It's a strong approximation that the universe forms, like an origami model.

In particular, the way the various elements of the cosmic web are spinning are very explicit in this model. We see in the universe that neighboring galaxies tend to be rotating in the same direction, and that actually relates to this origami model.

NARRATOR: Neyrinck is now working with students to create a more complex model that captures how dark-matter folds intersect to build the cosmic web.

The dots on the paper represent the galaxies, as observed by telescopes. Whenever the paper is overlapping, there is an accumulation of dark matter, and therefore, a greater number of galaxies. Astrophysics is now being enriched with a new vision of a folded universe, inspired by the ancient art of origami.

ROBERT LANG: So, by thinking about origami and by how we generalize origami into broader mathematical spaces, we can learn things that turn out to apply to the real world that we live in.

You would think that as a field of exploration, origami would have been played out long ago, but the opposite is true. It's as vibrant and growing as ever. And furthermore, as we look to the future, there are no limits on the horizon of what's possible, either artistically or in the applications of origami-inspired design.

NARRATOR: Back at the Massachusetts Institute of Technology, a 10-year endeavor is coming to an end. Erik Demaine reviews the final details of the proof he is about to publish with Tomohiro Tachi. It has taken 60 pages to write a universal algorithm, called Origamizer, which shows the precise mathematical steps needed to fold a flat surface into any three-dimensional object.

As a proof, Origamizer is a theoretical coup, but are there real-world applications?

ERIK DEMAINE: Yeah, it's kind of mind-blowing. For example, maybe you're an engineer, you've designed a robot on your computer, and you want to build it; or you're an artist, and you've sculpted a model of a face, and you want to translate it into paper, Origamizer gives you a way to do that. So, it's really exciting. You can make anything by folding.

NARRATOR: According to Demaine and Tachi, Origamizer will translate a 3D model into a precise blueprint of how to fold any object out of one sheet of material. The crease pattern generated by the computer can then be printed on paper. Fold all the lines, and eventually, you will get your desired 3D structure.

In the future, Demaine and Tachi believe, folding can also be automated, but it all comes down to working out the math.

ERIK DEMAINE: The nice thing about approaching origami from a mathematical perspective is you get at kind of the core of what is possible, just, sort of, universal truths for any kind of folding. It doesn't matter whether you're folding paper or sheet metal or whatever. There're some core principles that just never change, and you have to follow those rules. And so, if you show that something's impossible mathematically, then it's not going to be possible, no matter what material you try to translate it into.

NARRATOR: Origami is helping us understand the universe, from the vastness of outer space to the core of our cells. The journey began with a unique mix of art and science. How could one imagine simply folding a flat surface would help us discover the world around us? Yet, it appears, from whatever level we observe the universe, the logic of folds is at work.