Planes, boats, bow ties, frogs … Who has not ever folded a piece of paper to make one of these figures? Origami, known internationally as origami, is available to everyone. It might seem that this art of Japanese origin is mere entertainment, but the reality is far from that . Its creative and artistic aspects are clear, but its characteristics and enormous potential have also led it to become the basis for important technological innovations. In fact, if we carefully observe the world around us, we will find in the folds of nature a source of inspiration for origami. Accompanied by mathematics, it has become a research tool that is producing incredible advances .
The relationship between origami and geometric concepts appears naturally: when you fold a paper, you are drawing lines on it. If you look closely, you will be able to locate, among others, segments, angles, common points to segments, polygons, plane figures and three-dimensional figures. If you also identify the sheet of paper with a plane, giving it a coordinate system where each point is described as a pair of numbers, numerical concepts will appear: numbers and lengths. This other approach allows us to broaden the field of research and address problems related to origami through number theory – a branch of mathematics that studies the properties and relationships of numbers, most of which are integers.
After years of effort and research by engineers, physicists and mathematicians to formalize this relationship between mathematics and this art, theoretical bases and rules have been developed in order to determine when a figure can be built with this technique, what types of maneuvers can be performed and what characteristics an origami crafting has. This theory has been consolidated in the last fifteen years and is the basis for applications to various technological sectors.
At first, the steps to make an origami model were communicated orally. This made it difficult to pass models on from generation to generation, and some traditional models were lost along the way. It was not until the end of the 20th century when the Japanese Akira Yoshizawa endowed this field with its own symbolic language that allowed for the first time a new means of communication. This origami master invented codes based on lines and arrows that describe the maneuvers to be carried out in order to fold a model . The set of steps that describe a construction using these symbols is called a diagram . Parallel to the diagrams, a figure can be folded by interpreting its fold pattern –c rease pattern -, which shows the folds produced in the paper once the whole figure has been made.
No glue or scissors
Today, origami is an easily accessible art: through the internet, where diagrams, fold patterns and diverse audiovisual material are shared; or national origami associations, which organize regular meetings to share knowledge and creations. In Spain, the entity in charge of organizing these events is the Spanish Origami Association , which currently has about four hundred members.
The rules in origami design are clear in its orthodox version: a single paper and no glue and scissors. Likewise, the design is divided into two parts: the folding of the base and that of the details . The base is a geometric figure with a structure similar to the shape of our lens; and mathematics intervenes in its elaboration process. The details, meanwhile, transform the base into a more elaborate model and are the most artistic aspect of the figure. Techniques can start from known bases, but these are increasingly being used to create new ones.
There are various established techniques, among which we can highlight point-splitting or grafting , which serve to transform a single paper flap into several , all without the need to cut or paste; originally, they are used for the design of figures with various limbs. We will also find techniques to reproduce patterns in the form of mosaics and achieve a textured effect in the creations. Circle packing is also a common technique that uses circles to design bases that have different size flap combinations. Other examples of design methods are tree theory, which links a tree-like graph to the fold pattern of a creation and was curiously developed by two people at the same time – Japanese biochemist Toshiyuki Meguro and Robert J. Lang, key figure in origami worldwide–; and box pleating . This is a style that uses accordion-shaped pleats and is often used to fold boxes.
These techniques are applied both to develop artistic creations and to develop various applications in the field of technology. Starting from algorithms with basic folds in the valley or in the mountains, complex structures can be achieved; and, applied to other materials, such as metals –bronze or aluminum–, they are the basis for transferring the advantages and properties of origami to practical and real applications . The material’s own properties – lightness, strength, resistance, transparency – will make it suitable for one use or another. As for the measurements of origami creations, they can range from very small sizes to the scale of real buildings .
An application close to our daily lives and to which we may never have paid attention is the design of containers. This is the case of cardboard boxes and tetrabrik-type containers. In fact, origami has a lot to contribute to an issue that is becoming increasingly important in our society every day. We refer to recycling and, more specifically, to the storage of recyclable objects . Properly planned designs can help optimize the space that our waste occupies.
Cars, trains, rockets …
Popcorn containers for exclusive use in the microwave are yet another example of industrial coconut science : a box can contain several packages, practically flat, that unfold and take on a three-dimensional structure when the corn inside explodes. Another common configuration in packaging design is the honeycomb structure, which helps protect its contents by reducing vibrations. And what are its applications? It goes from cardboard boxes to the floor of the Japanese bullet train or the walls of artificial satellite rockets.
Origami has also paid off in the engineering sector. In the automotive industry, algorithms are developed that allow vehicle airbags to lay flat once folded. Interestingly, we found airbag folding algorithms that rely on the origami molecules model, originally used to fold large birds. It represents a sample of inventions and designs that start from the same bases as artistic creations .
On the other hand, various research teams in Germany and Japan are taking inspiration from origami to take advantage of its advantages in the emerging universe of three-dimensional printing. One of the drawbacks of today’s 3D printers is their slowness, so the idea behind the use of origami in this field is to get the computer to decompress three-dimensional data to print practically flat objects with a series of established cuts and patterns. Once printed, these items are ready to be easily folded into bulky items . Nobody is aware that this type of printing is faster and cheaper.
Aeronautics is also very interested in studying the possible uses of origami in its sector. NASA scientists are investigating to be able to launch their satellites so that their solar panels are sent folded and deployed once in space , a situation that is simulated by computer using techniques and calculations based on the mathematics of origami. To make these structures, the solar panels are identified with a sheet of paper and the different ways to fold it are studied. The best known solar panel folding model is the Miura fold : it is part of the branch of a type of rigid origami, which studies folding structures with rigid flat sheets, joined together by hinges.
There is a project in which American researchers – from NASA’s Jet Propulsion Laboratory (JPL), the National Aeronautics and Space Administration and Brigham Young University – are working together with the aim of reducing the size ten times of the solar panels once packed . Also in aeronautics, folding mirrors for space telescopes have been designed, such as the one in the James Webb (photo above), made up of eighteen hexagonal elements of beryllium .
On the other hand, origami is a source of inspiration in medicine and biotechnology . Some models are copied and adapted to medical instruments. In the field of cardiovascular surgery, spring-shaped devices have been designed to help correct narrowing of the arteries . We are talking about the stents , which are kept flat and, once inside the body, they self-unfold to form a 3D tube-shaped structure – something like when a ship is put inside a bottle. Using a catheter, the stent travels to the narrowed vessel and, as it unfolds, increases its diameter to improve blood circulation. Depending on its application, the tissue can even grow around the stent, which remains permanently inside the patient’s body .
Research projects based on origami are also in force to assist alveolar movement in patients receiving treatment for lung diseases or even to develop retinal implants .
Another field in which origami is a source of inspiration is nanotechnology. After ten years of evolution and research of DNA origami, today there is the possibility of folding DNA molecules into concrete shapes . This advance could have important applications, such as the design of new drugs, photonic devices – with the same functions as electronic devices but that use light as a transmission vehicle – or chemical reactions in industry.
Of course, origami is also closely related to physics. A direct application in this field is the creation of optical systems in which origami is used to simulate the behavior of reflections of light rays. In Australia, artist Matthew Gardiner (pictured above) has opened up a new field of research called oribotics , combining art with science. His creations, known as oribots , are static structures without any program that use electricity as a source of life. This is the case of some lamps, with a structure similar to a flower, that open (unfold) when you bring an object closer to them and close (fold) when you move it away.
Folding buildings
Architects also show their interest in origami. The way to fold wood or metal panels for the construction of structures and the design of folding buildings and tents is investigated. And even the fashion universe has taken advantage of origami: dresses that are inspired by flower folding patterns in nature , like an Issey Miyake model; umbrella and fan designs, and so on.
Mathematics is present in all these advances, but it is also that this relationship between science and origami works in both directions: on the one hand, advances in the field of mathematics help the design of new origami figures; and, on the other hand, the advances in origami pose challenges that translate into advances for mathematical research . The results of these investigations are reflected in many publications in international journals such as Nature Materials . Some of these works have even led to doctoral theses in mathematics, which was unthinkable a few years ago.
Another way to disseminate these scientific conclusions is through origami congresses that are organized in different countries, such as the OSME (acronym for Origami in Science, Mathematics, and Education), which illustrate the use and usefulness of knowledge transversality . They are attended by architects, artists, designers, engineers, mathematicians … People from very different backgrounds who share their interest in origami.
What will the future hold for us in this field? Will we have micromobiles that will unfold when used? Can we still work on a smaller scale, at the level of atoms ? Will it help us conquer space? It is the era of origami, an art and a science to which thousands of people in the world dedicate themselves and that affects and will continue to affect our daily lives.
