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The Art of Origami – Interview with Robert J. Lang

Updated: May 23, 2020

Origami, the Japanese art of paper folding, has existed since ancient times, bringing us aesthetic pleasure to create paper figures of animals and flowers. Nowadays, origami evolves even further with a mix of advanced mathematical theories and laws. Robert J. Lang is one of those artists who merges origami and mathematical language and creates breathtaking complex origami pieces.

His passion for origami can be witnessed through his books “Twists, Tilings, and Tessellations: Mathematical Methods for Geometric Origami”, “Origami Design Secrets”, “Origami in Action,” and much more.

Interview and words by Anna Durbanova

How did it all start? How did you find your passion for origami?

I started origami when I was about six years old. I found some instructions in the origami book, and I thought it would be a fun puzzle to follow the instructions and fold the figures. Throughout my childhood I pursued origami as a hobby, looking for books that had instructions and trying to fold everything I could find. Eventually, I started making up my own designs because I wanted to make origami subjects that were not in any books.

I really never thought it would be anything but a hobby, and so I pursued other interests as well. In high school I enjoyed mathematics, science and natural history and I chose my career in science. I went to Caltech and studied electrical engineering for my BS and MS, and then switched to applied physics for my Ph.D., focusing on semiconductor lasers. After graduation, I worked at JPL, a national laboratory, and then SDL, a Silicon Valley company, doing laser research and development.

My scientific focus was on theoretical modeling of lasers, developing mathematical models of their function and behavior, but I was also pursuing origami on the side, trying to develop more complex structures. I had the idea of developing the mathematical underpinnings of origami; if I could describe origami using mathematical language, then I could use the tools of mathematics to accomplish the artistic goals I wanted in the world of origami.

That’s what led me to merge the two, and that merging worked. Putting origami into mathematical language allowed me to use mathematics to develop new design techniques that let me create the things I wanted to create. Besides that, I was also able to teach a lot of these techniques to other people, which helped them to advance their own art.

The language of math and science, applied to origami, also made it possible to apply origami structures and mechanisms to engineering problems. That got me involved in the consulting of how to use origami to create deployable structures and folded products.

In the Photo: Artwork “A Miura-ken Beauty Rose, Opus 482Photo Credit: Robert J.Lang

In your TED Talk, you mentioned that origami could be used in space. How? (See TED Talk video below)

That’s another area of applying folded patterns, structures and mechanisms from origami to deployables in space, in particular, things that are big and flat in space, like solar arrays, telescopes or antennas. Origami can improve their performance by providing a folding pattern that meets engineering needs, usually by providing a way to bring space objects down to a much smaller size in a controllable way.

Where else can origami be applied?

There are a lot of different fields like product design, packaging, consumer goods, containers, and sometimes just things that you want to make smaller, like furniture that collapses down for storage or shipping. Origami can also be used for purely decorative forms, for example, to create architectural facades and diffusers for lighting. Origami is also useful for medical devices. As an example, implants, should be small when they go in the body, but once they are inside, they should expand.

In the Photo: Artwork “Allosaurus Skeleton, Opus 326Photo Credit: Robert J.Lang

You applied four simple math rules in your origami process. Can you tell us more about them?

Yes, those four math rules are specifically for flat origami, for things that fold completely flat. Flat origami can be described entirely by those four rules. That’s nice, but it can also be a little deceptive because one of the things that we often see in mathematics is that even very simple rules can give rise to very rich and complex behavior. We certainly see this in the case of origami; even though simple or flat origami can be described completely by those four rules, we are still exploring all of the ramifications of those rules, all the ways they affect origami designs. There is still a lot of complexity and a lot of opportunities for theoretical developments to be worked out even from those four simple rules.

In the Photo: Artwork “K2, Opus 391Photo Credit: Robert J.Lang

Should people who learn origami learn mathematical laws to do origami?

Well, interestingly, you don’t necessarily need to know those four laws to do origami, because you can certainly follow instructions without knowing any mathematics at all. You can also design a lot of origami pieces using geometric ideas that are built on those four laws, but you don’t need to know the laws themselves. You can use the geometric concepts derived from the laws to turn an assembly of flaps into the patterns of folds on the paper that gives you the plan for folding.

When people want to start to design origami, I usually recommend they start with a book I wrote called “Origami Design Secrets”, which teaches people how to design origami. They will learn those four laws along their way, but the focus of the book is to teach the layers of ideas above those four laws, ideas that people can use in design.

I like to suggest for people who are designing origami that there is not a linear, step-by-step process for design, but rather that they develop a “bag of tricks,” a collection of design concepts that are akin to tools in a mental tool-chest of design. As they learn more ideas, they add more tools to their tool-chest. Once you’ve got a good collection of tools, when you are doing a design, you can select whatever tool helps with the particular design problem.

So it is possible to design a lot with just a few simple tools, but you can create a greater variety and, perhaps, more beautiful and vary patterns if you have a large toolkit. You have also created some computer programs for origami design. Can you tell us more about them?

Yes, I have written a couple of programs for the design of origami. One of them is called TreeMaker. What this program does is the following: if you draw a stick figure of the shape that you want, then it will calculate a crease pattern that folds into that stick figure.

It is particularly useful if you want to make, for example, an insect with six legs and antenna. You draw a little stick figure in TreeMaker, specify how long each of the legs and appendages needs to be, and then TreeMaker will calculate a crease pattern that folds into that shape. If you wish, you can print it out and fold it or you can also (as I often do) use that as a starting point and then refine that pattern in ways to make it more artistically interesting.

In the Photo: Artwork “Pegasus (mini)” by Robert J. Lang and Kevin Box Photo Credit: Bill Stengel Photo

What is for you the most exciting part of the origami design process?

It varies from day to day. Perhaps, the main thing that keeps origami interesting to me is the fact that there is always something new. I can try an idea in one conceptual area and then switch to something completely different. The common factors that keep me excited are novelty, solving problems, and creating something that did not exist before. Usually, that’s also something that’s aesthetically beautiful as well.

It sounds that origami can never be boring for you?

It is rarely boring, although sometimes it is if I am folding a pattern that has a lot of repetition in it. Just doing the same folds over and over again can get pretty tedious, but I am willing to go through that bit of boredom to accomplish the greater goal of the thing I am trying to fold.

In the Photo: Artwork “Raptor” by Robert J. Lang and Kevin Box Photo Credit: Bill Stengel Photo

How many hours do you spend to fold complex origami objects?

It varies a lot. For fairly simple designs I may only need about 5 or 10 minutes to fold. At the other extreme, the longest time I have ever spent folding a single object was spread over about seven years, but that was an unusual case. I would say that most of my complex pieces take a few hours to a couple of days to fold. That’s separate from the amount of design time, which might have taken anywhere from a few hours to a few weeks.

What are your future plans?

There will be a couple of traveling exhibitions with my artwork around the US. I also have a few art commissions and I am in discussions with a couple of venues to do some exhibitions for the next year.

For upcoming exhibitions of Robert Lang, click here.

Words by by Anna Durbanova. Special thanks to impakter


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