Newly discovered origami patterns put the bloom on the fold

The art of origami goes back centuries — enough time to explore every possible crease that can be made in a sheet of paper, one might think.

And yet, researchers have now found a new class of origami that they call bloom patterns. Resembling idealized flowers, many bloom patterns are rotationally symmetric around the center.

The bloom patterns, with their set of attractive properties, appear promising for future engineering uses, especially for large structures that are sent to outer space. They fold up flat and compactly, they can be constructed out of one flat sheet, and they can be extended to ever larger shapes.

The discoveries originated from the paper-folding explorations of Zhongyuan Wang, a sophomore at Brigham Young University in Utah.

“I love to do origami, but if I can use origami to make practical applications that benefit the world, that will be a dream come true,” Wang, who also goes by Kelvin, said in a video produced by BYU.

Wang, along with Larry Howell, a professor of mechanical engineering at BYU, and Robert Lang, an origami artist and theorist who lives in Pasadena, Calif., report their findings in a paper published in the journal Proceedings of the Royal Society A.

The researchers have also provided an archive of images, videos and other help for anyone wishing to fold their own bloom patterns.

Lang said “the biggest novelty here” is that the bloom patterns fold flat.

Origami artists have long used patterns that they call “flashers,” which are also radially symmetric and expandable. But in their folded-up configuration, flashers are cylindrical, not flat. Other rotationally symmetric origami patterns, including one called a simple flat twist, fold flat but cannot be readily extended to larger sizes.

In an email, Wang said he started folding origami when he was 8 or 9 years old, growing up in Beijing. Then he followed online tutorials. In his explorations, he folded a few bloom patterns centered around a hexagonal base.

“At that time, I was trying a lot of new patterns,” he said. “It wasn’t until several years later that I recognized that these patterns are truly special.”

Browsing videos on YouTube, he learned about Howell and his work “turning origami into applications I never imagined,” Wang said. Howell, for instance, is working with NASA on an origami design for a future space telescope.

Wang applied to BYU mainly to join Howell’s research group.

Lang visited Howell’s laboratory in December last year and met Wang and the bloom pattern for the first time. Lang told Wang, “I don’t recall seeing something like this before.”

Wang had “found this really elegant way of not just scaling a simple flat twist but developing an entire family of these things,” Lang said. “This is a very pleasant surprise.”

The bloom patterns can be broken down into repeating tiles of creased patterns, called wedges, around a central polygon. Larger structures, which can still be folded flat, are created by expanding the wedges into larger shapes with additional creases. When folded up, the wedges stack up in a helical shape.

Howell said that a search through the scientific literature turned up a few individual bloom patterns that had been folded previously, but the new paper provides a general mathematical framework that describes a new class of possible foldings.

“It has basically an infinite number of origami patterns,” he said.

Tomohiro Tachi, a professor and an origami expert at the University of Tokyo who was not involved with the research, said, “Their key contribution lies in providing a generalizable method for generating these patterns.”

That increases the repertoire of origami designs available to scientists, engineers and designers, Tachi said.

Howell’s research group has made physical manifestations of the bloom patterns, not just out of paper but also from other materials like 3D printed plastics.

Real-world applications, like solar panels, will not be as thin as paper, and the folds may need to be wider to accommodate the thickness of the tiles. Still, the fundamental flat-folding nature of bloom patterns means that it should be easier to pack a structure into the limited space of a rocket.

Lang added that the advances are not just practical but aesthetic. He pointed out a bowl-shaped pattern by Wang, with its sides curving upward like an intricate vase.

“The real folded thing — he’s actually folded those — is really beautiful,” Lang said. “I would not be surprised to see that in a museum.”