When talking about the intersection of art and science, Stavros Georgakopoulos likes to quote Albert Einstein, who once said, "I am enough of an artist to draw freely upon my imagination. Imagination is more important than knowledge."
"It's absolutely true. If we became engineers and we stuck always to the book, there wouldn't be new breakthroughs," said Georgakopoulos, an electromagnetics specialist and assistant professor in Florida International University's department of electrical and computer engineering.
"Where does imagination come from? Art. Artists don't have any laws, or limits," he added.
It's from this line of thinking that Georgakopoulos is helping transform the field of electrical engineering and electronics design using the mathematical properties of a paper crane.
The art of origami, he says, is the key to unlocking whole new conceptual modes of thought for scientists.
While folding smartphones into your jacket pocket like the front page of a newspaper is still a futurist fantasy, electronics that compress and change shape are now possible if designed the right way. They're currently in development, aided by Japan's centuries-old paper-folding techniques, an art form that spread worldwide around the mid-1900s.
The immediate benefit would be in putting electronics into orbit -- or into soldiers' cargo pockets -- that are smaller and lighter than ever before. Yet they also would be multipurpose, designed to reconfigure themselves both to optimize for space and to access various technical functionalities through morphing form factors. The unforeseen applications are as limitless as the geometry of origami structures themselves.
"What happens is that we have an origami structure that can change," Georgakopoulos said. "For example, if I look at the accordion -- it can change its height, it can collapse, or it can expand, and have a large height. We can control the geometric configuration."
Origami antennas: The next generation of electronics design
Of course, we're still a ways off from introducing roll-up tablets and smartphones that can pleat like a pair of jeans. But the underpinning geometric techniques of paper folding are becoming increasingly important for achieving breakthroughs in scientific device design and manufacturing processes.
The newest avenue of development in this respect is antenna design, one of a series of specialities for which Georgakopoulos received both his master's degree and his doctorate, studying under Constantine Bolanis, the prolific antenna and electromagnetics pioneer.
Now Georgakopoulos is part of a joint research team spanning Georgia Tech University and FIU that is working on origami-influenced antennas. The team has a $2 million grant from the National Science Foundation's Origami Design for Integration of Self-assembling Systems for Engineering Innovation.
A mouthful for sure, but the program is an entirely origami-based initiative that is extending beyond antenna design into work on DNA folding and mechanical structure design.
"When we think of origami, its nature is perfect for this type of thing," Georgakopoulos said of antennas. "Origami really helps to miniaturize the antenna during launch, and when it's up in space, it can become very large."
Besides space shifting, an unfolding antenna will be able to move beyond linear functionality. "Even though I have the same structure, I can achieve different performance for the antenna, work at two different frequencies for instance," the Florida scientist added.
Paper prototypes are already in use now. Designs with ascending diagonal folds and pancake-like discs that flower outward with the mathematical motion of an accordion are early-stage ideas. And the researchers used special ink-jet techniques to deposit conductive materials onto the paper including copper and silver.
The field, still a nascent research area, Georgakopoulos said, could evolve from paper to include plastics and flexible dielectrics. "We're examining all different materials like liquid crystal polymers, thin crystal substrates. ... As long as a material is flexible and can bend, it's a candidate for this type of development," he explained.
Thanks to advancements in simulation software, namely the industry-standard high-frequency structural simulator (HFSS) from a company called Ansys, the extent to which the team can conceptualize new antenna models is limited only by their imagination. That's a fitting parameter for the Einstein-quoting Georgakopoulos.
"The software has been really instrumental in doing this. You can't just build these geometries one at a time," he explained. Antenna design was changed forever in the early '90s when simulation software like HFSS made expensive and serial physical prototyping unnecessary, he added.
However, that's one aspect central to the artistic aesthetic of origami -- paper cranes cannot and should not be mass-produced, but hand-crafted, the logic goes -- that doesn't translate to the world of component design.
The science behind the art of paper folding
Origami, from the Japanese words for "folding" and "paper," was confined to the island nation since its inception as an art form in the 17th century, until it expanded to other countries during and after World War II. Though it's mostly associated with the surprising serenity found in complex transformation, it has always been an inherently mathematical pursuit.
After all, the crafting of structures from paper with only a basic series of folds and, with few exceptions, no cutting or use of adhesives, involves understanding the geometric limitations of lines and space and how the two properties interact. There are subsets of origami that address the various schools of thought, both from a conceptual and technical standpoint.
For instance, action origami -- think paper frogs that move by applying pressure to the tail end or the childhood favorite paper fortune teller -- is a widely recognized form. Origami masters, like former NASA physicist Robert Lang, design complicated structures that can be animated, like his instrumentalist series featuring musicians that can be made to play their instruments by pulling back on their heads.
Scientists like Lang, who have contributed greatly to understanding the mathematics of origami and helped create computational origami simulators, have pushed the boundaries of the field in the last few decades, yielding stunning real-world applications in the world of engineering.
This technical origami, known in Japan as "origami sekkei," has descended deep into the study of theoretical geometry. And it has manifested itself practically in everything, from packaging design and airbags to medical devices, like stent implants that unfold within the body and prevent collapse of certain areas during surgery.
In fact, there's a conference, the Origami Science Mathematics Education meet-up, the sixth of which will be held in Tokyo this August, that addresses the intersection of the fields. The 2010 documentary "Between the Folds" -- with the tagline, "the science of art, the art of science" -- featured prominent origami masters talking about the expansive reach of the art form in all manners of disciplined academic study and real-world engineering.
When it came to antennas, however, Georgakopoulos and his team had little precedent when designing working structures that were electromagnetically sound.
"Origami started with satellite dishes. But this type of work we're doing is breakthrough work. That started about a year ago," he said. "We [FIU] were working on wireless power transfer, and what we were doing there was folding, and Georgia Tech was doing antenna work without thinking of origami."
The two research teams had, in Georgakopoulos' words, an aha moment. "We said, 'What about origami?' We realized it is very well-suited and could really help us create a completely new area in antennas. Antennas are actually driven by geometry," he said.
Now the team is beginning to rope in dedicated origami masters to inform the research, grabbing prominent artists featured in "Between the Folds," like Chris Palmer of Berkeley, Calif.
Palmer is the manager of UC Berkeley's computer-aided design workspace, the Digital Fabrication Lab. But in the origami world, he is well-known for taking the techniques of modular origami master Shuzo Fujimoto -- a teacher of Palmer's for the last two decades whose credits include popularization of origami tessellation techniques and his hydrangea sculpture -- and applying them to textile art.
"The engineers can find some little examples of how they want something to function, but they won't have before them the full breadth of folded structures to choose them," Palmer said. That's where the origami artists come in. "The artist and the engineer can both work together."
For Georgakopoulos, it's not only an iconic bringing together of artists and scientists under the same roof, but also a teachable moment for future generations of engineers.
"The more we pursue engineering, we realize that engineering is actually similar to what Einstein said. We're telling our students it's OK to work with artists," he said. "It's a very exciting program when students realize that engineering can be very creative."