They take puzzles to infinity and beyond

PALENVILLE, NY – On a meandering mushroom hunt along North-South Lake in New York’s Catskill Mountains, Jessica Rosenkrantz discovered a favorite mushroom: the hexagonal pore mushroom. Ms. Rosenkrantz has a fondness for life forms distinct from humans (and from mammals in general), although two of her favorite people joined the hike: her husband Jesse Louis-Rosenberg and their toddler Xyla, who set the pace. Ms. Rosenkrantz loves mushrooms, lichen and coral because, as she says, they are “quite strange compared to us.” From above, the hexagonal polypore looks like a boring brown mushroom (albeit with an orange tinge at times), but flip it over and there’s a perfect arrangement of six-sided polygons tessellation of the underside of the cap.

Ms. Rosenkrantz and Mr. Louis-Rosenberg are algorithmic artists who create, among other oddities, laser-cut wooden puzzles at their design studio Nervous System in Palenville, NY. Inspired by how shapes arise in nature, they custom write software to “grow” intertwined puzzle pieces. Their signature puzzle cuts have names like dendrites, amoebas, labyrinths, and waves.

Beyond the natural and algorithmic realms, the couple draws their creativity from many points around the compass: science, mathematics, art, and the blurred zones in between. Chris Yates, an artist who makes hand-cut wooden jigsaw puzzles (and a collaborator), described their jigsaw-making as “don’t just push the envelope—they tear it apart and start fresh.”

On the day of the hike, Ms. Rosenkrantz and Mr. Louis-Rosenberg’s latest puzzle came hot out of the laser cutter. This creation combined the centuries-old craft of marbling paper with a time-tested invention of the nervous system: the infinity puzzle. Since there is no fixed shape and no set limit, an infinity puzzle can be assembled and reassembled in numerous ways, seemingly to infinity.

Nervous System introduced this conceptual design with the “Infinite Galaxy Puzzle” featuring a photo of the Milky Way on either side. “You can only see half of the picture at a time,” said Louis-Rosenberg. “And each time you solve the puzzle, you’re theoretically seeing a different part of the picture.” Mathematically, he explained, the design is inspired by the “stunning” topology of a Klein bottle: a “non-orientable closed surface” with no inside , outside, above or below. “It’s all continuous,” he said. The puzzle goes on and on, wrapping from top to bottom, side to side. With a trick: the puzzle “tiles with turns”, which means that each piece is connected from the right side to the left side, but only after the piece is turned over.

Ms. Rosenkrantz recalled that the debut of the infinity puzzle on social media led to some philosophers saying, “‘A puzzle that never ends? What does that mean? Is it even a mystery if it doesn’t end?’” There were also questions about his mastermind’s motivations. “What evil, insane, insane people would ever create such an insidious puzzle that you can never finish?” She said.

Ms. Rosenkrantz and Mr. Louis-Rosenberg were educated at the Massachusetts Institute of Technology. She earned two degrees, biology and architecture; he dropped out of mathematics after three years. They call their creative process “nested” – they get caught up in the seed of an idea and then search for its telos.

Almost a decade ago, they began exploring paper marbling: ink drops—swirled, distorted, stretched in water, and then transferred to paper—capture patterns similar to those found in rock that has turned into marble. “It’s like an art form that’s also a science experiment,” Ms. Rosenkrantz said.

In 2021, the Nervous System duo entered into a collaboration with Amanda Ghassaei, an artist and engineer who had built an interactive physics-based paper marbling simulator using fluid dynamics and mathematics. (She has refined her approach over time.) Ms. Ghassaei created the turbulent streams of psychedelic color that cascade across the rippling puzzle pieces. Mrs. Rosenkrantz and Mr. Louis-Rosenberg specially designed the serrated edge for the marble infinity puzzle, which is available in different sizes and colors.

“There are so many more things to discover when you’re not constrained by the physical realities of working with a tray of water,” Ms. Ghassaei said. Leveraging classic marbling patterns like bouquets of flowers and bird wings, the simulator allowed for freer results: she could combine the Japanese style of blowing ink with breath, or a fan with the European style of pushing ink in different directions with combs. And she could change the physical properties of the system to get the most out of each technique: when combing, the fluid needs to be more viscous; Blowing requires lower viscosity and faster flow.

However, there is a fine line between psychedelic splendor and “allowing color to stretch and warp too far,” Ms. Ghassaei said. “This is where the undo button came in really handy.”

Trial and error is the methodology of the nervous system. Ms. Rosenkrantz and Mr. Louis-Rosenberg began making jewelry in 2007 (a current line uses their Floraform design system), followed by 3D printed sculptures (Growing Objects) and a Kinematics dress, which is in the MoMA collection. Science magazine presented their 3D printed organ research with Jordan Miller, a bioengineer at Rice University. They also make software for New Balance that is used for data-driven midsoles and other aspects of sneaker stylization. The same code was repurposed in collaboration with fashion designer Asher Levine to create a dragonfly wing-inspired bodysuit for musician Grimes.

The path from one project to the next is marked with mathematical concepts such as Laplace growth, Voronoi structures and the Turing pattern. These concepts, which roughly determine how forms arise and evolve in nature, “cultivate the algorithms,” Ms. Rosenkrantz has written. The same algorithms can be applied to vastly different media, from the intricate pieces of maze to the intricate components of 3D-printed organs. And the algorithms also solve practical manufacturing problems.

A project that came to fruition this year, the Puzzle Cell Lamp, built on research into how curved surfaces can be cut so the puzzle pieces can be flattened efficiently, making manufacturing and shipping easier.

“When you’re trying to build a curved object out of flat material, there’s always an underlying tension,” said Keenan Crane, a surveyor and professor of computer science at Carnegie Mellon University. “The more cuts you make, the easier it is to flatten it, but the harder it is to put it together.” Crane and Nicholas Sharp, senior research scientists at NVIDIA, a 3D technology company, have developed an algorithm that attempts to find an optimal solution to this problem.

Using this algorithm, Ms. Rosenkrantz and Mr. Louis-Rosenberg designed 18 flat puzzle pieces that are shipped in a kind of large pizza box. “By joining the curved shapes together,” explains the Nervous System blog, “you create a spherical lampshade.”

From Dr. Crane’s Nervous System work follows a philosophy similar to that of great artists like da Vinci and Dalí: an appreciation of scientific thought as “something to be integrated into art, and not as an opposed category of thought”. (He noted that Dalí described himself as a fish swimming between “the cold waters of art and the warm waters of science.”) Ms. Rosenkrantz and Mr. Louis-Rosenberg have made their careers searching for deep connections between the worlds dedicated to creativity and creativity the world of mathematics and science.

“It’s something that people imagine more of than is actually happening,” said Dr. crane. “The reality is that it takes someone willing to do the very, very dirty work of translating between worlds.”

The Puzzle Cell Lamp gets its name from the interlocking puzzle cells found in many sheets, but this lamp isn’t really a puzzle – it comes with instructions. On the other hand, one could ignore the instructions and organically develop an assembly strategy.

According to Mr. Louis-Rosenberg, that makes a good puzzle. “You want the puzzle to be a strategy-making experience — recognizing certain patterns and then turning that into a methodology for solving the puzzle,” he said. The psychedelic swirls of the marbled infinity puzzles may be daunting, he added, but there are zones of color that guide the way, one piece to the next.

Nervous System’s most challenging infinity puzzle is a map of the earth. It has the topology of a sphere, but it is a sphere flatly unfolded by an icosahedral map projection, which preserves the geographical area (unlike some map projections that distort the area) and gives every inch of the planet the same bill .

“I’ve had some complaints from serious puzzlers about how difficult it is,” Ms. Rosenkrantz said. The puzzle pieces have more complex behavior; Instead of tiling with a flip, they rotate 60 degrees and “rip the seams of the card,” she explained. Ms. Rosenkrantz finds the infinity factor particularly important in this context. “You can make your own map of the Earth,” she said, “and center it on what you’re interested in — making all the oceans contiguous, or making South Africa the center, or whatever you want to see in a privileged position.” In other words, she advised on the blog, “Start anywhere and see where your journey takes you.”

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