PALENVILLE, NY — While on a winding mushroom hunt at North-South Lake in New York’s Catskill Mountains, Jessica Rosenkrantz spotted a favorite mushroom: the hexagon-pore polypore. Ms. Rosenkrantz likes life forms other than humans (and mammals in general), though two of her favorite humans joined the walk: her husband Jesse Louis-Rosenberg and their toddler, Xyla, who set the pace. Ms. Rosenkrantz likes fungi, lichens and coral because, she said, “they’re pretty strange compared to us.” From above, the hexagonal polypore looks like a dull brown mushroom (albeit sometimes with an orange glow), but flip it over and there’s a perfect array of six-sided polygons covering the bottom of the hat.
Ms. Rosenkrantz and Mr. Louis-Rosenberg are algorithmic artists who create laser-cut wooden jigsaw puzzles—among other curiosities—at their design studio, Nervous System, in Palenville, N.Y. Inspired by how shapes and forms emerge in nature, they write custom software to create intertwined puzzle pieces to grow. Their signature puzzle pieces have names like dendrite, amoeba, maze, and wave.
Beyond the natural and algorithmic worlds, the pair draw their creativity from many points around the compass: science, math, art, and fuzzy zones in between. Chris Yates, an artist who creates hand-carved wooden jigsaw puzzles (and a collaborator), described their puzzle-making as “not just pushing the envelope — they’re tearing it apart and starting over.”
On the day of the walk, Mrs. Rosenkrantz and Mr. Louis-Rosenberg’s latest puzzle came out hot from the laser cutter. This creation combined the age-old craft of paper marbling with a time-tested invention of the nervous system: the infinity puzzle. Because it has no fixed shape and no fixed boundary, an infinity puzzle can be assembled and reassembled in countless ways, seemingly ad infinitum.
Nervous System debuted this conceptual design with the “Infinite Galaxy Puzzle”, which featured a picture of the Milky Way on both sides. “You can always only see half of the image at a time,” Mr Louis-Rosenberg said. “And every time you do the puzzle, you’re theoretically seeing a different part of the picture.” Mathematically, he explained, the design is inspired by the “baffling” topology of a Klein bottle: a “non-orientable closed surface,” with no inside, outside, up or down. “It’s all continuous,” he said. The puzzle goes on and on, wrapping from top to bottom, left to right. With a trick: the “tiles with a flip” puzzle, meaning that each piece from the right side connects to the left side, but only after the piece is flipped.
Ms. Rosenkrantz recalled that the debut of the infinity puzzle sparked some philosophizing on social media: “’A puzzle that never ends? What does it mean? Is it even a puzzle if it doesn’t end?’” There were also questions about the motivations of the masterminds. “What evil, crazy, maniacal people would ever make such a dastardly puzzle that you can never finish?” she said.
A ‘complicated’ process
Mrs. Rosenkrantz and Mr. Louis-Rosenberg were educated at the Massachusetts Institute of Technology. She earned two degrees, biology and architecture; he dropped out after three years of math. They call their creative process “complicated” – they become fascinated with the germ of an idea and then hunt around for the telos.
Nearly a decade ago, they began exploring paper marbling: Droplets of ink—swirling, warping, stretched in water, then transferred to paper—record patterns similar to those found in rock transformed into marble. “It’s like an art form that’s also a science experiment,” Ms Rosenkrantz said.
In 2021, the Nervous System duo teamed up with Amanda Ghassaei, an artist and engineer who had built an interactive, physics-based paper marbling simulator powered by fluid dynamics and math. (She’s refined her approach over time.) Ms. Ghassaei created the turbulent streams of psychedelic color that crash over the undulating puzzle pieces. Mrs. Rosenkrantz and Mr. Louis-Rosenberg created the wave cut specifically for the Marbling Infinity Puzzle, which comes in a variety of sizes and colors.
“There are so many more things to explore when you’re not limited by the physical reality of working with a bucket of water,” said Ms. Ghasaei. Riffing on classic marble patterns like bouquet and bird wing, the simulator allowed for more free-form results: she could combine the Japanese style of blowing ink, using breath or a fan, with the European style of pushing ink in different directions using 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 was a fine line between psychedelic finery and “letting the color stretch and warp too far,” Ms. Ghassaei said. “The Undo button came in very handy there.”
Trial and error is the method of the nervous system. Ms. Rosenkrantz and Mr. Louis-Rosenberg started making jewelry in 2007 (a current line uses their Floraform design system), followed by 3D printed sculptures (Growing Objects) and a Kinematics dress that is in the collection of the MoMA . Science magazine presented their 3D printed organ research with Jordan Miller, a bioengineer at Rice University. They also make software for New Balance – used for data-driven midsoles and other aspects of sneaker styling. The same code was reused, in collaboration with fashion designer Asher Levine, to create a dragonfly wing-inspired bodysuit for the musician Grimes.
The route from one project to the next is marked with mathematical concepts such as Laplace growth, Voronoi structures and the Turing pattern. These concepts, which loosely govern how shapes and forms originate and evolve in nature, “cultivate the algorithms,” Ms. Rosenkrantz has written. The same algorithms can be applied to very different mediums, from the winding maze pieces to the intricate components of 3D printed organs. And the algorithms also solve practical production problems.
A project that came to fruition this year, the Puzzle Cell Lamp, built on research into how to cut curved surfaces so that the puzzle pieces can be efficiently squashed, making fabrication and shipping easier.
“When you try to build a curved object out of flat material, there’s always a fundamental tension,” said Keenan Crane, a geometer and professor of computer science at Carnegie Mellon University. “The more cuts you make, the easier it is to smooth out, but the harder it is to put together.” Dr. Crane and Nicholas Sharp, a senior researcher at NVIDIA, a 3D technology company, developed an algorithm that tries to find an optimal solution to this problem.
Using this algorithm, Ms. Rosenkrantz and Mr. Louis-Rosenberg delineated 18 flat puzzle pieces that are shipped in what appears to be a large pizza box. “By snapping the sinuous shapes together,” the Nervous System blog explains, “you create a spherical lampshade.”
From the perspective of Dr. Crane’s work of Nervous System adopts a philosophy similar to that of great artists such as Da Vinci and Dalí: an appreciation of scientific thinking as “something that should be integrated with art, rather than an opposing category of thinking .” (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 devoted their careers to finding deep connections between the worlds of creativity and the worlds of mathematics and science.
“It’s something that people think is happening more than it really is,” said Dr. crane. “The reality is it takes someone willing to do the very, very grungy job of translating between worlds.”
The Puzzle Cell Lamp takes its name from the interlocking puzzle cells found in many leaves, but this lamp is not a true puzzle – it comes with instructions. On the other hand, one could ignore the instructions and organically devise an assembly strategy.
According to Mr. Louis-Rosenberg, that’s what makes a puzzle good. “You want the puzzle to be an experience of strategies — recognizing certain patterns and then turning that into a methodology for solving the puzzle,” he said. The psychedelic swirls of the marbling infinity puzzles may seem terrifying, he added, but there are zones of color that lead the way, one piece to the next.
The most challenging nervous system infinity puzzle is a map of the Earth. It has the topology of a sphere, but it is a sphere expanded flat by an icosahedral map projection, preserving the geographic area (unlike some map projections that distort the area) and billing every inch of the planet equally.
“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 flap, they rotate 60 degrees and “zip the seams of the card,” she explained. Ms. Rosenkrantz finds the infinity factor particularly useful in this context. “You can make your own map of the Earth,” she said, “by centering on whatever you’re interested in — making all the oceans continuous, or centering South Africa, or whatever you want to see in a privileged environment.” . position.” In other words, she advised on the blog, “Start anywhere and see where your journey takes you.”