They take jigsaw puzzles to infinity and beyond

PALINVILLE, NY — On a winding mushroom hunt at North South Lake in New York’s Catskill Mountains, Jessica Rosenkrantz spotted a favorite type of mushroom: the multiporous mushroom. Mrs. Rosencrantz is partial to lifeforms that are different from humans (and mammals in general), though two of her favorite humans join on the trip: her husband, Jesse Louis Rosenberg, and their young child, Zilla, who set the pace. Ms. Rosencrantz loves fungi, lichens, and corals because, as she puts it, they are “so exotic compared to us.” From above, the hexagonal polypore looks like any boring brown mushroom (albeit sometimes with an orange glow), but flip it over and you’ll find a perfect set of six-sided polygons covering the underside of the cap.

Ms. Rosencrantz and Mr. Louis-Rosenberg are algorithm artists making laser-cut wooden jigsaw puzzles—among other things—in their design studio, Nervous System, in Ballinville, New York. Inspired by how shapes and forms appear in nature, they write custom software to “grow” the pieces. Interlocking puzzles. Their signature puzzle pieces have names like dendrite, amoeba, maze, and wave.

Far from the natural and algorithmic realms, the pair draw their creativity from the many points around the compass: science, math, art, and the hazy regions in between. Chris Yates, artist who makes hand-cut wooden jigsaw puzzles (W.A cooperating), described their puzzle-making method as “don’t just push the envelope—they tear it down and start over.”

Picnic Day, Mrs. Rosencrantz and Mr. Louis Rosenberg The latest puzzle It emerged hot from the laser cutter. This creation combined the centuries-old craft of papier-mâché with the tried-and-true invention of the nervous system: the infinite puzzle. Because it has no fixed shape and no definite boundary, the infinity puzzle can be assembled and reassembled in many ways, seemingly ad infinitum.

Nervous System debuted this concept design with the “Infinite Galaxy Puzzle,” featuring an image of the Milky Way on both sides. “You can only see half of the picture at once,” said Mr. Louis Rosenberg. “And every time you do a puzzle, in theory you see a different part of the picture.” Mathematically speaking, he explained, the design was inspired by the “mind-boggling” topology of the Klein bottle: a “closed, non-orientable surface,” with no inside, outside, up, or down. He said, “It’s all going on.” The puzzle goes on and on, winding from top to bottom, and from side to side. With a trick: the puzzle is “tiles with a heart”, which means that any piece from the right side connects to the left side, but only after a piece is flipped.

Ms. Rosenkrantz noted that the first appearance of The Infinity Puzzle prompted some philosophy on social media: “A puzzle that never ends? What does that mean? Is it even a puzzle if it never ends?” There were also questions about the mastermind’s motives. “Which villains, madmen, lunatics would create such a dastardly mystery that you can never finish?” She said.

“complicated” process

Ms. Rosenkrantz and Mr. Louis-Rosenberg trained at MIT. I have two degrees, biology and architecture. He dropped out after three years of mathematics. They call their creative process “complex” — they are drawn in by the seed of an idea, and then search for its ends.

Nearly a decade ago, they began researching paper marbles: droplets of ink—twisted, twisted, expanded in water and then transferred onto paper—picking patterns similar to those found in rock-turned-marbles. “It’s like an art form and it’s also a science experiment,” said Ms. Rosencrantz.

In 2021, Neuroscience Duo collaborates with Amanda Ghassaei, an artist and engineer who has built an interactive physics program Simulation of paper marbling Powered by fluid dynamics And the Maths. (She has refined her approach over time.) Ms. Gacy designed Turbulent flows of psychedelic color that plunge through undulating puzzle pieces. Ms. Rosenkrantz and Mr. Louis-Rosenberg created the wave pieces specifically for the Marbling Infinity Puzzle, which come in different sizes and colors.

“There are so many things to explore when you are not limited by the physical realities of working with a bowl of water,” said Ms Gasai. Drawing on classic marble patterns such as the bouquet and bird wing, the simulation allowed for more Freeform results: She can combine the Japanese style of blowing ink, using breathing or a fan, with the European style of pushing ink in different directions using combs. And they can alter the physical properties of the system to get the most out of each technology: With combing, the fluid should be more viscous; Inflation requires lower viscosity and faster flow.

However, there was a fine line between psychedelic embellishment and “allowing the color to stretch and wrap too much,” Ms. Gasai said. “This is where the undo button came in very handy.”

Cultivation algorithms

Trial and error is a nervous system methodology. Ms. Rosenkrantz and Mr. Louis-Rosenberg started the business in 2007 jewelry (Uses their existing font Floraform design system), followed by 3D sculpting (growing objects) and a Kinetic dress Housed in the MoMA Collection. Their science journal appeared 3D printed organ research With Jordan Miller, a bioengineer at Rice University. They also make software for New Balance – published for Data-driven midsoles and other aspects of sports shoe design. The same symbol was reused, in collaboration with fashion designer Asher Levine, to create a bodysuit inspired by the musician’s dragonfly wing. Grimes.

The route from one project to another is marked with mathematical concepts such as Laplasia growthAnd the Voronoi structures and the Turing pattern. These concepts, which loosely control how shapes and forms emerge and evolve in nature, “grow algorithms,” Ms. Rosenkrantz writes. The same algorithms can be applied to completely different media, from twisted maze pieces to complex components of 3D-printed organs. Algorithms solve practical manufacturing problems, too.

A project that came to fruition this year, a puzzle cell lamp, is built upon Find out how to cut curved surfaces So puzzle pieces can be leveled efficiently, making manufacturing and shipping easier.

“When you try to build a curved object out of flat matter, there is always an underlying tension,” said Kenan Crane, professor of geometry and 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 together.” Dr. Crane and Nicholas Sharp, chief researcher at NVIDIA, a 3D technology company, formulated an algorithm that attempts to find the optimal solution to this problem.

Using this algorithm, Ms. Rosenkrantz and Mr. Louis-Rosenberg identified 18 flat puzzle pieces that were shipped in what looked like a large pizza box. The Nervous System blog explains, “By snapping together the jagged shapes, you’ll create a spherical lamp shade.”

In Dr. Crane’s view, the Nervous System’s work espouses a philosophy akin to that of great artists like da Vinci and Dalí: an appreciation of scientific thinking as “something to be combined with art, rather than a category opposed to thought.” (Note that Dali describe the same Like a fish swimming between “the cold water of art and the warm water of science.””) Ms. Rosenkrantz and Mr. Louis Rosenberg have dedicated their careers to finding deep connections between the worlds of creativity and the worlds of mathematics and science.

“It’s something that people imagine is happening more often than it actually is,” said Dr. Crane. “The truth is, it takes someone who is willing to do this very hard work of translating between worlds.”

Earth reconfiguration

The Puzzle Cell Lamp takes its name from the interlocking puzzle cells found in many papers, but this lamp isn’t a proper puzzle—it comes with instructions. Then again, one can ignore the instructions and organically devise a grouping strategy.

In Mr. Louis Rosenberg’s opinion, that’s what makes a good puzzle. “You want the puzzle to be an experiment in strategizing—recognizing certain patterns, and then turning them into a methodology for solving the puzzle,” he said. The psychedelic swirls of the marble infinity puzzles may seem daunting, he added, but there are areas of color leading the way, piece to piece.

The most neurologically challenging infinite puzzle is the map of the Earth. It has a sphere topology, but it is a sphere exposed flat by icosahedral projectionmaintaining the geographic area (as opposed to some map projections that distort the area) and giving every inch of the planet equal billing.

“I’ve had some complaints of serious riddles about how hard it was,” Ms. Rosenkrantz said. Puzzle pieces have a more complex behavior; She explained that instead of tiling the core, they rotate 60 degrees and “squeeze the layers of the map”. Ms. Rosenkrantz finds the infinity factor to be particularly meaningful in this context. She said, “You can create your own map of the Earth, focusing on what you’re interested in — making all the oceans continuous, or making South Africa the center, or whatever you want to see in a prime location.” In other words, she advised on the blog, “Start anywhere and see where your journey takes you.”