Palenville, NY – On a mushroom hunt that meanders across the North and South Lakes of New York’s Catskill Mountains, Jessica Rosenkrantz discovered a favorite mushroom: the hexagonal pore bacteria. Ms. Rosenkrantz favors life forms different from humans (and mammals in general), though two of her favorite humans join the hike: her husband, Jesse Louis-Rosenberg, and their toddler, Xyla, who set pace. Ms. Rosenkrantz likes fungi, lichens and corals because, she says, “they’re weird compared to us.” Viewed from the top, the hexagonal porous bodies look like any boring brown mushroom (although they sometimes glow orange), But flip it over and you’ll see a perfect set of hexagonal polygons tessellated under the lid.
Ms. Rosenkrantz and Mr. Louis-Rosenberg are algorithmic artists who create software for laser-cut wooden jigsaw puzzles and other antique “growth” interwoven puzzles at their Nervous System design studio in Palenville, New York. Their signature jigsaw cuts have names like dendrites, amoebas, mazes and waves.
Outside of the realms of nature and algorithms, the pair draws creativity from many areas around the compass: science, math, art, and the nebulous zone in between. Chris Yates, an artist who makes hand-cut wooden puzzles (and collaborator) described their puzzle-making as “not just pushing the limits—they’re breaking the limits and starting over.”
On the day of the hike, Ms. Rosenkrantz and Mr. Louis-Rosenberg’s latest jigsaw puzzle Hot air coming out of the laser cutter. This creation combines the centuries-old art of marbled paper with a proven neurological invention: the infinite puzzle. Infinite puzzles have no fixed shape and no fixed boundaries, and can be combined and recombined in a seemingly endless number of ways.
Nervous System debuted this concept design with the “Infinite Galaxy Puzzle,” featuring a picture of the Milky Way on either side. “You only see half the image at a time,” Mr Louis-Rosenberg said. “Every time you do the puzzle, you theoretically see a different part of the image.” Mathematically, he explained, the design was inspired by the Klein bottle’s “incredible” topology: A “non-orientable closed surface” with no interior, exterior, top or bottom. “It’s all on a continuum,” he said. The puzzle continues, top to bottom, side to side. There is a trick: the puzzle is “tiles with flips”, meaning that any piece on the right side is connected to the left side, but only after being flipped.
Ms. Rosenkrantz recalls that the debut of the infinity puzzle sparked some philosophical thinking on social media: “‘A never-ending puzzle? What does that mean? If it doesn’t end, is it even a mystery?'” And others question the motives of its masterminds. “What kind of evil, crazy, crazy person would create such dastardly puzzles that you can never complete?” she said.
A “complicated” process
Ms. Rosenkrantz and Mr. Louis-Rosenberg were trained at the Massachusetts Institute of Technology. She got two degrees in biology and architecture; he dropped out after three years of math. They call their creative process “complicated”—they get sucked in by the seed of an idea, and then hunt around for its purpose.
About a decade ago, they began studying marbling on paper: droplets of ink swirled in water, twisted, stretched, and transferred to paper—capturing patterns similar to those found in rocks that had been turned into marble. “It’s like an art form, but also a science experiment,” Ms Rosencrantz said.
In 2021, the neurological duo entered into a partnership with artist and engineer Amanda Ghassaei Paper Marbling Simulator powered by Hydrodynamics and math. (She refined her method over time.) Ms. Ghassaei created Turbulence of psychedelic colors Make your way through the wavy puzzle pieces. Ms. Rosenkrantz and Mr. Louis-Rosenberg created the wave cut specifically for the Marbling Infinity Puzzle in different sizes and colors.
“When you’re not limited by the physical reality of using a plate of water, there’s so much more to explore,” Ms Ghassaei said.Modeled after classic marbling patterns such as bouquets and bird wings, the simulator allows for more free form results: She can combine the Japanese style of blowing ink using breath or a fan with the European style of using a comb to push the ink in different directions. She can change the physical properties of the system to get the most out of each technique: for combing, the fluid needs to be more viscous; for blowing, it needs to be less viscous and flow faster.
However, Ms. Ghassaei says there’s a fine line between psychedelic clothing and “overstretching and distorting color.” “That’s where the undo button comes in very handy.”
Trial and error is a neurological methodology. Ms. Rosenkrantz and Mr. Louis-Rosenberg started production in 2007 jewelry (a current row uses their Flora design systems), followed by 3D printed sculptures (growth target), and a kinesiology dress In the collection of MoMA. The journal Science published their 3D printed organ research In collaboration with bioengineer Jordan Miller of Rice University.They also make software for New Balance – for Data Driven Midsole And other aspects of sneaker stylization.Working with fashion designer Asher Levine, the same code was repurposed for the musician’s dragonfly wing-inspired onesie Grimes.
The route from one item to the next is marked with mathematical concepts such as Laplace growth, Voronoi structure and Turing modelThese concepts roughly govern how shapes and forms emerge and evolve in nature, Ms. Rosencrantz writes, “fostering algorithms.” The same algorithm can be applied to very different media, from pieces of a tortuous maze to the complex components of a 3D printed organ. These algorithms also solve practical manufacturing problems.
The project that came to fruition this year, Puzzle Cell Lamp, was built on Investigate how to cut surfaces Puzzle pieces can thus be effectively flattened, making manufacturing and shipping easier.
“When you’re trying to build a curved object out of flat materials, there’s always a fundamental tension,” said Keenan Crane, a geometer and computer science professor at Carnegie Mellon University. “The more you cut, the easier it is to flatten, but the harder it is to assemble.” Dr. Crane and Nicholas Sharp, a senior research scientist at 3D technology company NVIDIA, devised an algorithm to try to find the best solution to the problem.
Using this algorithm, Ms. Rosenkrantz and Mr. Louis-Rosenberg mapped 18 flat puzzle pieces that fit into what looked like a large pizza box. “By piecing together curved shapes,” explains the Nervous System blog, “you’ll create a spherical lampshade.”
According to Dr. Crane, the work of the Nervous System adopts a philosophy similar to that of great artists such as Leonardo da Vinci and Dali: to see scientific thinking as “something that should be combined with art, rather than an opposing category of thought”. (He pointed out that Dali described himself Like 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 world of creativity and the world of mathematics and science.
“People imagine more things are happening than they actually are,” Dr. Crane said. “The reality is that someone needs to be willing to do the very, very crappy translation between worlds.”
rebuild the earth
The Puzzle Cell Lamp gets its name from the interlocking puzzle cells found in many leaves, but this lamp isn’t really a puzzle — it comes with instructions. Again, one can ignore these instructions and organically devise an assembly strategy.
According to Mr. Louis-Rosenberg, this is a good puzzle. “You want the puzzle to be a strategy-making experience — identifying certain patterns and then translating that into a solution to the puzzle,” he said. The psychedelic swirls of the marbled infinity puzzle might seem intimidating, but there are areas of color leading the way, one after the other, he added.
The most challenging infinite puzzle for the nervous system is Earth Map.It has the topology of a sphere, but it is composed of a Icosahedral map projectionpreserve geographic areas (in contrast to some map projections that distort areas) and provide equal billing for every inch of the globe.
“I’ve had some complaints from serious puzzle lovers about how difficult it is,” Ms Rosencrantz said. The puzzle pieces have more complex behavior; instead of flipping the tiles, they rotate 60 degrees and “tighten the seams of the map,” she explains. Ms. Rosenkrantz finds the infinity factor particularly interesting in this regard. “You can create your own map of the Earth,” she said, “and focus it where you’re interested—make all the oceans contiguous, or have South Africa be the center, or whatever you want to see in the franchise.” East and West.” In other words, she advises on the blog, “Start anywhere and see where your journey takes you.”