Puzzling entry: They’re taking jigsaws to infinity and beyond

On a meandering mushroom hunt at North-South Lake in the Catskill Mountains of New York, Jessica Rosenkrantz spotted a favorite mushroom: the hexagonal-pored polypore. Rosenkrantz is partial to life-forms that are different from humans (and from mammals generally), although two of her favorite humans joined on the hike: her husband Jesse Louis-Rosenberg and their toddler, Xyla, who set the pace. Rosenkrantz loves fungi, lichens and coral because, she said, “they’re pretty strange, compared to us.” From the top, the hexagonal polypore looks like any boring brown mushroom (albeit sometimes with an orange glow), but flip it over and there’s a perfect array of six-sided polygons tessellating the underside of the cap.

Rosenkrantz and Louis-Rosenberg are algorithmic artists who make laser-cut wooden jigsaw puzzles — among other curios — at their design studio, Nervous System, in Palenville, N.Y. Inspired by how shapes and forms emerge in nature, they write custom software to “grow” intertwining puzzle pieces. Their signature puzzle cuts have names like dendrite, amoeba, maze and wave.

Beyond the natural and algorithmic realms, the couple draw their creativity from many points around the compass: science, math, art and fuzzy zones between. Chris Yates, an artist who makes hand-cut wooden jigsaw puzzles (and a collaborator), described their puzzle-making as “not just pushing the envelope — they’re ripping it apart and starting fresh.”

The day of the hike, Rosenkrantz and Louis-Rosenberg’s newest puzzle emerged hot from the laser cutter. This creation combined the centuries-old craft of paper marbling with a tried-and-true Nervous System invention: the infinity puzzle. Having no fixed shape and no set boundary, an infinity puzzle can be assembled and reassembled in numerous ways, seemingly ad infinitum.

Nervous System debuted this conceptual design with the “Infinite Galaxy Puzzle,” featuring a photograph of the Milky Way on both sides.

“You can only ever see half the image at once,” Louis-Rosenberg said. “And every time you do the puzzle, theoretically you see a different part of the image.” Mathematically, he explained, the design is inspired by the “mind-boggling” 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 around top to bottom, side to side. With a trick: The puzzle “tiles with a flip,” meaning that any piece from the right side connects to the left side, but only after the piece is flipped over.

Rosenkrantz recalled that the infinity puzzle’s debut prompted 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 its masterminds’s motivations. “What evil, mad, maniacal people would ever create such a dastardly puzzle that you can never finish?” she said. Rosenkrantz and Louis-Rosenberg trained at the Massachusetts Institute of Technology. She earned two degrees, biology and architecture; he dropped out after three years of mathematics. They call their creative process “convoluted” — they get captivated with the seed of an idea, and then hunt around for its telos.