They can solve jigsaw puzzles up 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 loves lifeforms different from humans (and all mammals), but her husband Jesse Louis Rosenberg and their child Zilla are her favorites. They set the pace. Ms. Rosencrantz is a big fan of lichens, corals, and fungi because they are so exotic in comparison to us. Although the hexagonal polypore appears like any other boring brown mushroom, it has an orange glow sometimes. However, if you flip it over, you’ll see six polygons covering its underside.

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. They are inspired by the way shapes and forms appear in nature and create custom software to “grow” the pieces. Interlocking puzzles. Their puzzle pieces are known by their distinctive names, such as wave, amoeba and dendrite.

The pair are far from the algorithmic and natural realms. They draw their creativity from all points of the compass, including science, math, art and the hazy areas in between. Chris Yates, an artist who creates hand-cut wooden puzzles for jigsaws (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 & Mr. Louis Rosenberg The latest puzzleIt was hot out of 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 does not have a fixed structure or a defined boundary, the infinite puzzle can be assembled and disassembled in many different ways.

Nervous System presented this concept design, the “Infinite Galaxy Puzzle,” which featured an image of the Milky Way on each side. “You can only see half of the picture at once,” said Mr. Louis Rosenberg. “And you can see a different piece of the picture every time you solve a puzzle.” Mathematically speaking he explained that the design was inspired from the “mind-boggling”, topology of the Klein bottles: a “closed and non-orientable” surface, with no inside, out, or down. He said, “It’s all happening.” The puzzle continues winding, from top to base, and side to side. There is a trick to this puzzle: “Tiles with a Heart” means that any piece on the right side will connect to the left side. However, it is only possible after a piece has been 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 this mean? Is it even a puzzle if it never ends?” There were also questions about the mastermind’s motives. “Which madmen, villains, or lunatics would create such an egregious mystery that you can’t finish it?” She agreed.

“Complicated” process

Ms. Rosenkrantz, Mr. Louis-Rosenberg were trained at MIT. I have two degrees: architecture and biology. After three years of math, he quit. 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. Ms. Rosencrantz stated, “It is like an art form, and it’s also science experiment.”

Neuroscience Duo teams up with Amanda Ghassaei (an artist and engineer who created an interactive physics programme) in 2021 Simulation of paper marblingPowered by fluid dynamicsAnd the Maths. (She has refined her approach over the years.) Ms. Gacy designed Turbulent flows of psychedelic colorThat plunge through undulating puzzles pieces. The wave pieces were created by Ms. Rosenkrantz, Mr. Louis-Rosenberg for the Marbling infinity Puzzle. They come in different sizes.

“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. The simulation used classic marble patterns like the bouquet and bird wings to allow for more Freeform resultsIt can combine the Japanese technique of blowing ink with breathing or a fan with European techniques of pushing ink into different directions using combs. They can also alter the physical properties of each technology to get the best out of each: For combing, the liquid should have a higher viscosity; for inflation, it requires a lower viscosity and a faster flow.

Ms. Gasai stated that there was a fine line to be drawn between psychedelic embellishment, and “allowing the color stretch and wrap too much.” “This is where Ms. Gasai said that the undo button was very useful.”

Cultivation algorithms

Trial and error is a nervous-system method. In 2007, Ms. Rosenkrantz & Mr. Louis-Rosenberg founded the business. jewelry(Uses an existing line Floraformdesign system), followed closely by 3D sculptinggrowing objects) and a Kinetic dressIt is housed in the MoMA Collection. Their science journal appeared 3D printed organ researchJordan Miller, a Rice University bioengineer. They also develop software for New Balance – which has been published. Data-driven midsolesOther aspects of shoe design. The same symbol was re-used in collaboration with Asher Levine (fashion designer), to create a bodysuit inspired from the musician’s Dragonfly Wing. Grimes.

The mathematical concepts used to mark the route from one project into another are: Laplasia growthThen there’s the Voronoi structuresThe Turing pattern. These concepts, which loosely govern how shapes and forms emerge and evolve in nature, “grow algorithms,” Ms. Rosenkrantz writes. The same algorithms can also be applied to completely other media, including twisted maze pieces and complex parts of 3D printed organs. Algorithms can be used to solve manufacturing problems.

This year’s project, a puzzle-cell lamp, was completed. Find out how to cut curved surfacesIt is possible to level the puzzle pieces quickly, making shipping and manufacturing 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, it’s easier to flatten it and the more difficult it is to put it together. Dr. Crane, Nicholas Sharp, chief researcher at NVIDIA (3D technology company), devised an algorithm that attempts the best solution to this problem.

This algorithm was used by Ms. Rosenkrantz, Mr. Louis-Rosenberg to identify 18 flat puzzle pieces. They were shipped in what looked almost like a large pizza container. The Nervous System blog explains that “By snapping together jagged shapes, it’ll create an spherical lamp shading.”

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: 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.

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

Reconfiguration of the Earth

The Puzzle Cell Lamp takes its name from the interlocking puzzle cells found in many papers, but this one isn’t a proper puzzle—it comes with instructions. One can ignore the instructions to create an organic grouping strategy.

According to Mr. Louis Rosenberg, this is what makes a puzzle good. “You want the puzzle to be an experiment in strategizing — recognizing certain patterns, and then turning that into a methodology for solving the puzzle,” he said. He said that although the infinity puzzles made of marble may seem overwhelming, there are areas of color that will guide you, one piece at a time.

The map of Earth is the most challenging infinite puzzle. It has a topology that is a sphere, but it’s a flat sphere. icosahedral projectionMaintaining the geographical area (in contrast to some map projections which distort it) and giving every inch equal billing.

“I’ve had some complaints of serious riddles about how hard it was,” Ms. Rosenkrantz said. Puzzle pieces exhibit a more complicated behavior. She explained that instead tiling the core they rotate 60 degrees and “squeeze” the layers of the map. Ms. Rosenkrantz believes the infinity fact is particularly meaningful in this situation. 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.” On the blog, she said, “Start anywhere, and see what your journey takes.”