“The main reason why I draw the patterns out first, besides the fact that the designs have gotten too complicated for me to hold in my brain and solve on the fly, is because I like to have the pattern rotated so that the repeats of the pattern align with the edge, which you can only do if you have the information of how the repeats of the pattern line up with the background grid,” she explains.
Using a simple tool called a bone folder (Yoder says she’s had hers for years and could pick it out of a pile by the wear pattern), she presses and creases and rotates the paper into an elaborate pattern that could, in theory, go on forever. The end result is a beautiful, satisfyingly symmetrical array of repeated, interlocking shapes that look especially impressive when held up to the light, bringing to mind a stained-glass window.
Scholars debate whether the ancient tradition of origami began in Japan or China, but the art really took off globally in the 1950s and ’60s when publishers printed and mass-marketed diagrams showing people how to fold paper into figurative objects such as birds, fish, and animals. Paper tessellations have roots in Germany in the 1920s, when the artist Josef Albers added folding to his introductory design course at the Bauhaus. This geometric tradition started gaining popularity in the 1980s and 1990s, and now, Yoder says, there are perhaps tens of thousands of people who participate. The broader universe of origami practitioners likely numbers in the millions.
These aficionados attend conferences, watch YouTube videos, and take online courses, most of them to learn existing patterns. Yoder creates her own: In addition to the peer-reviewed academic papers she’s authored on the mathematical underpinnings of her tessellations (with titles like “Symmetry Requirements and Design Equations for Origami Tessellations” and “Hybrid Hexagon Twist Interface”) and regular presentations at origami conferences across the globe, she’s designed 696 original patterns. Each year in an event she calls Advent of Tess, she teaches thousands of online participants a new design every day of December leading up to Christmas, and her website, Gathering Folds, has become a go-to source, not just for Yoder’s artwork but for instruction.
Her EAPS degree from MIT may not seem like a foundation for a career as an artist, but Yoder, who studied geology with a secondary focus on ecology, says there are connections between the fields. “There is a lot of carryover between the crystal structures and the tessellation symmetries,” she explains. “Every repeating 2D pattern obeys one of the planar symmetry groups … There are things that repeat like a hexagon, things that repeat like a square, things that repeat like a triangle, and things that repeat like a parallelogram or rectangle. And then there are things that are not rotationally symmetric. Those ideas of how things connect and how things repeat definitely carry over from my crystallography class.”
Yoder cites the origami artist and physicist Robert Lang as one of the current practitioners who influenced her the most. He, like Yoder, has a math and science background but forged a career in art.
“The thing that has set her above the current crowd is that she’s really systematically explored the building blocks of tessellations and the different little patterns that can be considered building blocks, and the rules for connecting these blocks,” he explains. “Madonna’s knowledge and understanding of mathematics and geometry gives her a broader tool kit to create art, and that’s led to her success as an artist. You can’t separate the art from the science background. It’s part of the thinking process, even if the end goal is very much in the fine art world.”
For Yoder, the process, both computational and tactile, is also an end in itself. It is almost a meditation—a way to slow down and contemplate. Some of her students have even suggested there might be a spiritual component to it. One said to her: “You know, the name for that connection to infinite things is called God, right?”
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