New exhibit shows mathematical patterns abound in nature


This weekend, the Franklin Institute opens its summer exhibition about mathematical patterns that recur in nature. Its centerpiece is a 1,700-square-foot maze of mirrors, set in a grid of equilateral triangles.

It’s no confusion of Halloween hay bales or a charming hedge maze — it’s a dimly lit warren of mirrors infused with a brooding electronica soundtrack. Every angle is exactly 60 degrees, allowing you to watch three or four copies of yourself heading in different directions.

The result is disorienting and, frankly, a little creepy; imagine David Lynch as geometric field.

Larry Dubinski, the Franklin Institute president and CEO, borrowed this exhibition from the Museum of Science and Industry in Chicago.

“Several of us saw this exhibit in Chicago — I’d seen it in Chicago twice — and I thought it did a good job of, 1) being fun, but, 2) bringing mathematics to life in a way that many people hadn’t see before,” said Dubinski.

The Museum of Science and Industry has the maze on permanent display. It created a traveling version of the same size, and the Franklin Institute is its first stop.

This exhibition focuses on four mathematical patterns: spirals; Voronoi patterns like you see in turtle shells and corn on the cob; the “golden ratio” describing the ideal proportions of architecture, musical instruments, and the human body; and fractals, predictable branching patterns seen in lightning bolts and cardiovascular systems, but memorably described in a TV commercial for shampoo.

“It was so good, I told two friends about it,” said Heather Locklear in 1982, holding a bottle of Faberge Organics, the image repeating itself into a fractal grid. “They told two friends, and so on, and so on, and so on.”

“It helps us understand how the world can get so complicated,” said Jayatri Das, the Franklin’s chief bioscientist. “If you understand one simple rule underlying it, it makes sense.”

The exhibition invites visitors to closely inspect different example of Voronoi patterns, sometimes occurring in uniform shapes such as snakeskin and sometimes irregularly like the spots of a giraffe or corn kernels.

“A Voronoi pattern is a way of subdividing space in the most efficient way possible,” said Das. “Each smaller space has a seed point. The edges of its cell are closest to that seed point than any other seed point in the space.”

Most of the mathematical patterns manifest themselves visually — as spirally ram horns or the arrangement of seeds in a sunflower. Some can be described audibly.

Symmetry — the concept of absolute balance on either side of a divide — is often used to explain why some faces are more attractive than others. It also appears in music. An exhibit uses a three-note sequence printed on a block; mirror reversals of that cluster are printed on other blocks, making four variations of the same pattern. Visitors can arrange the blocks by hand and listen to them played in sequence.

Pushing the blocks around is a simplified but remarkably effective method of mimicking Philip Glass’ minimalism as an infant’s toy.

“It gets at how these mathematical patterns are embedded in our culture,” said Das. “We find these pleasing in ways over and over and over again — whether in architecture or music, we find symmetry to just work.”

“A Mirror Maze: Numbers in Nature” will be on display until Labor Day.

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