‘Nature’s algorithm’ found in Chinese money plants

Look up at the clouds. What do you see? A sailboat? A seahorse? Your great-aunt Rosemary? As humans, we’re prone to seeing patterns where they don’t actually exist. This behavior is so common there’s a name for it: apophenia. But sometimes, those patterns really do exist. Cold Spring Harbor Laboratory Associate Professor Saket Navlakha specializes in finding them.

Voronoi diagrams are geometric patterns used to divide space into regions. Each region contains a given central point. For example, when dividing a town into school districts (regions), a Voronoi diagram guarantees that all students living within a district are closer to that district’s school (central point) than to any other school. “Voronoi diagrams have been used for centuries in a variety of applications ranging from city planning to network design,” Navlakha says.

Voronoi-like patterns are common in nature—giraffe stripes, for example. However, the keyword there is “like.” The difference between textbook Voronoi patterns and what we see in nature is that the latter usually lacks visible “schools.” Now, Navlakha and former graduate student Cici Zheng have found an exception in Pilea peperomioides, the Chinese money plant.

Chinese money plants are perennials native to China’s Yunnan and Sichuan provinces. You may have received one as a housewarming gift from great-aunt Rosemary. Its round, flat leaves feature prominent pores called hydathodes, surrounded by looping reticulate veins that transport water and nutrients to and from the leaf. By mapping Chinese money plants’ pores and veins, Navlakha and Zheng discovered a naturally occurring Voronoi pattern.

The team then turned to world-renowned scientist Przemysław Prusinkiewicz, who has studied vein patterning for decades. Together, they worked out the “natural algorithm” used to form looping veins around central pores in Chinese money plants’ leaves.

“Just as humans have to solve problems to survive, the same goes for other organisms,” says Zheng, now a postdoc at the Allen Institute. “But unlike humans, plants cannot explicitly measure distances! Instead, they rely on local biological interactions to achieve the same Voronoi solution.”

“We think of these algorithms in nature as an explanation for how organisms will behave and as a way to try to make sense of the world,” Navlakha says. “This example is a nice merger of classical geometry, modern plant biology, and computer science.”

“It’s remarkable how mathematical yet another aspect of plant form and patterning turns out to be,” Prusinkiewicz adds. “For decades, the question of how reticulate veins form has remained open, and finally we have a plausible answer” in Chinese money plants’ Voronoi patterns.

Navlakha and Zheng hope exploring this phenomenon can help tell us how plants work out complex problems in nature. Understanding that may provide a new framework for making sense of the math underlying evolution, development, and life itself.

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