People often find familiar shapes in random places. You may have looked at a cloud and imagined a sailboat, a seahorse, or even your great-aunt Rosemary staring back at you. Scientists call this tendency to find meaningful patterns in randomness “apophenia.” But in some cases, those patterns are very real. Associate Professor Saket Navlakha of Cold Spring Harbor Laboratory studies hidden structures that appear throughout nature.
One of the most well-known examples of organized patterning is the Voronoi diagram, a geometric system that divides space into discrete regions around a central point. A simple example is a school district. Each school district (region) is located so that students are always closest to their assigned school (center point).
“Voronoi diagrams have been used for centuries in a variety of applications, from urban planning to network design,” says Navlakha.
Patterns similar to Voronoi diagrams are often found in nature, such as giraffe patterns. However, these natural versions usually do not include the obvious center point found in textbook examples. Navlakha and former graduate student Shishi Zhen recently identified a rare exception to Pilea peperomioides, better known as China’s money plant.
China’s money tree reveals hidden mathematical patterns
Chinese money plant is a perennial plant native to Yunnan and Sichuan provinces in China. It is a popular ornamental plant as a gift. The circular leaves have prominent pores called antral nodes and are surrounded by a network of looped veins that move water and nutrients through the leaf.
After carefully mapping the pores and veins, Navlakha and Zheng discovered that the leaf structure naturally forms a Voronoi pattern.
To better understand how this pattern develops, the researchers teamed up with Przemysław Prusinkiewicz, a scientist internationally known for his work on leaf venation in plants. Together, they identified a “natural algorithm” that is responsible for producing loop-like veins around the pores of leaves.
“Just as humans have to solve problems to survive, the same is true for other organisms,” says Zheng, now a postdoctoral fellow at the Allen Institute. “However, unlike humans, plants cannot explicitly measure distance; instead, they rely on local biological interactions to achieve the same Voronoi solution.”
Algorithms hidden in nature
The discovery highlights how organisms can build highly organized systems without conscious planning or measurement.
“We think of these algorithms in nature as a way to explain how organisms behave and try to understand the world,” Navlakha says. “This example is a great blend of classical geometry, modern plant biology, and computer science.”
Professor Prusinkiewicz said the discovery may finally solve a long-standing scientific mystery about leaf vein formation.
“It is remarkable how yet another aspect of plant morphology and patterning turns out to be mathematical,” Prusinkiewicz added. “For decades, the question of how reticulated leaf veins are formed has remained unanswered, but we finally have a plausible answer in the Voronoi pattern of the Chinese money plant.”
Navlakha and Zheng hope future studies of these patterns will reveal more about how plants solve complex biological challenges. They believe this research could ultimately help scientists better understand the mathematical principles that shape evolution, development, and life itself.
