Fish Schools Swim in Ladders, Not Diamonds

For half a century, marine biologists believed they had fish figured out. Schools of fish, the thinking went, would glide through water in flat diamond formations to save the most energy—like aerial squadrons of fighter jets cutting through the sky.

But after tracking six giant danios for ten straight hours, researchers at Princeton and Harvard discovered something unexpected: fish don’t swim in diamonds at all.

Instead, they move in what scientists are calling “ladder formations”—three-dimensional patterns where fish stagger above and below each other like rungs on a ladder tilted through the water. The finding overturns decades of assumptions about one of nature’s most mesmerizing spectacles.

Swimming Against the Current of Scientific Belief

The diamond formation theory emerged in the 1970s from elegant mathematical models. Scientists proposed that fish swimming side-by-side in synchronized formations could reduce drag and boost efficiency, much like cyclists drafting behind each other. The idea seemed logical enough that it spawned countless studies and even inspired underwater robot designs.

But there was a problem: most experiments forced fish into shallow tanks, essentially flattening their natural three-dimensional world into two dimensions. “When swimming, fish on average generate a jet going backward, like the jet engine of a plane,” explained Hungtang Ko, the study’s lead author and a postdoctoral researcher at Princeton. Because of this jet effect, fish benefit from avoiding positions directly behind one another.

Ko’s team used computer vision software—originally designed to track individual animal movements—to capture the first comprehensive 3D data on fish school formations. Working with Harvard biologist George Lauder, they analyzed giant danios swimming in a tank with recirculating flow that mimicked river conditions.

The Ladder Revolution

The results were striking. Out of 264,173 video frames analyzed, the famous diamond formation appeared in less than 0.1 percent of observations. Meanwhile, the newly discovered ladder formation dominated 79 percent of all fish pairs.

Key findings from the ten-hour marathon swimming sessions:

• Only 25.2% of fish pairs swam in the same horizontal plane
• Of those planar pairs, 54.6% were inline, 30.0% were staggered, and just 15.4% were side-by-side
• Fish constantly rearranged positions, with formations changing every 32-48 seconds
• At higher speeds, ladder formations became more elongated and pronounced

The ladder pattern offers similar hydrodynamic benefits to the theoretical diamond shape, Ko noted, but requires less precise coordination between individual fish. “They can stagger in multiple planes instead of just one,” he said, making the formation more practical for real-world swimming.

Implications Beyond Fish Tanks

This discovery has immediate applications for underwater robotics. The Nagpal lab is developing fish-inspired robot swarms that could eventually patrol coral reefs and kelp forests. Understanding how real fish schools navigate in three dimensions could make these mechanical swimmers far more efficient.

The research also reveals something profound about scientific assumptions. For decades, the diamond formation seemed so logical that few questioned whether fish actually used it. The new findings suggest that nature often finds solutions more elegant and practical than human theories predict.

“The collaboration is a two-way street,” Ko reflected. “We can use computer vision to discover how and why animal groups do things together. And then we can ask, what kind of real-world robotic system could this biological insight be applied to?”

The study appears in the journal Scientific Reports, opening new questions about collective behavior in marine environments where fish have the full freedom of three-dimensional space. After 50 years of swimming against the current of established wisdom, science is finally catching up to what fish have known all along.