One of my all-time favorite paintings is Starry Night by Vincent van Gogh. I've always been drawn to the colors, the abstract swirly night sky, and it's something that I have tried to emulate several times with some of my personal astrophotography. 

Van Gogh painted Starry Night in June 1889, while he was living in an asylum in southern France as he recovered from a mental breakdown that resulted in the self-mutilation of his left ear around six months earlier. The oil-on-canvas masterpiece shows the view of a swirling sky from the window of the painter's room with an imaginary village added in the foreground, and is famous for its detailed brushstrokes and use of bright hues.

But it turns out that there may be more than meets the eye with the painting. A new analysis by physicists based in China and France suggests the artist had a deep, intuitive understanding of the mathematical structure of turbulent flow.

As a common natural phenomenon observed in fluids — moving water, ocean currents, blood flow, billowing storm clouds and plumes of smoke — turbulent flow is chaotic, as larger swirls or eddies, form and break down into smaller ones. It may appear random to the casual observer, but turbulence nonetheless follows a cascading pattern that can be studied and, at least partially, explained using mathematical equations.

“Imagine you are standing on a bridge, and you watch the river flow. You will see swirls on the surface, and these swirls are not random. They arrange themselves in specific patterns, and these kinds of patterns can be predicted by physical laws,” said Yongxiang Huang, lead author of the study published in the scientific journal Physics of Fluids. 

The atmospheric motion of the painted sky cannot be directly measured, so Huang and his colleagues precisely measured the brushstrokes and compared the size of the brushstrokes to the mathematical scales expected from turbulence theories. To gauge physical movement, they used the relative brightness or luminance of the varying paint colors.

They discovered that the sizes of the 14 whirls or eddies in “The Starry Night,” and their relative distance and intensity, follow a physical law that governs fluid dynamics known as Kolmogorov’s theory of turbulence.

Of course, Huang said, van Gogh would not have been aware of such equations but likely he spent a lot of time observing turbulence in nature.

“I think this physical relationship must be embedded in his mind so that’s why when he made this famous ‘Starry Night’ painting, it mimics the real flow,” Huang said.

So, next time you see Starry Night, take a closer look at the movement of the sky and know that it has much closer ties to nature than even the painter, van Gogh, knew!