In 2004, NASA published an image by the Hubble Space Telescope of turbulent eddies of dusty clouds moving around a supergiant star. The agency noted that this "light echo" was reminiscent of Vincent van Gogh's masterpiece, Starry Night. Now, two Australian graduate students have mathematically analyzed the painting and concluded it shares the same turbulent features as molecular clouds (where literal stars are born). They described their work in a paper posted to the physics arXiv.

The notion that van Gogh's often troubled life was reflected in his work is not especially new. In a 2014 TED-Ed talk, Natalya St. Clair, a research associate at the Concord Consortium and coauthor of The Art of Mental Calculation, used Starry Night (1889) to illuminate the concept of turbulence in a flowing fluid. In particular, she talked about how van Gogh's technique allowed him (and other Impressionist painters) to represent the movement of light across water or in the twinkling of stars. We see this as a kind of shimmering effect, because the eye is more sensitive to changes in the intensity of light (a property called luminance) than to changes in color.

In physics, turbulence relates to strong, sudden movements within air or water, usually marked by eddies and vortices. Physicists have struggled for centuries to mathematically describe turbulence. It's still one of the great remaining challenges in the field. But a Russian physicist named Andrei Kolmogorov made considerable progress in the 1940s when he predicted there would be a mathematical connection (now known as Kolmogorov scaling) between how a flow's speed fluctuates over time and the rate at which it loses energy as friction.

That is, some turbulent flows exhibit energy cascades, whereby large eddies transfer some of their energy to smaller eddies. The smaller eddies, in turn, transfer some of their energy to even smaller eddies, and so forth, producing a self-similar pattern at many spatial size scales. Experimental evidence since then showed that Kolmogorov wasn't that far off with his prediction. Jupiter, for instance, has a turbulent big red spot where this kind of scaling can be observed.

The 2004 Hubble image in particular intrigued a group of physicists from Spain, Mexico, and England, led by José Luis Aragón of the National Autonomous University of Mexico in Queretaro. Aragón and his colleagues decided to find out if that perceived connection between the turbulence in the dust eddies around a star and van Gogh's famous painting might hold up mathematically. They examined digital photographs of several van Gogh paintings and measured how the brightness varied between any two pixels, calculating the probability that two pixels at a given distance would have the same luminance.

They found evidence of something remarkably close to Kolmogorov scaling, not just in Starry Night, but also in two other paintings from the same period in van Gogh's life: Wheatfield with Crows and Road with Cypress and Star (both painted in 1890). Tellingly, van Gogh's Self-Portrait with Pipe and Bandaged Ear (1888), painted during a calmer period, doesn't show signs of this turbulent scaling. Neither does Edvard Munch's The Scream (1893).

"We think van Gogh had a unique ability to depict turbulence in periods of prolonged psychological agitation," Aragón told Nature in 2006. "We have examined other apparently turbulent paintings of several artists and find no evidence of Kolmogorov scaling."

Van Gogh Museum, Amsterdam?Public domain

Kröller-Müller Museum/Public domain

In other words, as physicist Marcelo Gleiser wrote at NPR's 13.7 blog, "Van Gogh's creations during his most turbulent period mirrored nature's turbulent flows, as if his mind somehow tapped into a universal archetype where luminous becomes numinous—and the painter's brush and nature's brush become one and the same."

This latest paper builds on Aragón et al.'s work. James Beattie of the Australian National University in Canberra usually studies the structure and dynamics of molecular clouds. He and another student, Neco Kriel of Queensland University of Technology, used the same techniques they used in the simulations of turbulent dynamics. By picking a square section in the sky portion of a digital image of Starry Night, they were able to build 2D maps in three different color "channels." Then they calculated the 2D power spectrum.

Like Aragón et al., they found evidence of turbulent scaling in Starry Night. But whereas the earlier team found Kolmogorov scaling—the subsonic turbulent flow underlying the convection currents in stars as well as Earth's atmosphere—Beattie and Kriel found supersonic turbulence, just like that found in the molecular gas clouds Beattie studies.

"This leads us to believe that van Gogh's depiction of the starry night closely resembles the turbulence found in real molecular clouds, the birthplace of stars in the Universe," the authors write.