Their study revealed a striking parallel with Kolmogorov’s law of turbulence, which predicts how energy moves through turbulent flows, with larger swirling currents of energy – known as eddies – transferring energy to smaller ones in a process called an energy cascade. Equally significant was the further discovery of the painting’s alignment with Batchelor’s scaling, which describes how smaller eddies of energy behave within turbulent movement.
Researchers analysed the length, luminance, and spacing between the brushstrokes in each of the painting’s fourteen whirling spirals. The spacing and length of each brushstroke captured the shape, energy, and scale of atmospheric patterns - akin to “leaves swirling in a funnel of wind,” they noted - whilst the luminance mirrored the kinetic energy of motion.
“Imagine you are standing on a bridge, and you watch the river flow,” said Yongxiang Huang, one of the lead authors of the study. “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.”
The famous oil painting illustrates the view from the window of Gogh’s room during his time in a French psychiatric facility in 1889, which he admitted himself to after cutting off his left ear. It depicts a mesmerising night sky, alive with swirling blue currents, glowing stars and a hypnotic crescent moon and framed by towering cypress trees and a cosy village nestled in the distance.
While often interpreted as a reflection of Gogh’s inner turmoil and stormy mental state, the painting’s swirling explosion of colour and light also “reveals a deep and intuitive understanding of natural phenomena,” Huang added.
The whirling spirals sweeping across Gogh’s night sky paint a vivid picture of atmospheric movement with a striking resemblance to modern understandings of turbulent flow. The shapes and sizes of each swirl closely align with the distinct patterns described in both Kolmogorov and Batchelor’s laws, though it remains uncertain whether Gogh consciously studied cloud movements to achieve this or simply had an innate sense of the natural flow of the sky.
Renowned for its intricate brushwork and evocative depiction of the night sky, The Starry Night has not only become one of the most recognisable artworks in the world but also offers a stunning insight into physical truths that Gogh may have intuitively captured within his work decades before their scientific discovery.
