Is The Starry Night Turbulent?

TL;DR

This paper analyzes Van Gogh's The Starry Night to determine if its swirling patterns resemble real turbulence in space, finding that the power spectrum of the painting's night sky shares characteristics with supersonic turbulence in molecular clouds.

Contribution

It introduces a novel method of analyzing art through turbulence theory, revealing that The Starry Night's sky mimics the turbulence observed in astrophysical phenomena.

Findings

Power spectrum follows a k^{-2.1} law similar to supersonic turbulence.

Identifies a driving scale at k=3 and dissipation at k=220.

The painting's patterns resemble turbulence in star-forming regions.

Abstract

Vincent van Gogh's painting, The Starry Night, is an iconic piece of art and cultural history. The painting portrays a night sky full of stars, with eddies (spirals) both large and small. \cite{Kolmogorov1941}'s description of subsonic, incompressible turbulence gives a model for turbulence that involves eddies interacting on many length scales, and so the question has been asked: is The Starry Night turbulent? To answer this question, we calculate the azimuthally averaged power spectrum of a square region ($1165 \times 1165$ pixels) of night sky in The Starry Night. We find a power spectrum, $\mathcal{P}(k)$, where $k$ is the wavevector, that shares the same features as supersonic turbulence. It has a power-law $\mathcal{P}(k) \propto k^{-2.1\pm0.3}$ in the scaling range, $34 \leq k \leq 80$. We identify a driving scale, $k_\text{D} = 3$, dissipation scale, $k_\nu = 220$ and a bottleneck. 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.