A Non-Invasive Fractal Technique Identifies Van Gogh Forgeries by Mapping the 3D Texture of Paint

The technique is entirely non-invasive, requiring no physical contact, paint sampling, or even specialized photography beyond high-resolution images, making it safe for priceless artworks .

Test results: spotting a fake, confirming a masterpiece

The effectiveness of the method was demonstrated through two key examples :

• Forgery identified: The Plowmen (also reported as The Ploughmen): This well-documented fake was presented alongside authentic works. The fractal analysis clearly identified it as a strong outlier, with its brushstroke texture bearing no resemblance to van Gogh's verified paintings.
• Disputed work supported: Sunset at Montmajour: This painting, which had been contested for years before recent authentication by traditional experts, aligned perfectly with Van Gogh's known body of work in the fractal analysis. The test provided independent, quantitative evidence supporting its official attribution.

The broader study analyzed the surfaces of eight Van Gogh paintings from his Dutch and French periods, successfully confirming the veracity of the long-contested specimen while correctly flagging the known forgery .

Beyond 2D images: why 3D texture matters

This work represents a significant departure from earlier mathematical authentication methods. Prior digital techniques have analyzed Van Gogh's work using "geometric tight frame" stylometry, directional texture statistics from 2D images, brushstroke texton analysis, and machine learning classification of brushstroke features .

What sets the new method apart is its focus on surface topography—the actual 3D relief of the paint—rather than a 2D image of it . A brushstroke is not just a shape of color; it is a physical trace of an artist's hand movement, with a unique height, depth, and roughness profile. This topographical information provides a fundamentally different and complementary data source to traditional 2D visual analysis, capturing the physical kinetics of the artist's technique .

A complement, not a replacement, for human expertise

The researchers are clear that their technique is designed to be a powerful supplement to, not a replacement for, the nuanced world of traditional art authentication . The gold standard for determining a painting's legitimacy still involves a chain of evidence: examining historical provenance, archival documents, the canvas, pigments, ground layer, signature, condition, and restoration history .

Lead researcher Francois Berkmans stated, "Fractal analysis gives us a measurable fingerprint of an artist's brushwork without needing to sample or disturb the painting. This approach won't replace traditional expertise, but it significantly strengthens it" . By adding an objective, measurable layer of surface topography analysis to the art historian's toolkit, museums, collectors, and auction houses can reach more reliable conclusions, especially when combined with complementary analyses like chemical pigment examination .