In a groundbreaking exploration merging the realms of art and mathematics, an international team of researchers has unveiled a hidden structural code beneath abstract paintings—a code that appears to govern how humans perceive and respond to visual stimuli. Published recently in the open-access journal PLOS Computational Biology, this study employs advanced mathematical techniques from the field of computational topology to decode the subtle architecture of abstract art and its profound impact on human cognition.
For centuries, artists and scientists have sought to uncover what it is about certain artworks that move us so deeply, stirring emotions, capturing attention, and fostering profound aesthetic appreciation. Despite extensive psychological and artistic inquiry, pinpointing direct, quantitative relationships between the formal properties of visual art and the viewer’s perceptual experience remained a formidable challenge. This new research, led by Jacek Rogala of the University of Warsaw and Shabnam Kadir of the University of Hertfordshire, provides a pioneering approach by applying a topological lens to the mysteries of abstraction.
At the heart of their analysis lies a sophisticated mathematical tool known as persistent homology. Originating from computational topology, persistent homology is designed to evaluate the shape and connectivity of data by capturing its structural essence across multiple scales. Translated to the visual domain, this method can dissect and characterize the complex geometric patterns and voids present within an image’s texture and composition—attributes often invisible to conventional analysis. The research team applied this technique to two distinct datasets: authentic abstract paintings by recognized masters and artificially generated “pseudo-art” images created by AI algorithms mimicking artistic styles.
Remarkably, persistent homology offered a clear demarcation between genuine abstract artworks and AI-generated pseudo-art. This finding underscores that genuine human creativity in visual art imparts distinct topological features that current artificial methods struggle to replicate fully. Beyond classification, the study delvé deeper into the mathematical properties distinguishing eminent artists such as Wassily Kandinsky, Mark Rothko, and Jackson Pollock. These maestros’ works exhibited a fascinating phenomenon: convergence toward a specific degree of distortion—termed a violation—of a central mathematical principle known as Alexander duality.
Alexander duality traditionally relates structures within a shape’s interior to its boundaries in topological terms. The research identified that these abstract artists intuitively balance compositional elements between the edges and the interior of their canvases following a ‘golden rule’—a precise rate at which this duality is systematically violated. This novel insight into their creative process hints at an underlying universal rule, possibly untaught yet inherently understood, that guides the delicate arrangement of forms and spaces in impactful abstract art.
The study also ventured into the neurological correlates of this visual processing. By monitoring eye movements and measuring brain activity of observers viewing the two sets of images—both in controlled lab conditions and real gallery environments—the scientists uncovered compelling differences in engagement patterns. Genuine artworks elicited more stable, integrative brain states associated with focused attention and cognitive coherence, whereas pseudo-art evoked exploratory eye movements tied to uncertainty and fragmented perception. These empirical findings suggest that the topological structures identified by persistent homology not only describe visual complexity but actively direct viewer attention and perceptual stability.
Integrating these strands, the researchers mapped eye-tracking data onto the topological features of images, revealing a striking correspondence between where individuals fixated visually and where the most significant topological structures lay within the compositions. This convergence blends abstract mathematical morphology with real-world cognition, affirming the validity of the topological approach in understanding the nuanced mechanics of visual art appreciation.
The implications of this research ripple beyond art history and psychology, reaching into fields such as artificial intelligence, neuroscience, and even gallery curation. Senior author Jacek Rogala highlights the transformative power of context: “We observed measurable effects of the gallery environment itself—beyond just serving as a backdrop—modulating how long and how deeply images captured attention. This is quantifiable evidence that immersive settings amplify the perceptual experience in a way that can be scientifically tracked and analyzed.”
This interdisciplinary study charts a bold new course in the scientific study of art by unveiling a hidden mathematical topology that underpins human aesthetic experience. Persistent homology emerges as a powerful analytic bridge linking the formal abstract qualities of artworks with their neural and behavioral effects on viewers. As AI-generated art gains prominence, such insights could also guide future development of algorithmic tools, ensuring they incorporate these mathematically grounded principles to better mimic the immersive qualities of genuine human creations.
Through this melding of topology, psychology, and gallery science, the study opens windows not only into how we create and engage with abstract art but also into the fundamental cognitive and mathematical frameworks shaping human perception. By deciphering this previously invisible structural code, we gain a deeper appreciation of art’s timeless allure and the scientific elegance underlying creativity.
Subject of Research: Not applicable
Article Title: Art’s hidden topology: A window into human perception
Web References: http://dx.doi.org/10.1371/journal.pcbi.1014156
References: Dmitruk E, Bajno B, Kot L, Dreszer J, Bałaj B, Ratajczak E, et al. (2026) Art’s hidden topology: A window into human perception. PLoS Comput Biol 22(5): e1014156.
Image Credits: Credit to Emil Dmitruk, CC-BY 4.0
Keywords
persistent homology, abstract art, computational topology, Alexander duality, visual perception, eye tracking, brain activity, neural processing, art and mathematics, artificial intelligence, aesthetic experience, cognitive neuroscience
