Scientists Found a Hidden “Golden Rule” in Abstract Art — and Your Eyes May Already Know It

Abstract art has a bad reputation. For many people, it’s just shapes and lines, sometimes also some smears of paint thrown in seemingly randomly. Stand in front of it long enough and the same awkward question creeps in: am I missing something, or is there simply nothing there?

That suspicion has haunted abstract and modern art for more than a century. But now, a new study argues that abstract art carries a hidden mathematical structure. This structure doesn’t necessarily show up in the shapes, but rather in the way the “holes”, loops, and textures unfold across an image.

Real vs AI-made art

In the Wozownia Art Gallery in Toruń, Poland, visitors stood before two exhibitions of abstract images. One was made by the Polish artist Lidia Kot, who had created a set of black-centered works for a solo show. The other was made by a machine — a customized image-generating neural network, stripped of much of the order that normally guides its output. The researchers ensured that this AI-made pseudo-art matched the artist’s works in broad visual properties like brightness and color difference. Both sets were printed at the same size, using the same paper and technology, and shown in the same gallery space.

Researchers used two matched sets of abstract images, one from Kot, the other created by algorithms. The pseudo-art had titles, exhibition framing, and a curatorial text generated with AI and proofread by an artist. Participants believed they were viewing “real”, human-made artworks.

Subjects wore eye-tracking glasses while viewing either the art exhibition or the pseudo-art exhibition, which researchers used to track their gaze. Participants also rated their aesthetic experience, including emotional intensity, perceived elements, understanding of the artist’s intent and flow.

Another set of experiments was carried out in the lab, where the same images were shown one by one for a fixed interval. In the lab, researchers tracked EEG brain activity, looking at patterns of brain connectivity while people viewed the artworks. Afterward, participants gave aesthetic ratings for each image,

The Eyes Know

In the lab, where the images appeared one by one on a screen for a fixed time, the artist-made works produced a stronger response than the pseudo-art images. Participants gave them higher aesthetic ratings across several measures, reporting clearer perception of visual elements, stronger emotional intensity, greater understanding of the artist’s intent, clearer context, and a stronger sense of flow. Their eyes also lingered longer on the artworks during the first lab visit, which the researchers interpreted as a sign of more sustained visual processing.

Viewing real art was associated with more stable, integrative brain processing, while pseudo-art prompted more exploratory eye movements and greater perceptual uncertainty.

But in the gallery, the pattern became more complicated.

Participants spent more time with the pseudo-art images than with the real artwork, and their visual intake was longer for the pseudo-art during the first visit. Their eyes also moved less while viewing pseudo-art, which suggests a more constrained, searching pattern of looking.

The researchers interpreted this not as evidence that the machine-made images were more powerful art, but as evidence that context can change the viewer’s task. In a gallery, visitors had been told they were seeing an exhibition. Faced with abstract images that lacked deliberate artistic intent, they may have worked harder to find coherence, meaning or intention. The pseudo-art, in other words, may have held them because it was harder to resolve.

But the more interesting part came from a mathematical analysis.

The Hidden Geometry Artists Seem to Share

The participants’ eye movements suggested that people were reacting to this hidden structure, even if they could not explain it. Their eyes tended to focus on areas with certain visual patterns — places where shapes, loops, textures, or edges created more structure. In simple terms, the same hidden features that the math detected also seemed to guide where people looked.

The researchers looked at a mathematical relationship called Alexander duality. That relationship is complex, but in this context, it’s basically saying that a flat image, dark shapes and the light spaces around them are linked. A hole in one view can become an island in the opposite view. Flip the image’s logic and many of the same structures should reappear in a mirrored mathematical form.

But real paintings don’t behave like ideal mathematical objects, especially because their shapes meet the edges of the canvas. They’re not endless mathematical objects, and the edge (frame) interactions create what the researchers called violations of Alexander duality.

Pseudo-Art Lacks the Structure

The pseudo-art images, generated without a coherent human compositional intent, showed a different pattern of duality violation from artist-made abstract works. Armed with this information, researchers analyzed works by eminent abstract artists, including Wassily Kandinsky, Mark Rothko and Jackson Pollock. They found that many of them seem to have a particular rate of violation of this duality.

The authors describe this as something like a “golden rule” of abstract composition. It’s not a literal formula artists follow, but a structural balance they may arrive at through trained perception, practice and intuition. This is a type of hidden compositional balance that human-made abstract art seems to often follow.

The study doesn’t say all abstract art can be described through an equation. Art is historical, cultural, bodily, emotional and stubbornly personal. A Pollock painting, for instance, is more than just its loops and color density. It is also scale, gesture, postwar myth, paint physics, market history, museum lighting and the viewer’s own memory.

But it does push back against the old idea that modern art is empty, random, or easy to fake. The study suggests that strong abstract art can carry real structure beneath the surface. Modern art may not always explain itself in familiar images, but that does not mean there is nothing to understand. Sometimes, its substance is hidden in how it teaches the eye to move, pause, search, and feel.

The study was published in PLoS.