Namuth Hans / Getty Images
Our subconscious love for fractals may tell an evolutionary story.
In one way, Jackson Pollock’s mathematics was ahead of its time.
When the reclusive artist poured paint from cans onto vast canvases laid out across the floor of his barn in the late 1940s and early 1950s, he created splatters of paint that seemed completely random. Some interpretations saw them as a statement about the futility of World War II, others as a commentary on art as experience rather than representation. As Pollock refined his technique over the years, critics became increasingly receptive to his work, launching him into the public eye. “We have a deliberate disorder of hypothetical hidden orders,” one critic wrote, “or ‘multiple labyrinths.’ ”
In 1999, Richard Taylor, a physicist at the University of Oregon, expressed the “hidden orders” of Pollock’s work in a very different way. Taylor found that Pollock’s patterns were not random after all. They were fractal—and the complexity of those fractals steadily increased as Pollock’s technique matured.
Now, Pollock would not have known what a fractal was, nor would anyone else have at the time. It wasn’t until 1975 that the eminent mathematician Benoit Mandelbrot coined the term to describe patterns that are self-similar across different-sized scales, a “middle ground” between order and chaos. The “Nautilus” section of one famous fractal pattern named after Mandelbrot, for example, looks like a spiral, as does a magnified view of one of its sections, and so on.
Fractals are characterized by their “fractal dimension,” which is a non-integer number. Where the dimension of a straight line is one, and a rectangle is two, a fractal line drawn on a piece of paper will have a dimension between one and two. The greater the complexity of the line, the closer its dimension is to two. Similarly, a fractal area will have a dimension between a non-fractal surface (with dimension two), and a volume (with dimension three).
Taylor calculated that the fractal dimensions of Pollock’s work hovered close to 1 in the early days of his experimentation, in 1943, which means they were barely fractal at all. But over the next decade, they increased regularly, hitting just over 1.7 in 1952, 20-odd years before Mandelbrot’s seminal work. Pollock seemed to be drawn to the patterns on a strictly intuitive basis. “If he spent 10 years refining his fractals,” Taylor wondered, “then why?”
On a warm September evening in 2002, two men attacked a middle-aged furniture salesman named Jason Padgett from behind as he left a karaoke bar, knocking him unconscious. When he came to, he found that the blows he’d sustained had left him with a severe concussion, post-traumatic stress disorder, and, quite literally, a new worldview. All around him, he claimed, familiar scenes now appeared as discrete geometric patterns—as shapes that under re-scaling maintained some semblance of themselves. He saw fractals everywhere: in trees and clouds, in drops of water, in the number pi. “Geometrical blueprints,” as he called them, were superimposed over his vision.
Padgett’s astonishing new worldview drew the attention of a team of neuroscientists who scanned his brain to determine which regions were responsible for his newly acquired synesthesia. But in a sense, the transformation may have been revealing an underlying bias toward fractal visual processing in all of us. Taylor believes we have evolved to be efficient interpreters of the fractals that surround us in nature—from lightning and waterfalls to the spiral arms of the Milky Way. Our bodies exploit fractal networks to maximize surface areas and help distribute oxygen, cells, and signals. Blood vessels branch out like root systems; the brain houses folds within folds. According to Taylor, this fractal-rich environment means we don’t simply enjoy looking at fractals—we are designed to process them effortlessly, and even have a need to be looking at them.
In a 2015 experiment, Taylor and a team of researchers showed test subjects computer-generated fractals on a screen, and then gradually faded the images. At the faintest levels, subjects were best able to detect images whose fractal dimensions were most prevalent in nature. “That’s also why you might see a face in a cloud,” Taylor says, or a profile in a rock face. “You’re so fluent at processing that information that your visual system gets a little trigger-happy and starts to see things in the image that aren’t actually there.”
Our fractal fluency begins with the movement of our eyes. When we look at a fractal, our eyes trace a fractal trajectory with a dimension of around 1.4 —no matter what the fractal’s dimension is. Nature’s most prevalent fractals share this dimension, falling within a range of 1.3 to 1.5. “If we lived on a planet where 1.8 was prevalent, we would have ended up with an eye trajectory of 1.8,” Taylor says. “Clearly what’s happened is our visual system has evolved.”
And we feel good when we do what we’ve evolved to do. In another set of studies, Taylor used skin conductance and EEG measurements to measure test subject’s reactions to viewing the mid-dimension fractals found most often in nature. He and his colleagues found the images reduced the mind and body’s physiological stress by as much as 60 percent, “an enormous amount for a non-pharmacological approach.”…