A fractal is a geometric shape which repeats itself slightly differentiated to an infinite scale, thus often described as infinitely complex. In art, such shapes appear in different cultures through time, in cases like the mandala, the well-known paisley, and, of course, in Islamic Art.
Thanos Makris, "Ephemeral Exercises: Caving Diary", p.53
In her 2017 article for Nautilus, "Is Consciousness Fractal?", Jordana Cepelewicz highlights the significance of these shapes, as shown in studies by neuroscientists and medical doctors.
The art of Jackson Pollock is the example the writer uses, mentioning the following: "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. In 1999, Richard Taylor, a physicist at the University of Oregon, 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."
Jackson Pollock, Number 1 (1949)
"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."
short zoom-in of the Mandelbrot set
"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."
"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."
It is for this reason, according to the scientist, that we often tend to notice "faces" in clouds or profiles in rock formations.
"In a set of studies, Taylor measured test subjects' 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.' That may be why, for instance, we tend to gaze out the window to refresh ourselves when we’re tired or having trouble focusing at work. Or why patients recover more quickly when their hospital room has a natural view, and why art that takes nature as its subject helps lower anxiety and stress levels. 'The parts of the brain that recognize a beautiful view are very rich in endorphins, a feel-good, anti-pain molecule,” says Esther Sternberg, an immunologist and the founding director of the University of Arizona Institute on Place and Wellbeing."
Yria Chorianopoulou, "Dragonflies"
"The fractal dimension of art is not always obvious. The bare-boned Zen meditation garden of Kyoto’s 15th-century Ryoanji Temple, for example, contains just 15 rocks positioned across a rectangular swath of raked gravel. In 2002 a group of researchers decided to investigate the mathematical reason for its appeal to tourists and meditators. Using a technique called medial-axis transformation, they found that the axes of symmetry between the rock clusters formed the fractal contour of a tree. When the rocks were rearranged in computer simulations, that tree-like structure and its meditative effect were lost. 'The people who built the temple didn’t know about fractals,' says Sternberg, who was not involved in the study. 'But they understood at some unconscious level that placing the rocks in that way made people feel calm.'”
2002 Nature Publishing Group
The writer also refers to fractal correlations in music and literature and wonders: "if so many of our deepest acts of expression have a fractal nature to them, could it be that our consciousness itself has a fractal character?".
"In the mid-1980s, Harvard Medical School cardiologist Ary Goldberger discovered that the fluctuations in our heart rates that occur over the course of seconds correlate statistically to those that occur over minutes and hours. In other words, our heartbeats are fractal—and the more fractal they are, the healthier. A fractal system, Goldberger explains, strikes an optimal balance between variability and order. When the heartbeat loses its fractal correlations, for example, it becomes erratic, resulting in arrhythmias such as atrial fibrillation. On the other hand, a steadier, more predictable and periodic pulse rate may point to congestive heart failure or cancer. 'Being fractal is a way for a system to be in touch with itself, talking to itself, but not locked in,' Goldberger says. 'You can’t exist if you’re fixed at one frequency, but if you’re all over the place, that also doesn’t fly. It’s a compromise.'"
Zacharias Papantoniou, "Forged in blood, she breaks the vowel"
"This intersection between our experience and fractals may run even deeper than Taylor’s evolutionary hypothesis. 'Any act of creativity is an act of physiology,' Goldberger says. 'The extent that we are fractalized in our essence makes you think that maybe we would project that onto the world and see it back, recognize it as familiar. So when we look at and create art, and when we decide what to take as high art, are we in fact possibly looking back into ourselves? Is creation in part a re-creation?'
On a different level, the philosopher, Kerri Welch, notes that "'Infants live purely in the present, not dividing time, surely not experiencing it the way we do now. And then, as we grow into childhood, we start seeing faster brain waves, theta brain waves … then alpha waves, and finally beta waves once we reach adolescence.' This layered understanding of time', she says, 'corresponds to how we increasingly divide time into smaller and smaller pieces.' And with it, 'it’s also our internal density increasing,' Welch adds. 'As we get older, we switch, taking in the complexity that surrounds us and recreating it inside. Our internal fractal dimension —that internal density— is increasing.'”
Antonia Iroidou, "La Sombra"
Cepelewicz concludes: "in this view, it was quite natural for Pollock’s drip paintings to become more and more fractal as he grew older. They may simply have been mirroring the increasingly fractal nature of his own self. As he said himself, 'Painting is self-discovery. Every good artist paints what he is'”.
If you want to read the whole initial article, click here.