Why viewing fractals soothes

Jackson Pollock pictures copy patterns of nature - tree branches, snowflakes, waves - and the structure of the human eye

When Richard Taylor was 10 years old, in the early 1970s in England, he accidentally found a catalog of paintings by Jackson Pollock. He was mesmerized, hypnotized by Pollock. Franz Mesmer, an eccentric doctor of the 18th century, suggested the existence of animal magnetism between living and nonliving objects. Pollock's abstractions also project certain states of consciousness into the viewer. Now, working as a physicist at the University of Oregon, Taylor believes that he understood the secret of Pollock's paintings, and that he was firmly connected with human happiness.

Professionally this issue he was engaged not all the time. His main job was to search for the most efficient ways to transfer current — through many tributaries, like river systems, or the bronchi of the lungs, or neurons of the cerebral cortex. When current flows through wires, electrons travel in an orderly fashion. But in the new tiny devices, whose size can be only 100 times larger than the size of an atom, this order is violated, and becomes like an ordered chaos. The flow pattern of currents, like the circuits of the bronchi and neurons, is fractal, i.e. it is repeated on different scales. Taylor now uses “biological inspiration” to develop improved types of solar panels. If natural panels, trees and plants branch out, why not repeat it in the case of man-made?

Taylor speaks of himself as a thinker, moving in search of solutions from one discipline to another. In addition to his physical regalia, he is an artist and photographer with an appropriate diploma. On the campus of the Institute, he is known for his eccentricity. He often floats in a boat on Lake Waldo in Oregon in search of new thoughts, and his hair is so famous that it distracts from his personality. Long curly hair resembles the curls of Isaac Newton. The University Public Relations Center somehow used them to create a photo collage in Photoshop.
')


Moving along the curly trajectory of his career, Taylor did not lose his interest, or even obsession, with Pollock. In the Manchester School of Art, he built an unstable pendulum, throwing paint under the action of the wind, to see how nature draws, and whether it will look like Pollock (it turned out like). Then, a few years ago, he experienced a fruitful insight while working on nanoelectronics. “The more I looked at the fractals, the more they reminded me of Pollock's paintings,” he recalled in an essay . “And when I looked at his paintings, I noticed that the spots of paint on the canvas are distributed in much the same way as the flow of electricity in our devices.”

Using instruments to measure electrical currents, Taylor checked several Pollock paintings of the 1950s and found that the paintings were indeed fractal. It looked like you found your aunt talking in a secret, ancient language. "Pollock painted natural fractals for 25 years before their discovery!" He published this discovery in the journal Nature in 1999, causing a stir in the world of art and in the world of science.

Benoit Mandelbrot first coined the term "fractal" in 1975, discovering that simple mathematical rules apply to a vast range of phenomena that look visually complex or chaotic. He proved that fractal patterns can often be found in the tumult of nature — in clouds, coastlines, plant leaves, ocean waves, bends of the Nile River and clusters of galaxies. To present fractal patterns of different scales, imagine a tree trunk and a branch: between them there can be the same angle as between this branch and the smaller branch, and also between the veins of a leaflet growing on this branch. And so on. You can invent fractals that create something that looks like chaos.

Taylor was interested to find out whether the attractiveness of Pollock's paintings can be explained by the presence of fractals in them, as well as the attractiveness of similar screen savers and light shows in planetariums. Can great works of art be reduced to non-linear equations? Such a question could come to mind only physics. So Taylor conducted experiments, evaluating the psychological reaction of people to viewing images with fractal geometry. He measured the conductivity of the skin (corresponding to the activity of the nervous system) and found that people coped with stress by 60% better by considering the image of the mathematical dimension of fractals (which is denoted by D) from 1.3 to 1.5. D denotes the ratio of the size of large (coastline visible from an airplane, a tree trunk, large spots on the paintings of Pollock) and small details of the image (dunes, stones, branches, leaves, small specks on the paintings). The fractal dimension is indicated by a number in the range from 1 to 2. The more complex the picture, the higher D.

Then Taylor and Caroline Hagerhol [Caroline Hägerhäll], a Swedish specialist in environmental psychology specializing in people's aesthetics, turned several photographs of nature into simplified fractal silhouettes against the sky. They found that people preferred images with D in the range from 1.3 to 1.5, that is, from low to medium. To find out whether such a dimension causes a certain state of mind, they used the EEG to measure brain waves, while the subjects observed fractal images. They found that it was in this magic zone that the frontal lobe of the subjects' brain gave out alpha waves corresponding to a state of calm and pleasant wakefulness. This happened even when people looked at the images for just one minute.

EEG measures waves and their frequency, but does not mark specific active brain sites. For this task, Taylor turned to fMRI, which shows the parts of the brain that are currently working through measuring blood flow. Preliminary results showed that medium resolution fractals activate some predictable areas of the brain, such as the ventral prefrontal cortex associated with high-level image processing, and the dorsal cortex encoding long-term spatial memory. But fractals also caused a reaction in the gyrus of the hippocampus, which is responsible for managing emotions and activating when listening to music. Taylor found these discoveries extraordinary. “We were pleased to find that medium resolution fractals look like music,” he said. That is, the emotional effect of contemplating the ocean can be the same as listening to Brahms.

Taylor believes that our brain recognizes this connection in nature - Pollock's favorite sizes corresponded to trees, snowflakes and veins in minerals. “We analyzed the pictures of Pollock using a computer, compared them with the woods, and it turned out that they are essentially identical,” Taylor said. This resolution of fractals does not just soothe us, it can attract us, inspire reverence and make us think about ourselves.

But why exactly such a value D possesses such magical properties and attracts people? Taylor and Hagerhol came up with an interesting theory, not necessarily associated with a romantic desire for pastoralism and harmony with nature. In addition to the lungs, capillaries and neurons, people have another branching system: the visual system, expressed through the movement of the retina. Using a system to track eye movements and determine what people focus on, Taylor found that the search pattern followed by the eyes is itself a fractal. Eyes first scan large elements of the scene, and then make micromotations in the range of average values ​​of D. What is interesting, if you draw a path that animals move in search of food, for example, albatrosses that look at the ocean, you will also get similar fractal patterns. It's just an effective search strategy, says Taylor.

“Your visual system is in a sense tied to understanding fractals,” says Taylor. “The reduction of stress is triggered by a physiological resonance that occurs when the fractal structure of the eyes coincides with the fractal image.” If the scene is too complex, such as a city intersection, we cannot quickly perceive it as a whole, and this leads to subconscious discomfort. It makes sense to believe that our visual cortex feels best in the midst of common natural phenomena, among which we have evolved. Perhaps some of our comfort from being in nature comes from its quick visual processing.

If the reason for relaxation is not entirely romance of Henry Toro , then the solution is definitely there. Taylor says that we need to look at natural patterns, and we will never get tired of them. And, increasingly surrounding ourselves with Euclidean interiors with straight lines, we risk losing our connection with the natural stress suppressor - with visual simplicity. All this agitates even more for the return of greenery to the cities and for frequent trips outside the city.

For Taylor, I had the last question. I talked to him on Skype, since he was vacationing in Australia at the time. His soft curls went down to the bottom of the screen, like streams.

"Is your hair fractal?"

He laughed. “I suspect that yes. The only question is whether they cause positive physiological changes in the observer! ”