Eternally Fractal: The Real Connection Between Tree Branches, Wrinkles, and Geometry
Have you ever looked at your wrinkles in a magnifying mirror? Have you noticed they’re a rather complex network of teeny tiny lines that branch off into even smaller ridges?
Have wondered why complex figures fascinate our minds so much? There is a curious scientific explanation, and it has to do with fractals. But what is a fractal?
Fractals are repeating patterns. The best example of a fractal is the branching pattern in a tree. Picture the trunk of a tree and the angles of a branch. Then the angles of the next smaller branch. See leaves or needles on that branch and so on.
Fractal patterns are found in the network-like branching in trees, ferns, and roots. It’s also curious that the fractal pattern of one tree matches the fractal pattern of an entire forest.
At first the repeating pattern looks completely random, but there is a lot more to it. The Fractal Foundation defines fractals as “a never-ending pattern that repeats itself in different scales. This property is ‘self-similarity’. Although fractals are very complex, they are made by a simple process.”
Studies have found that fractals are patterns in nature that have been here forever. The basic pattern stays the same, and every iteration adds a new little bit.
We Are Fractal
What is surprising is that the human body is also fractal. The same signature patterns are observed in our arteries, veins, capillaries, lung bronchi, neurons, brains, kidneys, and even wrinkles!
When we look at fractals in nature, we are basically looking at ourselves.
Our heart beat rhythm in an EKG strip is fractal; the blood flow through our kidneys is fractal. The air moving through our lung bronchi is fractal. Our physiological processes are fractal.
Fractals appear in landscape, in space, and in living creatures.
Investigative journalist Florence Williams talks about fractals in her book, The Nature Fix: Why Nature Makes Us Happier, Healthier, and More Creative, which gives new insight about the real health benefits of nearby nature.
She wanted to know more about why looking at nature makes us healthier and nicer, so she interviewed nanoparticle physicist Richard Taylor at the University of Oregon. Taylor is also a painter and photographer with two art degrees who bridges art and science.
Taylor had been studying Jackson Pollock’s paintings and knew that there was something curious about them. Especially fascinating is the story of how a dejected and lost Jackson Pollock showed his friend how he paints.
Basically, he took a can of paint and at regular intervals splattered it on the canvas. He did this day after day on the same canvas, in the same way.
In the interview, Taylor shares that the more he looked at fractal patterns, the more he thought of Pollock’s paintings. He then measured the electrical currents in Pollock’s paintings. In his published study Taylor says, “Pollock painted nature’s fractals twenty-five years ahead of their scientific discovery.”
Why Fractals Draw Us In
But why do people like looking at fractals so much? Taylor decided to measure the skin conductance of study participants, and the results showed that “people recovered from stress by 60% when viewing computer images with mathematical fractal dimensions.”
Next in the study, Taylor measured people’s brain waves while they were viewing geometrical fractal images. Surprisingly, after looking at the image for just one minute, the frontal lobes of the brain started producing alpha waves of a relaxed state.
Taylor used functional MRI to find out where the blood flow (thus attention) goes when we look at fractals and found that fractals engage the parahippocampus. This is the part of the brain involved in regulating our emotions.
So, there seems to be direct correlation between fractals and our emotional state where looking at those patterns actually calms us down and produces happiness and content in our minds.
Kinship to the Natural World
Fractal Fluency: An Intimate Relationship Between the Brain and Processing of Fractal Stimuli is the scientific paper that maps out Taylor’s fractal findings. In it he says:
“We propose that the purpose of the eye’s search through fractal scenery is to confirm its fractal character (for example, the ability to confirm that a forest features only fractal trees and no predators would promote survival).”
Pollock’s regular layers of splattered paint is like tree branches and snowflakes. Understandably, Taylor proceeded to analyze those patterns with the help of a computer, comparing them to forests. He found that they were exactly the same.
In her book, Williams writes: “Taylor believes our brains recognize the fractal kinship to the natural world, and they do it fast.”
When describing how fractal fluency takes place, Taylor says we do not have to stare at a fractal. We can get the same effect by walking down a hallway with windows or working by a window.
According to Williams, “Taylor does not know how long these positive effects last. He is working with medical researchers to see if it is possible to restore brain function. He is showing stroke patients fractal patterns.”
Our Eyes Are Fractal
Taylor has also performed studies that showed the eye’s retina was fractal. He used eye tracking equipment to measure brain activity while looking at fractals and has been using artificial fractal-based implants to restore sight to the blind.
“Our studies are highlighting an effect called fractal fluency. The eye has evolved to process the fractal patterns found in nature’s scenery. This reduces the observer’s stress by up to 60 percent.
“If you don’t build fractal fluency into a bionic eye, not only have you lost the ability to navigate, you’ve also lost that symbiotic relationship with nature’s fractal patterns.”
Fractal science in nature comes from the 1970s work of the mathematician Benoit Mandelbrot. He wrote the book Fractal Geometry in Nature, where he explains the visual side of nature through math formulas.
Fractals: Nature’s Trademark
So, there you have it, fractal complexity is in nature, us, art, and mathematics. Taylor calls fractals “nature’s trademark,” because we need natural patterns to look at; they are a natural stress reliever to the busy, overwhelmed mind.
Fractals: Bio Inspiration
In the interview, Taylor said he was using fractal fluency as “bio inspiration,” and Williams decided to apply his research. She is currently working on developing her fractal recognition skills with her kids. Sounds like fun!
So, although fractal fluency is a completely new way of looking at the world, the basics of it have always been here, around us.
Fractals are everywhere you look in nature. Look at the formation of a perfect pebble, a cloud, the veins in a leaf, pine cones, water drops, or cracks in the ground. Think about the formation of our blood vessels, skin winkles, heart beat, and our breath.
No wonder they fascinate us so much!
What would you do to start developing your fractal recognition skills? Do you feel less stressed when your eyes land on a fractal pattern? (A trick is to think not of what you see, but what it took to make the endless repetition of patterns.) Let’s start a discussion and see where it leads us!