The shocking math behind what you find beautiful: Are fractals the invisible thread that connects art, nature, and the universe?
My patient consultation room has a photograph of a wooded area. When I see it, I always feel more relaxed.
But is beauty defined by mathematics?
Does that idea resonate with you?
Repel you?
Today, I want to share how these factors shape our responses to nature and human creativity:
- Fractals
- Symmetry
- Prime numbers
I begin with a general discussion of formalism, or how we can explain beauty with mathematics.
Why? Because what we visualize affects our physical and psychological well-being.
Before discussing practical ways to use the mathematics of beauty to reduce stress levels, I’ll give some examples.
Formalism: Explaining Beauty With Math
Formalism is an art theory that focuses on a work of art’s form or visual qualities rather than its narrative or historical context.
It’s a way of analyzing and appreciating art by examining the arrangement of its elements.
Formalism in art theory emphasizes the structural elements of a work — its visual characteristics — over its narrative or historical background.
This approach analyzes and values art by focusing on the arrangement of its constituent parts.
Fractals 101 – The Shocking Math Behind What You Find Beautiful
Have you ever wondered what a fractal pattern is?
Don’t worry. You don’t need to be a mathematician to understand.
I find the mathematical shapes known as fractals to be utterly fascinating.
I am fascinated by self-similarity, which refers to shapes that contain smaller copies of themselves within their structure (repeating patterns at different scales).
A fractal is essentially a repeating pattern that goes on forever.
The key is that each part of the pattern looks like the whole thing, whether small or large.
Think of a leaf: if you zoom in on its veins, you’ll notice they resemble the branching of a river system seen from above.
That’s a fractal in action.
While familiar geometric shapes have integer dimensions (e.g., a line is one-dimensional, and a square is two-dimensional), fractional dimensions often characterize fractal structures.
The Shocking Math Behind What You Find Beautiful: Jackson Pollack, Mom, and Me
My mom loves Jackson Pollock, so when I was little, we often visited the Museum of Modern Art in New York to see his paintings.
He’s known for this abstract, splattered paint style, and I remember thinking, “I could do that!”
But it turns out there’s more to it than just flinging paint.
What Pollock was doing was creating a kind of controlled chaos with his movements and the paint.
Pollack Paints Fractals
It’s like he was painting fractals.
Jackson Pollack created these works by laying the canvas on his studio floor and pouring and dripping household paint onto it.
He used brushes and other tools to fling and manipulate the paint.
His works look complex and detailed no matter how close or far away you are. That’s what’s so amazing about them.
Standing before a Pollock painting, I easily lose my sense of scale.
I can’t quite tell how big it is or how far away I am because the patterns keep repeating and drawing me in.
It’s like the painting never simplifies, even though, if you look close enough, you can eventually see the individual blobs of paint.
But I love the overall impression of Pollack’s work, that feeling of endless complexity.
Cezanne Does It, Too
Paul Cézanne’s Mont Sainte-Victoire is another example of fractals at work.
Look at the Provencal landscape Cézanne depicts, using one of his most repeated and varied themes:
I’ve seen the work hanging in Paris’ Musée d’Orsay, one of my favorite museums.
Fractals and Mental Health
So, you may wonder, where am I going with this essay?
I usually write about health.
But here’s the thing: We can connect beauty to fractals, which are, in turn, connected to health.
Exposure to nature, specifically fractal patterns, can reduce a person’s stress level by up to 60 percent.
Getting Practical – The Shocking Math Behind What You Find Beautiful
Richard Taylor leads a research network exploring the positive physiological effects of viewing fractal patterns.
Fractals in psychology and art
Fractal Vision: (Left) The red trajectory shows the fractal motion of the eye as the observer looks at one of Jackson…blogs.uoregon.edu
Using eye-tracking, EEG, and fMRI, Taylor and colleagues discovered that a specific type of fractal naturally draws people, which can reduce stress.
This stress reduction appears to happen because of a physiological resonance.
When the fractal structure of our visual system aligns with the fractal image, it triggers an automatic relaxation response.
How You Can Use Fractals
Stress-related illnesses cost the U.S. over $300 billion each year.
Researchers increasingly recognize stress as a contributing factor in severe disorders like schizophrenia.
How can we use fractals to promote our psychological well-being?
Feeling stressed? Try these nature-inspired solutions:
- Step outside. A 20-minute nature walk can lower stress hormones, blood pressure, and heart rate.
- Shift your view. Position your workspace near a window with a view of trees and grass. If that’s not an option, nature photographs can also reduce stress.
- Add some greenery. Even if you’re not a gardener, having plants around can be beneficial. While well-designed artificial plants can offer some benefits, real plants also improve air quality.
- Explore biophilic design. Fractals are a great example of biophilic design, bringing the natural world into our environments. Consider how you can further integrate these principles into your workplace to maximize their positive impact.
Biophilia
In his 1984 book Biophilia, biologist Edward O. Wilson introduced and popularized the term, derived from the Greek for “love of life.”
As a Harvard undergraduate majoring in biology, I got to know Professor Wilson.
E.O. Wilson, a Pioneer of Evolutionary Biology, Dies at 92 (Published 2021)
www.nytimes.com
He argued that the drive to connect with living things is a fundamental and complex aspect of human mental development, essential to our survival and deeply ingrained in our being.
He suggested that while the modern world now shapes our lives, our minds remain rooted in the natural environments where our species evolved.
Biophilia
is Edward O. Wilson’s most personal book, an evocation of his response to nature and an eloquent statement of the…www.amazon.com
Consequently, we are innately attracted to features like water and vibrant landscapes, as these historically signaled the presence of resources crucial for our sustenance and shelter.
Biophilic Design
Biophilic design is an architectural style that incorporates nature into buildings to create healthier and more productive spaces.
Design elements include:
- Natural light: Use natural light and ventilation to align with circadian rhythms
- Natural materials: Use natural materials like wood, stone, and linen to create a tactile connection to nature
- Plants: Incorporate living walls, houseplants, and green roofs
- Natural shapes and patterns: Use natural shapes, patterns, and processes
- Water: Incorporate water features like lakes
I live near an example of biophilic design, the Amazon Spheres in Seattle (USA).
Plants fill three glass domes at Amazon’s headquarters. The domes opened in 2018.
My London friends can find an example of biophilic design at the Barbican Centre, where structures mingle with lakes and wildlife.
Does Exposure to Nature Work?
For me, nature is restorative.
I immediately feel more relaxed as I head out for my daily walks.
I tend to be more creative; many of the ideas I have for writing emerge while I walk.
My stress drops.
And I love that my walk in nature bolsters my immune system.
I wish we thought of nature exposure as a public health strategy.
More Evidence: The Stanford University Experience
Stanford and other researchers have focused on rumination, a maladaptive thinking pattern that can lead to depression and other psychological problems.
Rumination involves dwelling on the causes and conditions of one’s distress without looking for solutions.
We all ruminate to some extent, some people more than others.
The brain’s prefrontal cortex, particularly the subgenual area, is also active during rumination. This region shows heightened activity when we are sad and can go awry by turning normal self-reflection into a depressive state.
Gregory Bratman (a Stanford University biopsychologist) and colleagues put the brains (and the bodies) of 38 healthy urban adults to a test.
The researchers randomly split the group into two groups, and each group spent 90 minutes walking in two drastically different settings.
One group walked alongside a traffic stream on El Camino Real, while the other walked the grassy slopes of the foothills above Stanford’s campus.
Study Results
Before and after the walks, researchers measured blood flow to the subgenual prefrontal cortex using functional MRI brain imaging. They also used a questionnaire to gather self-reports on rumination.
Did environmental differences play a role in increasing and decreasing this type of thought pattern?
The team found that walking around the nature preserve correlated with a significant drop in blood flow to the brain’s subgenual area, indicating less brain activity; participants also reported less rumination.
Those who walked along the busy Palo Alto road had little to no change in blood flow.
The researchers concluded that a natural experience can impact this brain pathway. Access to preserved open spaces may be a critical resource for improving urban areas’ “mental capital.”
Fractals and Brain Activity
Swedish EEG studies have shown a correlation between viewing natural, or “rough,” fractals and increased alpha wave activity in the brain.
Conversely, viewing artificial, or “exact,” fractals resulted in less alpha wave activity.
This finding suggests that the fractals found in nature have a calming effect.
Further research indicated that natural fractals of mid-range complexity, prevalent in the environment, stimulate alpha and beta brain waves.
This activity suggests a complex interaction within the brain: the alpha waves indicate a state of relaxation and restoration.
In contrast, the beta waves likely reflect the brain’s processing of the fractal’s spatial characteristics.
My Final Thoughts – The Shocking Math Behind What You Find Beautiful
Relieve stress and rebalance your body and hormones with the power of fractals.
Your brain can detect fractals in just 50 milliseconds, triggering a positive response before conscious recognition.
Of course, exposure to nature is not a panacea.
Listen to Stanford researcher Bratman:
“By no means do I say that nature cures depression. But as we continue to urbanize, the question becomes more and more relevant to more and more people: What are the repercussions if we don’t bring nature into the city or conserve it outside of it?”
What’s your go-to approach for stress reduction? Does it involve nature?
Get an email whenever Dr. Michael Hunter publishes.
drmichaelhunter.medium.com
Thank you for reading “The Shocking Math Behind What You Find Beautiful.”
