“We did not come into this world, we came out of it like buds out of branches and butterflies out of cocoons. We are a natural product of this earth, and if we turn out to be intelligent beings, then it can only be because we are fruits of an intelligent earth, which is nourished in turn by an intelligent system of energy.”
– from Gifts of Unknown Things by Lyall Watson
It is part and parcel of the human experience to seek one’s place in the world and to try answering existential inquiries like “What am I?” and “Where do I belong?” Nature and Forest Therapy Guide training and practice have been a pathway for me to a very simple yet profound realization, “I am Nature.” This realization came as spring storms do—suddenly; it bloomed as spring flowers do after a nourishing rain—overnight; and it filled me up with vitality and a zest for life as crystal-clear water from a natural spring fills a thirsty dried-out lake—profoundly and to the brim. And then, kudos to my busy mind, questions came, “What does it actually mean? How and in what ways am I Nature?” Such realizations and questions can be attributed to the relational aspect of Nature and Forest Therapy. This practice supports people in remembering and recognizing their connections with nature and in establishing new links and relationships with beings and elements that are part of the all-encompassing web of life. Nature and Forest Therapy is also about reconnecting with oneself and remembering that we humans are nature too, that we are one of millions of manifestations of Earth’s intelligence, and that the same fundamental principles guiding all life on Earth guide our existence as well. One of such principles is fractals. Fractals are self-similar, though not necessarily identical, patterns repeating at different scales. And they are everywhere.
During a nature therapy walk, a guide would offer a simple question to invite participants to share their experiences, “What are you noticing?” I’m inviting you now to step away from the screen for a minute and take a slow, careful look at a leafy plant in your space or maybe even in your fridge (think kale, spinach, cabbage, parsley). What patterns are you noticing? Maybe your gaze has followed the veining on a leaf or the arrangement of leaves along a stem. There’s a certain regularity to these patterns, isn’t there?
Fractal patterns in nature are all around us; they are also within us, in things and systems that we create, and in ways we live our lives. Are you intrigued yet? In this article, I explore different manifestations of fractals and offer invitations to bring them into your daily life.
Fractal patterns in nature can be easily noticed with our sense of sight. Trees are perfect examples. Their branches, leaves, flowers, and roots are composed of fractal structures. When you carefully follow a branch with your gaze, you might notice how it splits up into smaller branchlets that further split up into twigs. As time passes, the twigs will grow into branches themselves while splitting up into new branchlets and twigs. It’s a curious process of multiplication by division! Some studies even suggest that “the distribution of large branches to smaller branches in a single tree exactly replicates the distribution of large trees to smaller trees in an entire forest!”2 Thus, fractal patterns self-replicate in space and over time. On the planetary scale, fractal patterns can be observed in the shape of coastlines, ocean waves, watersheds, mountain ranges, as well as in lightning and cloud formations3. That’s right, clouds are not just random amalgamations of water vapor. “Clouds show self-similarity across scales ranging from 1 to 1,000 km.”4
Snowflakes are another example of a fractal, though their organizational principle is a bit different. A snowflake starts by expanding from the center in multiple directions. Each one of its rays is composed of fractal structures and is almost identical to the rest. Such regularity and complexity make snowflakes a Nature’s work of art.7
Fractal patterns can also be organized as a spiral. Logarithmic spirals are the most fascinating, with each curve appearing the same at an increasing scale with a growth factor of phi.9 Examples of a logarithmic spiral can be seen in shells of some mollusks, in the arrangement of sections in succulents or of seeds in a sunflower, and in spiderwebs. At a mega scale, most galaxies known to science are organized as spirals, including our home, the Milky Way.10
Fractal patterns exist in other forms, for example as sound. The crashing of ocean waves against a shore produces infinitely self-similar patterns of sound. The sounds of the more-than-human world are full of fractals too. A study by Roske et al. (2018)13 investigated the musical rhythm in thrush nightingale’s songs and determined that it is multifractal. There are recurrent patterns that are similar but not exactly the same, yet there’s “dynamically fluctuating predictability.”
Fractal patterns are also within us. The DNA is organized as a fractal globule. Our eyes inspect objects by moving in fractal patterns. Our respiratory, circulatory, and nervous systems are fractal structures as well. In this sense, they are like trees, like rivers, like lightning. They are Nature’s way to maximize efficiency while minimizing space. Did you know that “our lungs cram the area of a tennis court into the area of just a few tennis balls” or that our arteries, while taking up just 3% of our body by volume, can deliver nutrients to each and every cell?14 Within our bodies, different types of fractals are interwoven with one another, just like different fractal systems on our planet are enmeshed within each other. And the fractal composition of us, and of other animals with respiratory, circulatory, and nervous systems, is not limited to anatomy. It is also reflected in the way our neurons fire and our hearts beat. It was believed that hearts beat at regular intervals, but modern science has determined that there’s fractal patterning to the heart’s rhythm called heart rate variability. And an interesting fact is that the degree of self-similar irregularity in the heart’s rhythm can serve as a measure of heart health.15
Even the most distinguishing feature of the human species—language—is based on fractal patterns, and human language development is not linear, as previously thought, but displays fractal properties16. Let’s take syntax, for example. Syntax is the arrangement of words to form phrases and sentences. Any phrase and any sentence can be made more complex by adding structures that are similar to each other in their composition but display slight variation in the number of words or types of parts of speech used. Consider the sentence “Fractals are fascinating.” We can “build it out” by adding phrases that are similar to each other and to the initial sentence in their composition and relations. Here we go: Fractals are fascinating. – I think fractals are fascinating. – I think fractals are fascinating because I see them everywhere. – I think fractals are fascinating because I see them everywhere and because I am made up of fractals too. If we create a syntactic tree, or diagram, for the last, most complex sentence (yes, such “trees” exist, credit to linguistics), we can easily see how it resembles a tree branch. Researchers have also found that even the organization of keywords, or topic words, in a text displays fractal properties.17
Fractals are also present in the things we humans create, like music, art, architecture, and more. Self-similar recurrent patterns are found in the melodic organization of baroque, classical, and some folk music. Artists working with different media create art pieces that are pleasing to the eye and soothing to our nervous systems by consciously or subconsciously applying fractal organization or the golden ratio to their composition. Leonardo Da Vinci, Michelangelo, and other Renaissance masters used the golden ratio in their masterpieces. The waves in the famous painting by Hokusai, The Great Wave Off Kanagawa, curve in a logarithmic spiral and are made up of fractal elements. Van Gogh’s most famous painting, The Starry Night, contains logarithmic spirals, and the painting’s overall composition follows the golden ratio. These are just a few examples.
Folk art created in different parts of the world often has one thing in common – fractals, reflecting the patterns found in nature.
Ceramic Olla (Jar) from the Cleveland Museum of Art
The Anasazi Tribe, Arizona, circa 12th-13th century
Traditional Belarusian art of paper-cutting—Vytsinanka.
“Me and My Soul” by Volha Palunisa, 2021
*Photo shared with the permission of the artist
Benefits of viewing fractals: Because fractals are everywhere and a part of everything, it’s not surprising that engaging with them produces some beneficial effects. Scientists use fractal dimension (D) to determine how complex a self-similar structure is. This measure is usually represented by a number from 1 to 2. Fractal patterns in nature range from 1.3 to 1.5. In scientific experiments, people viewing such mid-range fractals experienced a wakefully relaxed state. The alpha activity in the frontal lobe was high and the beta activity in the parietal lobe was also high.19 The effects of alpha brain waves are associated with lowering stress, reducing anxiety, decreasing depression, and improving creative thinking. The beta waves signify attentiveness and alertness. These findings are in line with the Biophilia Hypothesis, which states that “human beings have an innate biological predisposition to react positively to nature,” and also support Attention Restoration Theory, according to which exposure to nature significantly improves cognitive functioning and mood.20
So, what can we do with all this information? We can deepen our relationship with nature outside and within by engaging with fractals in their different forms and representations.
Here are some invitations to explore fractals:
● Look for fractal patterns in your environment. Study your household plants with your gaze, with your fingers. Study the plants and trees on your walks. Give them time and attention, notice the similarity between branches, the veining on the leaves. Pick up a flower petal and look through it against the sunlight.
● Listen to fractals: ocean waves, birdsong, your own heartbeat, a pet’s heartbeat. Notice how it makes you feel.
● Follow a stream or walk along a shore. Imagine yourself soaring high in the sky and looking at it from above. I wonder what you would see.
● Take yourself to an art gallery or a museum. Spend some time looking for fractal patterns in paintings, sculptures, and art installations. Notice what you are noticing.
● Spend some time with folk art looking for reflections of nature’s fractal patterns in the artwork.
● Get curious about the fractal structures of the human body, of other beings. Study them intuitively and cognitively. You can start by making a handprint on a piece of paper and then study the lines and patterns, the concentric circles at the tips of your fingers. Just for fun, make a footprint and study that. If you have a pet, make a paw print, and notice the details!
● Sketch or draw trees, leaves, flowers noticing repeating structures, angles, and the big picture.
● Put together a “fractals” basket with leaves, pinecones, snail shells and take it to your sit spot. Use your senses to explore these items.
● Spend a few minutes being a mirror for a tree or plant. Reflect the branches and twigs with your arms and fingers.