The power of patterns

Throughout history, scientists have pondered the relationship between nature and humans, leading to discoveries, innovations, and questions about humans and nature’s mysterious workings. 

In that case, you’ve probably heard the phrase “no two snowflakes are alike,” or perhaps you’ve wondered why the branches of the world’s oldest trees look just like the stems and florets of the broccoli on your plate. 

Whether it’s within towering Redwood trees, mountain ranges, the blood vessels in our bodies, snowflakes, lightning, or how brain cells look under a high-powered microscope, fractals are simply everywhere — and once you start noticing them, it’s hard to stop. Fractals are self-repeating geometric patterns that are not only visually stunning but are the building blocks of nature’s smart and elegant design. They are essential to understanding nature and how we relate to it. 

The elusive science of fractals unites subjects such as mathematics, biology, and ecology as we try to understand the planet we call home.

What are fractals, really?

Hailed as the man who reshaped geometry, French-American mathematician Benoît Mandelbrot first coined the word “fractals” to describe how nature’s designs mimic irregular geometric shapes and patterns that are self-similar and self-repeating. 

In mathematics, fractals are infinite. With their irregular edges, ‘mathematically perfect’ fractals are infinitely self-repeating designs with no conceivable end or beginning. While Mandelbrot was more concerned with the mathematical enigma of fractals and how they defy our normal understanding of dimensions, fractals are easier to understand in living organisms. 

We’re quite familiar with trees, for example. By maintaining air purification through photosynthesis, trees are essential to Earth’s ecological balance and human health. Our lungs also have ‘trees’ in them, such as bronchioles. They are the smallest airways in our lungs that help us breathe and facilitate the exchange of oxygen and carbon dioxide. 

Though not infinitely self-repeating, bronchioles, tree branches, and other ‘trees’ all have fractals for one function: maximizing surface area. But what surface area are the trees in our backyard and the bronchioles inside our lungs trying to maximize, and why? 

Does the outside mimic the inside, or is it the other way around?

According to the theory of evolution, a species’ environment shapes biological features that maximize its survival. Future generations inherit features that help a species survive natural selection, or survival of the fittest. 

Through evolution, plants could have simply grown taller and sprouted larger leaves to take up more space and capture more nutrients from the sun. But this requires energy to grow and maintain, and the return on investment — absorbing more sunlight — isn’t large enough to compensate. Instead, evolution led to the formation of fractal-like branches.

By growing out each branch level as a smaller version of the previous, plants can maximize the surface area needed to capture the most sunlight while conserving space and energy. 

The same goes for our lungs: bronchioles are spread in a branch-like pattern to ensure no space or nutrients go to waste. These fractals are why our lungs have roughly the same surface area as a tennis court, despite being neatly packed in our chests. 

Other fractals include the 100,000 kilometres of blood vessels that transport blood and other nutrients throughout our bodies. The fractal branching of our blood’s interconnected highway — collectively known as the cardiovascular system — delivers nutrients efficiently from our heart to the tips of our pinkies, ensuring the energy used to transport blood stays at a minimum. 

But the power of these fractal patterns doesn’t stop there. If you look at a topographic map of the US’s comprehensive river systems, you’ll notice that rivers also arrange themselves through branches similar to our bronchioles, the fractal-patterned air sacs in our lungs.

The wisdom of nature

From amethyst crystals to the shape of brain cells, fractal designs dominate nature. But despite how common fractals are, there isn’t a unifying rule that determines whether predictable ‘branches’ will emerge or not. 

Snowflakes and ice crystals, for instance, don’t develop self-repeating fractals to maximize space and energy. Unlike inside our bodies, chemistry, temperature, and humidity determine if and how their ice branches will form. 

There isn’t a single gene, system, or overarching physical law that upholds fractals as the best shapes in the universe. Instead, various conscious and nonconscious systems have different ways of surviving and cooperating within a larger system. It just so happens that fractal branching helps nature survive with efficiency and elegance.