Light illuminates the inside of an empty snail shell.

Photograph by Layne Kennedy / Getty Images

Fractal Nature

words by willow defebaugh

Geometric, self-similar patterns known as fractals can be found all throughout nature: in snowflakes, galaxies, and even our own DNA. How can we apply their wisdom to enacting change within ourselves and the world?

“Over and over again, the world displays a regular irregularity…In the mind’s eye, a fractal is a way of seeing infinity.”

James Gleick

If you were to examine a leaf under a microscope, you would see branching networks of veins distributing fluid in a pattern that would repeat the closer you look. Similarly, a microscopic view of a snowflake would reveal crystalline structures that repeat and sprout from the center. But you don’t always need a microscope to see these phenomena; they are also observable in the spirals of plants, forking riverways, lightning across the sky, tree barks and branches. When you start to look for them, they are everywhere in nature: fractals.


First named by Polish-born mathematician Benoit Mandelbrot, fractals refer to complex, irregular geometric shapes that possess approximate self-similarity—forms whose individual parts reflect the whole. The patterns of such objects repeat at scales both small and large, carrying on indefinitely so that any isolated component appears the same when enhanced. In isolation, their shapes may appear random, but put into context, they reveal a configuration that’s anything but. The very concept of “isolation” is itself artificial—everything in the universe exists in a larger context. We only break it down so that we can try to understand it.


Some of the most well-known examples of fractals are those that contain the Fibonacci sequence: a collection of numbers in which each is a sum of the two before it: zero, one, one, two, three, five, eight, and so on. If you divide any number in the sequence by the one before it, you get the constant phi, also known as the golden ratio. This pattern shows up in spiral-shaped plants, pinecones, flower petal and seed formation, snail and nautilus shells, hurricanes, and galaxies. It’s even a part of us: the proportions of our faces and limbs, and our DNA.


So what happens when we apply a fractal understanding to systems theory and enacting change? In Emergent Strategy, author adrienne maree brown writes: “In a fractal conception, I am a cell-sized unit of the human organism, and I have to use my life to leverage a shift in the system by how I am, as much as with the things I do. This means actually being in my life, and it means bringing my values into my daily decision making. Each day should be lived on purpose.”


I do not believe that fractal theory should instruct us to focus only on individual behavior as opposed to collective action (if anything, it should break that binary altogether). Those in leadership positions who are capable of affecting wide-spread system change must do so, and urgently. But the reality is that many are not in that position—and when faced with the global nature of the problems we face, thinking too big can paralyze us into inaction. As Jane Goodall notes, this is the problem with the “think globally, act locally” approach we often hear. She frames it differently: “Think locally, and then you have the courage to act globally.”


The root of the word fractal is fractus, Latin for “fragmented” or “broken.” It’s a fitting description for how it feels to observe the state of our world. But fractal theory also reminds us that we are part of that world. And while the idea of an isolated individual may be artificial, it’s a useful tool for understanding and ultimately affecting the bigger balance that connects us. It allows us to make sense of the chaos so that we can act effectively within our spheres of influence: our everyday habits and behaviors, our local communities and relationships.


While undeniably overwhelming, understanding we are part of the broken patterns that burden our planet can be empowering, as well. We may be reflections of the whole, but the whole is also a reflection of us. If one part of a fractal changes, the rest has no choice but to follow suit. Individual and irregular as we may seem, we are fractions of a whole, fractals within fractals, capable of changing systems by changing ourselves—a spiral that leads both outward and in.

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