Fractals and the Patterns We Lead By

I was on a long training run and listening to an audio book on the concept of comfort vs. discomfort and the impact on growth. In a particular section the author mentioned fractals…. Ahhh fractals… it’s been awhile. When I was a high school math teacher, years ago, the concept of fractals fascinated me. If you’ve never heard of fractals, they are geometric shapes or patterns that repeat themselves at different scales. This means that if you zoom into a small piece of one, it looks similar to the whole thing – which is the property of self-similarity.

Fractals are often quite complex but they are generated from surprisingly simple mathematical rules or equations repeated over and over in a process called iteration. Nature has a surprising number of fractal-like patterns; in tree branches, snowflakes, and even Romanesco broccoli florets.

Fractals are interesting and intriguing but why talk about it here – on a courageous leadership blog? I couldn’t help but see the parallel structure in our lives and our leadership – both positively and negatively. Within who we are, how we are, how we were raised, what life events we’ve experienced, what we value and how all of that shows up for us – there are often fractal-like patterns of “repeated shapes on different scales.”

Here’s what I mean. The way you respond when a team member pushes back on your idea in a meeting? Zoom out, and it’s often the same ‘shape’ as how you respond when your partner or teenager questions your decisions. Different scale, same underlying pattern. The simple rule generating that pattern might be something like “disagreement equals disrespect,” and once it’s running, it iterates everywhere – the staff room, the boardroom, the kitchen table, the group text. We don’t usually see it as one pattern, because each instance feels like its own isolated event. But it’s the same equation, playing out at different scales.

This is true of our strengths too. The leader who learned early on that curiosity served them well, and that asking good questions instead of pretending to have answers built trust, will often show that same curious, steady presence whether they’re coaching a struggling employee, sitting with a grieving friend, or navigating their own hardest year. That’s a fractal worth repeating.

This is where the comfort-versus-discomfort piece comes back in. Most of us try to fix a fractal pattern as if in fact it is NOT a given scale of  a pattern. We white-knuckle our way through the hard conversation with this one employee, or we resolve once again to be more patient with this one family member, and then we wonder why the same pattern shows up somewhere else next month. It’s a bit like the Whack-a-Mole at Chuckee Cheese! It’s exhausting, and it doesn’t stick, because we’re editing the picture instead of the equation. The uncomfortable, growth-producing work is going back to the ‘rule’ that is creating the pattern. What might be the belief, the old wound, the story we started telling ourselves long ago that has insidiously and on different scales, run our lives, one fractal at a time? Another way to say this is - is it still serving you?

I think about my years as a superintendent this way now, too. Coaching emerging leaders, I could watch someone handle a tense moment in a small staff meeting and predict, almost exactly, how they’d handle a much bigger crisis months later – same hesitation, same deflecting, (or same loss of self-control and defensiveness), same shape, just a different scale of stakes. I didn’t think of it being a fractal. I just called it a “pattern.” Turns out I was watching fractals the whole time, in the leaders I coached and, if I’m honest, in myself.

That kind of looking is genuinely uncomfortable. It’s much easier to stay at the surface, to manage the visible scale such as the tone in this one email, the reaction to this one piece of feedback, than it is to sit with the deeper, repeating why. But here’s the encouraging flip side of self-similarity: change the generating rule, even slightly, and the shift doesn’t stay contained to one scale. It ripples outward. The leader who finally does the work to soften “disagreement equals disrespect” into “disagreement is information” doesn’t just get better meetings,  teams and outcomes - all their relationships improve.

So as you think about your own leadership, I’d invite you to zoom out. What shape keeps showing up, in different rooms, with different people, at different volumes? What’s the simple rule underneath it? And are you willing to sit in the discomfort of examining that rule, trusting that the growth you’re after is on the other side of it? Are you willing to consider that it is not simply at the scale you keep trying to fix, but at the one small, root pattern generating all the rest?

Courageous leadership, it turns out, might just be fractal too.