In the early 1950s, mathematician Lewis Fry Richardson set out to answer an unusual question: Can the length of a border predict how likely two countries are to go to war?
His intuition was simple but sharp: borders are pressure points. They mark the fault lines between identities—places where misunderstandings fester, tension simmers, and conflict ignites. Perhaps longer, more convoluted borders didn’t just reflect past hostilities; perhaps they made future ones more likely.
So he dove into the data. He compiled records from governments around the world, comparing what each said about the lengths of their shared borders. It seemed like a straightforward task—until he uncovered something peculiar.
When Richardson looked at Spain and Portugal, one country reported its shared border as 987 kilometers, while the other claimed it was 1,214 kilometers. That’s a staggering 25% discrepancy for the same stretch of land. And it wasn’t an isolated case. The deeper Richardson dug, the more contradictions he found. Border after border, the numbers refused to line up.
Was it laziness? Propaganda? Human error?
No. The answer was far more surprising: it was the ruler that had been used. What differed in all these border length estimations was the scale of measurement.
Imagine flying over a rugged coastline at 100 meters. From that height, the shore appears smooth—a gentle arc hugging the land. You'd miss countless details if you measured its length from that perspective. The result would thus be short, simple, and deeply misleading.
Now drop lower. Try measuring it with a 10-meter yardstick. Walk along the coast, laying it end to end. This will help you start to catch the bigger bends, which means the estimated length grows.
Once you switch to a 1-meter stick, you can capture even more dents and nooks. You can continue this game by using a ruler. And then a caliper. Each time your instrument becomes more precise, the coastline gets longer as you capture more texture and twists.
So, even though in all those measurements the land hasn’t changed, the total length of the coastline has. And that was Richardson’s unsettling insight: natural borders don’t have a fixed and well-defined length. Their measurement depends entirely on the scale you apply. The closer you look, the more complexity you uncover. There’s no single, final number—just a shifting approximation, shaped by your resolution; by how finely you choose to measure.
This phenomenon later became known as the coastline paradox: the idea that coastlines—and borders—defy definitive measurement. The more precisely you measure, the more elusive the answer becomes. And it started an avalanche of other discoveries.
Self-Similarity and Fractals
A decade after Richardson’s discovery, mathematician Benoît Mandelbrot picked up the thread and reframed the mystery entirely. In 1967, he posed a deceptively simple question: “How long is the coast of Britain?”
His answer was anything but simple. It was revolutionary.
Rather than chase a fixed number, Mandelbrot uncovered a deeper pattern—one that challenged the assumptions of classical geometry. Where others saw randomness, he discovered structure, where others measured smoothness, he measured roughness—and found that roughness, too, could be modeled.
Most things, especially those made by humans, become smoother and simpler the closer you look. You lose detail as you zoom in. But not a coastline. A coastline, Mandelbrot observed, looks jagged from an airplane—and just as jagged at sea level. Zoom in, and the main pattern persists. It doesn’t flatten—it replicates. And coastlines weren’t an exception. Nature is filled with these wild yet familiar forms: chaotic yet consistent, irregular but recognizably patterned.
Mandelbrot called these patterns fractals. By the 1970s, Mandelbrot had championed the term into the scientific lexicon—and with it, a new way of seeing.
Once you start looking, fractals are seemingly everywhere: in cloud banks, lightning bolts, tree limbs, lung passages, coral reefs, and river deltas. What unites them is a single astonishing trait: self-similarity across scales. Zoom in, zoom out—the form remains.
Think of a head of broccoli. Break it apart, and each floret mirrors the whole. Break it again, and the pattern holds. And in close-up shots, the pieces and the whole become almost indistinguishable. At each level, the shape retains its essence. This is not just complexity. It’s recursive complexity. A simple rule, repeated again and again, produces something rich, intricate, and alive. This is a scale-free structure: a form that transcends size, governed by rules that remain constant at every level.
The general idea wasn’t entirely new. Russian Matryoshka dolls nest one form inside another, and Gothic cathedrals echo their own spires. There are cultural reflections of the same principle: recursion in form and symmetry across magnitudes. But while most manmade things aren’t that way, Mandelbrot was the first to show how deeply embedded this structure is in the natural world. And he gave it a mathematical muscle.
Of course, perfect fractals don’t exist in nature. Trees stop branching and end in leaves. Broccoli can’t be divided forever. Coastlines blur into silhouette from a satellite’s view, and dissolve into dust under a microscope. What we see in the real world are bounded fractals—structures that approximate self-similarity within a limited range.
Yet even these imperfect patterns carry immense power. They reveal how scale can deceive, how order hides in apparent chaos, and how small things often echo bigger truths.
Mandelbrot’s insight sparked breakthroughs across disciplines: biology, economics, urban planning, art, architecture, and beyond.
Fractals are also at the heart of scale-smartness—an idea I explore throughout my book, Scale-Smart: The Fractal Path from Aspiration to Accomplishment.
Because I don’t believe fractals are just mathematical curiosities. They’re lenses. Tools for thinking, building, and navigating complexity—across systems, scales, and selves.
And that’s how I use the term here. Not as a mathematician. Not as a biologist. But as a systems thinker.
My Compendium on Scale-Smartness
A quick note on my book, which I no longer call “book”. What began as a book has evolved into something much bigger. I now call it a compendium—a layered body of work that will eventually span seven books. Three are already complete and ready to read. The others are in development, and every new chapter will be added as it grows.
Right now, I’m running what will likely be my last big promotion before the price settles at $50 with the release of Book 4. For the next few days, and with this code only, you can get the full compendium for 50% off. All future updates and books are included. And because I publish through Leanpub, every purchase comes with a 30-day money-back guarantee. If you’ve been curious, this is the best time to dive in.
👉 Get the compendium here
Conceptual Fractals
Humans make sense of the world through patterns. We don’t just observe—we compress, label, and frame. We take raw experience and distill it into concepts like “love,” “health,” or “Christmas.”
Interestingly, I’ve found that some of the concepts we use in our daily lives behave a lot like Mandelbrot’s fractals. They replicate across layers—micro to macro—retaining a recognizable shape wherever you look. Whenever I come across an idea that seems to echo itself across scales, I think of it as a conceptual fractal.
The most practical—and powerful—conceptual fractal I’ve found so far is the work unit. I’m talking about actions, tasks, and projects. These aren’t just static categories. If we look closely, they exist on a spectrum of effort. Zoom into a project, and you see tasks. Zoom into a task, and you uncover actions.
Each work unit is a structured set of intentions, each of which contains smaller ones. A project is a big intention composed of task-sized intentions, and a task is a small intention composed of action-sized ones. Seen this way, actions, tasks, and projects aren’t distinct boxes—they’re fractal forms of the same underlying shape. Each is a container nested inside another. And together, they form a fractal spectrum of work.
And once you see that, you can begin to play with it.
You can ask questions like: What’s smaller than a task? What’s larger than a project? That’s essentially how I uncovered the personal program—a higher-level structure that had been hiding in plain sight. I’d never heard anyone name it before. But looking back, I realized it had always been there, shaping how I think, build, and move through my work.
When people structure their workloads, they use terms like “to-do,” “subtask,” or “project” all the time—but often without clear distinctions and mental models around them. These labels are thrown around, yet they lack structure. They don’t carry weight. They don’t signal scale.
Fractals can fix that. They can bring clarity, hierarchy, and rhythm. Recognizing conceptual fractals doesn’t just sharpen vocabulary—it empowers thinking. It gives us a way to model systems, forecast energy, and design better flows. It helps us see both the forest and the trees and how they’re connected.
So when I talk about actions, tasks, projects, and programs, I’m not naming four disconnected categories. I’m describing a recursive continuum—one repeating structure, stretched across levels.
Programs are built from projects.
Projects are made of tasks.
Tasks are composed of actions.
Each is a vessel of intention, echoing both layers below and above it.
Fractaling
Fractals don’t just help us describe complexity—they help us engage with it. They make the overwhelming navigable by revealing elegant patterns hidden inside chaos. They don’t give us rigid formulas, but repeatable moves.
One of my favorite metaphors for complexity is The Forest—dense, tangled, and easy to get lost in. It’s what we fight through to accomplish anything meaningful. Fractals help us here not by hacking our way through with brute force, but by revealing the underlying structure. When we slice complexity into symmetric, scalable parts, we let the light in. We carve clarity from confusion.
That’s what it means to become scale-smart: learning to see—and move—through complexity with elegance.
Chaos in our lives often manifests as entropy: disorder, overload, resistance. I’ve found that the antidote is fractaling—the ability to move between levels of work with intention and agility, to shift perspective with precision.
Fractaling is the act of navigating up or down the layers of a fractal system.
It’s how we move between abstraction and action.
Whether you’re stuck in the weeds or lost in the clouds,
fractaling helps you find the level where progress lives.
Say you’re facing a tangled, high-friction problem. To get unstuck, you might zoom in to isolate a small, actionable piece. Or you might zoom out to reconnect with the larger purpose. That movement—that change in lens—is what I mean by fractaling.
Fractaling is a method. A technique. A mindset. A cognitive steering wheel. It lets you shift gears across the spectrum of intention.
When it comes to work units, fractaling means moving fluidly between actions, tasks, projects, and programs.
Sometimes you need to descend into detail. Then you fractal in; you narrow your focus. You silence the noise. You tighten the frame. You converge on what matters right now. It’s about applying constraints that create traction.
Other times, you need to rise above the noise. Then you fractal out to reclaim perspective. You zoom out from the micro-task and reconnect with the why. It’s especially powerful when you’re stuck, anxious, or spinning in low-level noise. By rising a level, you reframe the problem.
Fractaling matters because when we’re inside The Forest, we often get stuck in the weeds—or trapped in the canopy. We think at the wrong level. And when that happens, we stall. We misjudge. We drift. We delay. We procrastinate.
But not all fractaling is helpful. In fact, shifting layers without purpose can be exhausting. Every jump in abstraction carries a cognitive cost. And the brain—efficient as it is—prefers to stay put until something nudges it to move.
But once you learn to move between levels deliberately, you start to unlock flow. You cut through Perfectionism. You defuse Procrastination. You shake off Disorientation.
Deliberate Fractaling
Fractaling isn’t just a model. It’s a skill. A mental zoom lens. A practice for navigating complexity with clarity. It’s how we avoid getting lost in the weeds—or paralyzed by the big picture. It’s how we stay oriented inside The Forest.
But that doesn’t mean you should be fractaling all the time.
The goal isn’t to shift constantly—it’s to shift deliberately.
Use it when you’re stuck. That’s the signal.
When flow stalls—zoom. Up or down. Shift the scale until something clicks.
Here’s a little poem with mental hooks to remember:
When in doubt, zoom out. And when you stall, go small.
Zoom out to see. Zoom in to be.
But always remember: the shift is the key.
Neither direction is a cure-all. The magic lies in the motion. Fractaling isn’t about finding the perfect level—it’s about moving between levels until you find the one where progress becomes possible.
Let’s take an example.
Say you’re avoiding a big task, like writing a university paper with a looming deadline. You feel blocked. First, try fractaling in: isolate a smaller piece of the work. Write out a tiny goal for the day or even the next hour. Create a mini-deadline. A timebox. And suddenly, it might feel more manageable. Or, if that doesn’t work, flip it. Fractal out: Zoom out to the larger purpose. Ask: Why does this matter in the grand scheme of things? How does it connect to my long-term goals? That reconnection can reignite your drive. In both cases, the direction wasn’t the real solution. The shift itself was. The change of perspective. The re-separation of forest and trees.
To make fractaling easier and more effective, here are three practical things you can try to improve your fractaling. Each one helps reduce the mental cost of shifting—and sharpens your ability to notice when a shift is needed.
Define Clear Effort Levels: If you don’t know what level you’re operating on, you won’t know when—or where—to shift. So, create distinct effort categories — I recommend actions, tasks, projects, and programs—but you can adapt this to suit your needs. Your effort categories don’t need to be perfect; they just need to be legible and consistent. Once each of your work buckets has a defined size and scope, you’ll start asking better questions: Am I working too small? Too big? Am I missing the level where progress lives? This makes it easier to catch when you’re lost in detail, or floating too high in abstraction. A helpful essay in this regard:
Design Fractal Cues: We rarely notice we’re stuck—until something nudges us to look up. Adding tiny prompts that trigger scale awareness throughout your day can thus be a game-changer. You could add a question in your morning journal: At what level am I floating? Add a kaizen step to your weekly review. Or a daily task in your TAM. Or a time block in your calendar. Whatever your FOC is, put the cues there where you are most likely to reencounter them. Only then do they help you pause, shift, and reorient. You also might find this essay helpful in that regard:
Train your Fractal Awareness: The real goal isn’t just to react—it’s to sense early and shift fluidly. So, start observing your patterns. Do you tend to over-focus on details? Or stay too long in abstract planning? Track your tendencies. Reflect regularly. Pay attention to moments of flow and friction. Over time, you’ll develop an intuitive feel for when you’re on the wrong level—and shift before the cost builds up. Here’s the essay where I first defined and explained fractal awareness:
Put these into practice, and fractaling won’t just be a concept—it’ll become a reflex. A quiet, powerful skill that helps you stay fluid, clear, and in motion.
Even when the work gets messy, fractaling can give you back your agency. It lets you stay flexible inside complexity. It keeps us moving—not randomly, but strategically.
Thanks for reading. I hope this sparked something for you.
If it did, feel free to leave a 💛 below—and if you’d like to support my work, this is the perfect time to grab the Fractal Productivity Compendium while it’s still 50% off.
Three books are already live. All future updates are included. And because it’s published on Leanpub, every copy comes with a 30-day money-back guarantee.
👉 Get the compendium here