Fractal Thinking—Introduction

You're familiar with the 80/20 rule, right? Well, I've got something even bigger.

In fact, in this series, this new way of thinking will explain the 80/20 rule and so much more.

I'm talking about fractals.

Kinda a nerdy word, I know. But by the end of this edition, you'll see fractals are not that scary, are quite beautiful, and can bring you a host of benefits.

So, what are fractals?

Fractals are a pattern of reality. You walk right by thousands of them each day without noticing. Some are obvious to the naked eye, and others take more study.

(Like The Five Lightbulbs, once you see fractals, you can't unsee them.)

So why talk fractals in a newsletter about marketing?

Marketing depends on understanding humans, and there's no better way to understand humans than understanding fractals. I rank it above psychology. By the end of this series, you'll see why.

Ever since I began my deep dive into fractals, I've used fractal thinking to:

Make business decisions that better hit the mark
Do more fruitful customer research
Create hit new products
Boost my productivity
Cut away life stuff that was causing stress
Better understand music, stories, and movie plots

And many more benefits of being able to see fractals. But first, we need to train your eye.

Here's a fractal:

Sierpinski triangle showing infinite self-similar triangular patterns within triangles

The Sierpinski triangle: where every triangle contains smaller copies of itself, infinitely

You've likely seen puzzles like this before. The instructions ask, "How many triangles do you see?"

Those are fun.

You've also seen fractals on computer screensavers. They're those mesmerizing geometric patterns. Here's a famous one called a Mandlebrot:

$Mandelbrot set fractal showing infinite complexity at boundary with self-similar bulbs$

The Mandelbrot set: infinite complexity emerging from a simple equation, with patterns repeating at every zoom level

See the repeating pattern?

Attached to each of those black circles is an identical smaller circle. Zoom in, and you'll find another identical black circle. And on to infinity.

But fractals extend far beyond these mathematical, computer-generated fractals.

Look at nature. Coastlines, snowflakes, and trees are full of fractals.

Look at the fractal pattern of a tree.

$Complete tree demonstrating fractal pattern where the whole contains many smaller self-similar trees$

One tree containing many small trees—nature's fractal at work

When you zoom in, a branch looks just like the entire tree. And just like the main tree has multiple branches, a branch has its own branches.

See the fractal pattern:

$Tree branch showing self-similar fractal pattern where each branch mirrors the whole tree structure$

Each branch is a miniature version of the entire tree

$Tree showing fractal branching pattern with zoom highlighting mini-trees within branches$

Zooming in reveals the same branching pattern at smaller scales

No, fractals in nature aren't perfect like those computer fractals. But they're still fractals.

Nature's fractals are beautiful:

$Natural tree displaying perfect fractal branching pattern with symmetrical branch divisions against blue sky$

Nature's geometry: each branch divides into smaller branches following the same pattern

$Succulent plant showing perfect spiral fractal pattern with repeating geometric arrangement of leaves$

The spiral continues inward, each layer following the same mathematical pattern

$Single snowflake crystal showing fractal pattern with six-fold symmetry and self-similar branches$

Each arm of the snowflake branches into smaller arms following the same pattern

Getting a feel for fractals? Almost?

Commit this phrase to memory: "One and many." As in, "One tree contains many smaller trees."

That phrase will help you spot fractals. Here's another example: "One doll contains many dolls."

$Russian nesting dolls (matryoshka) showing fractal pattern with each doll containing a smaller similar doll$

Each doll contains a smaller version of itself—a human-made fractal

With the Russian Doll example, you might also say the dolls are nested. Nested is another good word for understanding fractals.

You might ask your friend, "Do you see all those little trees nested inside that big tree?"

This nested way of looking at the world feels unfamiliar. Today, our worldview is more linear, and that's led to major blind spots.

Later in the series, I'll show an example of one such blind spot and how the fractal lens eliminates it.

Now that you're trained on the beginner examples, are you ready to push yourself?

Below, you'll find a harder-to-spot fractal that's been hiding in plain sight:

Fractal hierarchy from cell to country showing one-to-many relationships at each level

Each level contains many of the previous level, creating a fractal pattern of organization

See the one-and-many pattern?

One human has many cells. And that human is one of many humans in a family. And that family is one of many families in a neighborhood.

See how the pattern repeats? It's just like our triangle, Mandelbrot set, and tree.

The Cell to Country example isn't as obvious because you can't see it with the naked eye as you can with the triangle or tree. But make no mistake: The Cell to Country example is a fractal pattern.

We'll wrap up this edition with our defining characteristic of fractals: self-similarity.

Again, a nerdy term. But so important. You can see why in the updated Cell to Country example below.

Now, notice how each level is similar in that both have a head and body:

$Self-similarity in fractal pattern showing head and body structure repeating from cells to country$

Notice how the head-body pattern repeats at every level—this is fractal self-similarity in action

Do you see the head and body pattern? I'll write it below in case the image is hard to read:

Cell: Nucleus (head) and organelles (body)
Person: Head (head) and body (body)
Family: Husband (head) and family members (body)
Neighborhood: HOA president (head) and residents (body)
City: Mayor (head) and citizens (body)
Country: President (head) and citizens (body)

That's what we mean by self-similarity: each level of the fractal pattern has similar characteristics.

This fractal self-similarity is even part our language and how we communicate.

We say things like:

"The brain of a cell"
"The head of the household"
"The heart of the city"
"The long arm of the law"
"The three legislative bodies"

Are you having a lightbulb moment? This sure was for me.

Now, if you're sitting there with a gut sense that this topic holds more than meets the eye, you're correct.

And if you're wondering, "Okay, Billy, this is cool, but can I use this?"

That answer is also yes. Fractals aren't just beautiful and trippy -- they're handy.

Next week, I'll give you a specific example of how I used fractal thinking to create a hit product.

Between now and next week, your mission is to spot a fractal.

It can be anywhere. In nature, art, music, literature, a social fractal, or anywhere else. For bonus points, reply back to me with your finding.

Rooting for you,

Billy

Read: How I used Fractal Thinking to Create a Hit Product >>