Fractals in Business: Insights on Patterns and Capital Allocation

During their recent episode, Taylor, Carlisle, and Ashton discussed Fractals in Business: Insights on Patterns and Capital Allocation, here’s an excerpt from the episode:

Tobias: Zeke, we do Jake’s veggies usually at the top of the hour. We’re a little bit late today. We missed it last week. And thanks to everybody who let me know that we missed it. We’re trying not to do that ever again.

Jake: The natives were restless.

Tobias: They were.

Jake: All right. Let’s just get this out of the way. Give the people what they want. So, this week, we are talking about fractals. And fractals are these complex patterns that are self-similar across different scales. So, zooming in, it looks the same as when you zoom out. And the pattern closer resembles the overall shape over and over again. These patterns are found in mathematics, nature, art. They’re very appealing to the human eye. There’s something about them. They’re really characterized by their infinite complexity.

So, the term fractal was coined by Benoit Mandelbrot in 1975. It’s from the Latin word fractus. Meaning, broken or fractured. They’re produced by repeating these simple processes with an ongoing feedback loop. So, basically, the output then becomes the input of the next part of it, and it just keeps running over and over again.

Mandelbrot’s journey into this world of fractals that he discovered are really more named. I think they existed already in nature, obviously, but it almost began by accident. While he’s working at IBM on these on signal noise problems, which should sound familiar if anybody remembers Kelly and Thorpe and Claude Shannon. But he started noticing these patterns that seemed too irregular to be described by traditional Euclidean geometry. And his curiosity led him to study coastlines, clouds and other natural phenomena where he recognized also these self-similar patterns. This interdisciplinary exploration was a real departure for the norm and was actually not well received by his peers. Like, it blocked him in his career [chuckles] to actually be using your mind in your own ways.

But his work was groundbreaking. And not only in mathematics, but also in the way that it bridged the gap between art and science. It really showed that these simple mathematical concepts could explain complex patterns in nature. And now, they’re all around us. You see them in trees, you see it like Romanesco, broccoli, coastlines, mountain ranges, even actually patterns in lightning have some similarities. And this repeat pattern at different scales, it explains things in a more simplified way.

So, basically, in computer graphics today, now the fractal algorithms are used to create realistic looking landscapes and textures without actually having to draw it all out. You could just run the math behind it, and it will then generate it and create this really infinite, rich complexity. A term that Mandelbrot used was roughness. So, the more there was to it, the more rough did it look, you think about a rough coastline.

And now, they play a really crucial role in digital signal processing, the design of antennas that go into mobile phones and other devices. So, this daydreaming French guy that just found these patterns, it ends up translating into all kinds of places in the real world that help us.

But let’s try to bring this back to business a little bit. So, I was having coffee with a guy last week. He’s running his own private mini-Berkshire holding company. We were talking about different principals and managers. It occurred to me that there’s a fractal nature at play there, where there’s like these Russian nesting dolls, which are called Matryoshka, I believe, or Matryoshka? My Russian friends will have to be making fun of me for that. But in effect, it affects capital allocation, actually. So, if you’re a large pool of capital, you’re looking for certain characteristics in your fund managers, like intelligence, enthusiasm, trustworthiness, dependability, maybe a conservative bent, maybe not, today’s day and age, independence of thought.

And then those fund managers are also looking downward into the CEO’s of their companies. They’re looking for the same things. And then the companies are looking to a lot of the same things in their employees. We get these the same patterns that we’re looking for, but then they’re at different scales. And no matter where you zoom in or zoom out, you see these same patterns. And so, my private Berkshire friend later, he sent me a tweet that he had what was a hot take on our conversation. I’ll just read it to you real quick, because I think it’s actually a better take than anything that I said while we were in the middle of it.

So, he says, “Capital structure ripples through management, and ultimately ripples through employee experience. If you work in a business run for cash flow, like a PE backed platform, a business run for growth or a business run for long-term hold, your experience as an employee could not be more different. The cash flow capital demands low overhead, fast ROI and has little patience for capacity building. The growth capital spends aggressively to build the company of tomorrow. Today, nobody worries about profitability. The PE capital is all about the exit, and everyone has managed aggressively around the corridor to maximize strategic value and EBITDA at the time of sale. And then the long-term hold capital worries about downside more than upside and tends to err on the side of conservatism. It’s a marathon, not a sprint.”

So, he says, “There’s no one right way, but it’s worth remembering that it’s the capital that ultimately designs the game that everyone else plays.” And so, there’s a fractal element of that as well. So, the owners of the business, the capital that’s provided shows up along the path and trickles all the way down. So, I think it’s interesting just to think about fractals and how they apply to the fund management level as that cascades down as well as inside the business and even all the way down to the employees.

Tobias: Mandelbrot’s autobiography, The (Mis)Behavior of Markets, is one of the all-time great books. I think he was Polish, because I think he escaped during— [crosstalk]

Jake: Polish, but raised in France.

Tobias: Is that right? All right, I’ll take it back. Superior knowledge. I bow to it.

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