Recently, while on our annual pilgrimage to Hawaii, my son, Beau, and I entered the local grocery store and began exploring the exotic fresh produce section. Among the shelves of papaya, mangos, avocados and starfruit, his eyes were immediately drawn to an almost alien-like vegetable, the Romanesco Broccoli. The Romanesco Broccoli (it’s actually closer to a cauliflower) has to be one of the most beautiful and complex vegetables in the world. Another example of the beauty of Roman aesthetics! While I’ve never actually tasted one, I suspect it looks better than it tastes. 

Beau’s attraction to the beauty and structure was magnetic. Not wanting to miss an opportunity to educate him in the esoteric mathematical beauty of fractals, we began to inspect the Romanesco in greater and greater detail. He was amazed by each spiraling array of pyramid-shaped florets that then descended into another smaller version of the same. As the size of each bud scales down it is an almost perfect replica of the whole. 

When asked what other examples of fractals he could think of he immediately referenced tree ferns, pinecones, redwoods, the scales of snakes and lizards (we have a pet bearded dragon), and the scutes of a turtle's carapace. Fractals (and the Fibonacci sequences that underpin them) are ever-present in our daily life. 

Fractals: The Underlying Structure of Power Law Systems

This interaction with the Romanesco Broccoli rekindled a hypothesis that I’ve been holding lightly, but have wanted to explore more deeply for a couple of years. While the presence of power laws has become a ubiquitous and dominant narrative to describe the distribution of fat-tailed outcomes, fractals deserve more attention as they provide an understanding of how the systems generating power law outcomes are built.  

Thanks to Beau’s recent enthusiasm for fractals, I decided to explore that hypothesis a little further and spew my thoughts onto the page here. What this work has revealed to me is that fractals aren’t rare or abstract. They’re everywhere. In oceans, in forests, in animal colonies, in the human body, in markets, in organizations, and in the quiet patterns of our everyday lives. By repeating simple, uniform, or structural patterns at different magnitudes, they allow complex systems to maintain efficiency, consistency, and structural integrity regardless of their size. Ultimately, I argue that there is a consilience between power laws and fractals that is inseparable. So what? If power laws describe outlier outcomes, an understanding of fractals can identify the underlying patterns, creating those outcomes. 

A Brief History of Fractals

I’ve been studying fractals ever since a mentor introduced the concept while I was floundering to find my edge as a quant trader in my early twenties. The godfather of fractals is maverick scientist Benoit Mandelbrot, whose work is memorialised in the fabled Fractal Geometry of Nature and his excellent memoir, The Fractalist. 

Mandelbrot’s work showed that rather than being made up of smooth lines and the perfect shapes described by Euclidean geometry, nature is rough, irregular and jagged. Further, Mandelbrot identified that this roughness is self-similar across scales (look at the Romanesco) and is present from the atomic to the cosmic. 

Mandelbrot’s most provocative insight was to highlight that the rough, jagged, self-replicating complexities of fractals are also present in many systems beyond nature. He pointed to the presence of fractals in physics, economics, computer science, cosmology, financial markets. Several practitioners have since deepened Mandelbrot’s work in specific verticals, for instance Michael Barnsley in computer graphics, Didier Sornette’s study of earthquakes and most famously Nassim Taleb’s work on Black Swans and tail risk in financial markets.

Rather than polite, linear systems, most systems exhibit recursive, dynamic, and complex characteristics. They don’t follow linear, human-made rules that are spreadsheetable. 

Fractals and Power Laws

My thesis is that fractals are more worthy of our attention than power laws. 

They are a critical organizing principle expressed in nature, human cognition and physiology, technology and capital markets. They deserve to be studied and applied more deeply in fields beyond nature and mathematics - particularly in domains where power laws are prevalent such as venture capital. By understanding the interplay between fractals and power laws I contend that we can better understand (and predict) the conditions necessary to drive extraordinary outlier outcomes across disparate domains. 

The empirical patterns that identified the presence of power laws were popularised by Vilfredo Pareto and subsequently labeled the Pareto Principle or 80/20 rule - the idea is that in many cases, outcomes are not normally distributed and a small number of cases usually aggregate a large portion of the outcomes or resources. Some everyday examples: 1) the top 10 most frequently used words in English comprise approximately 25% of all spoken and written text despite there being ~1 million words; 2) The Weeknd’s Blinding Lights has 5.2 billion streams on Spotify whereas 87% of all tracks have fewer than 1k streams; 3) “Baby Shark” has over 16 billion views on Youtube (God help us); 4) the impact or consequences of natural disasters is highly concentrated in a small number of catastrophic events. 

While power laws are certainly prevalent in many systems, there are several common distributions where Power Laws are not present, including the range of human height and IQ scores which follow a normal distribution or “bell curve” (there are no 20 standard deviation outliers here). 

As any start-up founder or venture capitalist is aware, a tiny number of extreme winners dominate return outcomes, consistent with power-law behavior. Where power laws are concerned with distributions and scaling outcomes, fractals are about the structure and form that repeats across scales, leading to power law outcomes. In nature, physical and biological constraints force optimization through branching networks (lungs, river systems, vascular networks) in order to minimize transport costs. It turns out that iterative, branching structures — the same rule operating recursively from the very large to the very small – are an optimal organizing principle across domains. They tell us about the architecture of the process that creates the conditions conducive to the outcome, not just its end state. 

Fractals in Outlier Technologies and Companies 

While power laws tell you how outcomes distribute. Fractals tell you how the systems that create the outcomes are structured. If power laws are the scoreboard, fractals are the playbook. Power law outcomes have become synonymous with venture capital and company building and rightly so. But acknowledging the presence of power laws doesn’t inform us of the conditions or patterns required to generate a power law outcome. I contend that fractals are actually a necessary condition for power law outcomes.

A great piece of software is fractal (functions → modules → products/services → platforms → ecosystems) as is the organization that built the software – many small, high-agency units pursuing local truth, while still cohering into a single organism. Recently I heard Tobi Lutke describe his life as a “fractal of toolmaking”, the ultimate manifestation is Shopify which is a tool that enables the self-replication of small, autonomous entrepreneurs to design products and build companies. 

An API is fractal. A neural network is fractal. Google’s small teams model is fractal, made up of small, autonomous units that design, develop, test, and iterate rapidly. These small teams are nested within groups of teams, nested within business units, nested within the whole company. The company behaves in the same way as the small units repeating the same core pattern of product/market fit across contexts and scales. The structure of the whole is mirrored in the structure of the parts. Fractal structures generate robustness, resilience, extreme outliers and in many cases antifragility.  

A Thermal Dome for Future Abundance

The Costa Rican Thermal Dome is an invisible engine of life in the Pacific Ocean where a convergence of currents and winds creates an oasis of life in the open ocean. Cold, nutrient-rich water is pushed towards the surface where it meets life-spawning sunlight, creating an explosion of life from microscopic phytoplankton to the largest animals to ever live, Blue Whales. The Costa Rican Thermal Dome, while invisible to the human eye, cultivates the foundational conditions necessary for abundance. It is an ecosystem fractal of architecture across scales that imbues robustness and complexity. For instance, there are micro domes that surround any small piece of driftwood or debris in the open ocean and there are macro domes such as the thin, boundary layer that surrounds Earth and the thermal dome that is our solar system surrounding the sun. There are thermal domes from the atomic to the cosmic scale. 

To me, the Thermal Dome is a metaphor for place-based ecosystems such as Silicon Valley for technology, New York for finance, New Orleans for jazz, Nashville for country music, Florence for the Renaissance, Hollywood for entertainment. These places are highly emergent - where startups, art, or wealth emerge at rates wildly disproportionate to their surroundings much like the Thermal Dome creates life at disproportionate rates to the surrounding ocean. 

The same conditions that have created the magic of Silicon Valley can be fractally replicated at a smaller scale to create an ecosystem around a venture capital firm. A living, evolving organism that is made up of a collection of smaller ecosystems. 

Beyond building a fund or even a firm we are building something much more ambitious, amorphous and alive: an ecosystem that creates the conditions for future abundance. We are architecting the conditions conducive to the power law outcomes we seek to create.

The foundational technologies needed to build this future of abundance are fractals themselves. Modern intelligence is fractal, aggregating many small neural nets to create vast networks of intelligence, embodied in physical infrastructure that is itself fractal (chips → servers → datacenters). Nuclear fusion is a fractal of the sun and stars. Solar PV is fractals all the way up, from the PV cell, to the panel, to the module to the solar farm. Robotics scales with fractal patterns, one robot is a unit, a fleet or swarm is the same unit repeated with embedded coordination. Material structures repeat from the microscopic to the macroscopic: atoms, molecules, proteins, lattices, grains. 

Systems that scale gracefully tend to have fractal properties. Ecosystems. Brains. Markets. Companies. Venture firms. Neural networks. Fractals aren’t just everywhere. They are leverage. They let you scale without losing coherence—whether you’re shipping software, coordinating robots, designing materials, or building a company that can compound.

Unleashing a Trophic Cascade

My conjecture is that fractals are both a physical and metaphysical phenomenon. They manifest not just in nature and physical realms, but in our consciousness and ways of thinking. Fractals are a critical organizing principle that are expressed in nature, matter, in biology, in physics, in human cognition, institutions and capital systems. 

Understanding the interplay between fractals and power laws offers a way to more deeply understand the conditions and environments necessary to drive extraordinary outlier outcomes across domains. Not through one giant structure, but through nested, self-similar systems that reinforce each other. 

That is why we’re designing our firm as a thermal dome for future abundance. A place where ideas, talent, trust, capital, and ambition converge. An intertwined ecosystem where stakeholders feel the pull because the conditions are right. 

By building the thermal dome for abundance we will unleash a trophic cascade where changes at one level ripple through the other levels, producing surprising and far-reaching consequences. 

I invite you to be part of our thermal dome for future abundance. 

*I would like to acknowledge Chris Begg who’s writing and discussion on the Costa Rican Thermal Dome triggered this stream of thought. 

Read more on Fractals, Power Laws and Thermal Domes:

1. Fractal Geometry of Nature, Benoit Mandelbrot
2. The Fractalist: Memoir of a Scientific Maverick, Benoit Mandelbrot
3. A Multifractal Walk Down Wall Street (Scientific American)
4. Fractals Everywhere, Michael Barnsley
5. Antifragile, Things That Gain from Disorder
6. The Power Law, Sebastian Mallaby
7. Environmental change in the eastern tropical Pacific Ocean: review of ENSO and decadal variability Paul C. Fiedler*