Why trees look like rivers and also blood vessels and also lightning…

Fractals are special self-similar shapes that appear in various forms throughout the natural world, and they reflect a fascinating aspect of how systems evolve. At its core, the concept of self-similarity explains that smaller parts of a shape can resemble the larger whole. Think of geometric patterns where triangles can contain infinitely smaller triangles—this is an example of perfect self-similarity. The mathematician Benoit Mandelbrot coined the term "fractal" to describe these intriguing shapes, which exist in a dimension that's not quite whole, creating an entirely new way to understand nature.

When mathematicians talk about dimensions, they refer not just to our usual concepts of length, width, and height, but to how shapes fill space as they change size. For instance, doubling the length of a line gives you double the line; scaling a square by the same factor results in four times the area. But with fractals, things become more complex. If you scale a fractal by a factor of two, you might end up with an area that's three times larger, revealing its fractional dimension.

Why do these fractal patterns appear in nature? Surprisingly, the concept of a "tree" is somewhat ambiguous. Many plants we label as trees are more closely related to non-tree plants. Instead, the tree-like structure may be a universal solution to a common problem: efficiently capturing sunlight and carbon dioxide. Different species have evolved various methods—growing tall or spreading out leaves—but fractal branching is particularly efficient, maximizing surface area without excessive energy expenditure.

This branching design allows trees to optimize their sunlight absorption while minimizing resource use. It’s not just trees; roots exhibit a similar fractal pattern, increasing their surface area to efficiently absorb water and nutrients. Inside our bodies, lungs also utilize fractal designs to maximize oxygen intake. With the need for approximately 15 liters of oxygen per hour, if our lungs were simple balloons, they wouldn’t be able to meet our demands. Fractal branching allows our lungs to have a surface area comparable to that of a tennis court while compactly fitting inside our chests.

Our circulatory system also mirrors this branching efficiency. With nearly 100,000 kilometers of blood vessels, the fractal structure ensures that oxygen and nutrients are delivered throughout the body without requiring excessive energy to maintain a vast plumbing system. In essence, these living systems—trees, lungs, and blood vessels—each tackle their unique challenges through fractal branching, enabling them to function effectively within their environments.

Fractals extend beyond living organisms to non-living systems, such as rivers, which naturally adopt branching shapes to efficiently drain water from a landscape. As rivers split and curve, they echo the same fractal principles, optimizing the flow of water and sediment. Similarly, lightning bolts and cracks in surfaces represent efficient pathways for energy dissipation, again illustrating how fractal structures can optimize function.

While it might seem there’s a universal rule behind these patterns, nature is unpredictable. Fractal shapes arise in various contexts due to different conditions—temperature, humidity, and chemical concentrations influencing how structures form. Yet, as systems evolved to maximize efficiency, many independently arrived at similar solutions through fractal branching.

This captivating interplay between form and function in the natural world offers us a new lens to view life. The patterns we observe in trees, rivers, and even the human body highlight an underlying principle of efficiency and adaptation. As we continue to explore these fractal designs, we gain deeper insights into the complex systems that shape our world, encouraging us to stay curious and appreciate the intricacies of nature.

Speaking of curiosity, if you’re interested in exploring more unique stories from fascinating perspectives, check out my other show, "Overview," on PBS Terra. We delve into compelling narratives that reveal the world from new angles—definitely worth a watch! And a big thank you to everyone who supports us on Patreon; your contributions make our exploration of science and nature possible.