Consider this pattern in nature:
The trunk of a tree divides into branches, which divide into sub-branches, which divide into twigs.
Water trickles from a puddle into a stream, which merges into a river, which merges into the ocean.
Blood from the heart travels through the aorta, which divides into arteries, which divide into capillaries.
The same branching ‘fan out’ pattern exists in the bronchioles of your lungs and dendrites of your nervous system.
If you ‘zoom in’ on a tree, you discover that a single, tiny twig shares the same basic structure and form of the whole tree, just smaller. You could think of the twig as a ‘fractal’ of the tree, a term coined in 1975 by Benoit Mandelbrot (1924-2010) to describe the geometry of nature. The natural world, he proposed, is not random at all, but it follows “strict order” self-similar, geometric properties.[^Mandelbrot, Benoit. (1977). Fractals: Form, Chance and Dimension. W. H. Freeman. p. 17] Thus, fractals provide a mathematical framework to measure the ratios and scales of ecological life.
Nature, honed for efficiency, works in scaling, self-replicating patterns. Life is created by repeating the form of itself at numerous scales of detail. In the domain of human invention and systems, our designs tend to follow similar fractal patterns:
Traffic from an expressway merges on to avenues, which divide into streets, which divide into driveways.
Decisions are made in boardrooms, disseminated through departments, assigned to teams, executed by individuals.
The data of an email message travels between routers, to a server, to a local network, to an email client.
Biological life is created as cells replicate themselves. The social and cultural lives we create for ourselves are, likewise, inherently self-replicating. A country is like a bigger version of a city, which is like a bigger version of a neighbourhood, which is like a bigger version of a family. A family, in turn, is like a bigger version of an individual — who is composed of mutually dependent cells giving rise to life. And yet, at the microscopic level, a single eukaryote cell looks like a bustling, complex metropolis, full of labour divisions and communication protocols. Here, in the world of fractals, we discover that everything is like a copy of something else.