Where centralised societies excel at extraction, African fractal systems allow for circulation, reciprocity and return

by Likam Kyanzaire  BIO

Labbezanga, Mali. Photo by Georg Gerster/Panos Pictures

is a freelance writer based in Toronto, Canada. His work has appeared in Briarpatch Magazine, the Toronto Star and The Weather Network, among others.

Edited byPam Weintraub

Ron Eglash was not looking for a revolution when he stumbled across one. The American ethnomathematician, who tracks mathematics embedded in culture, was studying African settlement patterns in the 1980s when he noticed something strange in aerial photographs and village layouts. The settlements weren’t laid out randomly. They had a pattern – and not just any pattern. The same shape seemed to repeat at every scale: a cluster of homes that echoed the arrangement of a larger compound, which in turn echoed the wider settlement beyond it. It was, he would later realise, a fractal – a geometric form in which the same structure recurs from the smallest unit to the largest. No mathematician had drawn it. It had been made by people building homes, compounds and villages according to rules they understood through practice.

That discovery sent Eglash across the continent. What he found – in settlement layouts, in art, and in political life – was that fractal organisation wasn’t an accident of African design. In many cases it was intentional.

One of the clearest architectural examples appears in Logone-Birni, in Cameroon, which Eglash explicitly calls a fractal settlement. There, the palace of the chief and the rest of the city is built from forms repeating at every scale: nested rectangles repeat the same pattern at different levels. The point is not just visual elegance. The geometry helps organise social life. As one moves inward through the palace, behaviour changes, hierarchy intensifies, and space itself encodes rank. In other African settlements, the same recursive logic appears in different forms. In southern Zambia, for example, family enclosures are arranged as rings within rings, so that the settlement as a whole mirrors the structure of its parts.

The city of Logone-Birni in Cameroon in 1936. The largest building complex is the palace of the chief. Photo courtesy Musée du quai Branly-Jacques Chirac

What fractal geometry makes visible in these settlements is a broader principle: large, complex forms can emerge from smaller units without requiring every decision to come from a single centre. That principle matters not only for architecture, but for politics and economics as well.

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Most modern economies don’t work that way. Governments and corporations push down decisions from on high and extract value outward – a platform fee here, a transaction charge there, money leaving the community that generated it and accumulating elsewhere. Since European empires spread their model of the centralised state across the globe, this has become so normal it barely registers as a choice. But it is a choice. And Africa’s precolonial societies, which ranged from the highly centralised empires of Egypt and Abyssinia to stateless communities governing themselves through interlocking institutions, made different ones. They were dismissed as primitive for it. Many were anything but.

To understand why, you have to go back to geometry. Fractals are geometric shapes built from repeating patterns – the same form recurring at every scale, from the smallest detail to the largest structure. In his book Les objets fractals: forme, hasard et dimension (1975) – revised and translated as Fractals: Form, Chance, and Dimension (1977) – the mathematician Benoît Mandelbrot gave them their name and their first rigorous description. He wanted to account for shapes that Euclidean geometry – the geometry of straight lines and perfect circles – couldn’t explain. ‘Clouds are not spheres, mountains are not cones, coastlines are not circles,’ he wrote in 1982. The most common shapes in nature are irregular, rough and repeating. They are fractals. Mandelbrot used the same mathematics to understand markets, and later researchers applied it to cities, networks and living systems. What fractal geometry kept revealing was that complex, large-scale structures could emerge from simple rules repeated at every level. A fern leaf is an example: each small frond resembles the larger leaf of which it is a part.

Fractals can appear at many scales, from the branching of blood vessels to the spread of river networks. Cosmic fractals like halos are larger than our solar system, while others, like those in quantum material, are infinitesimally small. Among the fractal rules that Mandelbrot set were:

Recursion: a process in which one pattern generates another like itself. Think of a tree branch that keeps splitting into smaller branches.

Self-similarity: resemblance across scale from small to large. The parts are not identical, but they share the same basic form.

Scaling: the way a pattern can expand or shrink while keeping its underlying logic.

Fractals give order to what looks like chaos – but not only in nature. The same three properties that shape a tree or a coastline can shape a society. Recursion means that what works at one level gets repeated at the next – a household rule becomes a village rule becomes a regional one. Scaling means those rules stretch upward without breaking, holding their logic whether you are governing 10 people or 10,000. Self-similarity means that each unit can organise itself according to the same broad principles, without waiting for orders from a distant centre. A society built on these principles doesn’t need a centre to hold it together. It holds itself together, from the bottom up, much like a tree.

Fractal patterns don’t appear only when designed on purpose. Sometimes they arise through growth itself

In 1988, Nathan Cohen was trying to pick up better radio signals without putting a new antenna........

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