Justice is geometric

Likam kyanzaire

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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 on his roof, which his landlord wouldn’t allow. So he tried something different. By shaping his original antenna according to fractal geometry, he found he could pick up multiple frequencies with better quality and in a fraction of the space. The invention turned out to be world-changing. Cohen’s work ended up inspiring the development of fractal antennas now used in mobile communication and GPS systems across the board. What Cohen had proved, almost by accident, was that arranging material in fractal patterns increases the effectiveness of any system without proportionally increasing its size.

Fractal patterns do not appear only when people design them on purpose. Sometimes they arise through growth itself. Cities are a good example. As they expand, neighbourhoods branch into streets, streets into smaller roads, and districts into larger urban systems, often repeating similar shapes at different scales. That does not mean every part looks identical. It means the same broad pattern keeps resurfacing as the city grows.

Shenzhen in southern China makes this apparent. In 1980, it was a fishing town. Today it is a metropolis of more than 17 million people. Its growth was driven by state policy, factories and migration, yet it happened so quickly that no central plan could dictate its final form. Looking at maps of Shenzhen over time, the researchers Yanguang Chen and Xiaoming Man at Peking University found that, even as the city changed, its parts and its whole retained similar patterns. In other words, the city kept expanding in ways that repeated across scale – one reason they described its urban form as fractal.

Chen and Man believe Shenzhen is similar to other cities that grow organically. As Chinese residents moved to work in Shenzhen’s booming factories, the city grew too fast for centralised planning to keep up and became a prime example of how large, complex urban worlds take shape.

In his book African Fractals: Modern Computing and Indigenous Design (1999), Eglash highlights centuries-old representations of fractal geometry throughout several African civilisations in forms like art, religion and numeracy. What interested him was not only the presence of fractal patterns, but the way they moved across domains: from architecture into ritual, from design into systems of knowledge and social order. As Eglash put it: ‘when grounded in specific locations the fusion of fractal geometry and cultural interpretation can be profoundly rewarding.’

According to a study by Michael Ediagbonya, Yemi Ebenezer Aluko and Duyile William Abiodun from Ekiti State University in Nigeria, the guild system in Benin created pieces for the royal court but also for everyday people. Each guild had a self-organising structure in its district and an interdependence with other guilds in its area. Guild leaders managed their physical space, administrative affairs, and even certain judicial processes. Like mini-prefectures, they could collectively control the conditions of their livelihood. The guild system operated with fluidity and autonomy but was also orderly – and responded with intent when the king ever requested an item.

One of those groups was the ‘age grade’: a formal association of people born within a few years of one another. Most of us know same-age peers mainly from school. Among the Igbo of Nigeria, though, age grades carried civic weight as well. According to a study by Bonaventure Chigozie Uzoh and Iheanyi Valentine Ekechukwu from Nnamdi Azikiwe University in Nigeria, age-grade groups helped raise funds for development projects, took part in conflict resolution, assisted vulnerable members of the community, and encouraged investment back into the village. These were not casual peer groups but working public bodies. While elders held the highest offices, younger people often carried much of the practical burden of community development through their age grades. Within each cohort, members chose leaders, made rules, and took responsibility for shared tasks. The fractal quality lay in the repetition of the form: each age grade governed itself, but did so as part of a larger society built from other self-governing groups.

Lineage was not just a matter of family background. It was a formal structure of mutual support

The Chokwe of Angola combined age-grade initiation with lusona – intricate designs drawn in sand that grew more complex as initiates moved through successive stages of seniority. The patterns mirrored the social process itself: one form unfolding from another, one stage leading to the next, one level nested inside a larger whole. As initiates learned to draw more elaborate lusona, they also entered deeper levels of shared knowledge and belonging. In that sense, the ceremony made the principle plain. These fractal forms were not accidental; they were deliberately built into the passage through life, something people could see, trace and pass on.

Lineage systems worked much like age grades, but through kinship. In many bottom-up societies, lineage was not just a matter of family background. It was a formal structure of mutual support, obligation and political belonging. Eglash notes these are examples of ‘segmented lineage systems’, in which the boundaries of kinship expand or contract depending on the context of the situation. A household belongs to a lineage, the lineage to a larger clan, and the clan to a wider network. The exact circle that matters can shift with the dispute at hand. That flexibility is what makes the system fractal: the same basic form repeats at larger and larger scales.

Kinship was one strand, age another, place another, economic life another. Eglash compares this to an artist working from a colour palette. Together, these overlapping memberships gave people multiple claims on one another – and multiple routes to resolution when things went wrong.

How would this operate in practice? In truly egalitarian, classless societies, there were typically no centralised rulers, no standing courts, and no professional judges in the modern state sense. Instead, disputes were worked out within the groups to which people already belonged, according to the legal anthropologist Simon Roberts, an expert on dispute resolution in Africa. In his book Order and Dispute (1979), Roberts draws on H P Gulliver’s classic 1963 ethnographic study of the Arusha of northern Tanzania.

Within this small but complex society, an Arusha man belonged to a lineage, an age set, and a parish, overlapping social units that linked kinship, generation, and place. Should a dispute arise in his parish, an Arusha man was able to achieve a settlement through his age set or his lineage, depending on the issue at hand. In one example from Gulliver’s work, a father’s land was given to his brother, but when his son came of age, he wanted it himself (as norms dictated). Within the lineage, a settlement was worked out: half the land went to the son, while the other half stayed with the uncle, even though this went against their (rather loose) rules. The incentive for the lineage is cohesion at all costs, even if against their own rules. Inside the parish (where economic activity happens) members can count on support and solidarity. Rather than the top-down needs of Western-style companies or governments, here the interest of the members are put first.

Not every African system that distributed authority across scales was a strict mathematical fractal. Edo, the site of present-day Benin City in southern Nigeria, offers a related but distinct case. Organised around the Oba’s (ruler’s) palace at the city core, from which major roads and streets radiated outward, Edo was a layered urban system: compounds gathered into neighbourhoods, neighbourhoods into districts, and districts into surrounding settlements. It was not a demonstrated fractal in the same way as Logone-Birni, but it did show how authority and exchange could be structured through nested space.

Edo, or Benin City, Nigeria. Courtesy the Internet Archive/public domain

In Edo, that design shaped not only how people lived but how they worked and exchanged value. The city’s craftsmen produced the Benin Bronzes, intricate cast-metal works, most of which now sit in museums across the Global North. Like other medieval cities, Edo supported a large and prosperous guild system whose artisans made goods both for the Oba and for the broader population. Within a monarchy, those guilds had unusual control over production, workspace and aspects of their own administration. Goods circulated among the people who made them before moving upward to the court.

None of this made Edo egalitarian. Much of what was made served elites. Even so, the city left room for organisation below the level of the palace. A brass-casting guild, for example, might train apprentices, oversee production, manage labour, and settle disputes within its own ranks while also supplying the royal court and exchanging skills and materials with neighbouring guilds.

Value moves outward and then back again, rather than being extracted and hoarded

Fractal or layered structure is no guarantee of fairness. The geometry is neutral. What matters is who controls it and toward what end. So, if fractal ideas are to serve equality rather than hierarchy, the models we build must prioritise generative justice – not just fairer distribution, but the repair and renewal of the social, labour and ecological relationships on which a community depends.

Eglash argues that this kind of generative justice is central to egalitarian fractal societies in Africa. The idea is close to a circular economy, but broader: value should not simply be taken from land, labour and social life, then concentrated at the top. It should circulate back, replenishing the people and systems that produced it in the first place. That means not just environmental renewal, but the renewal of work, reciprocity and communal ties. What makes fractal societies distinctive, in his account, is that their nested, self-similar structure can support these repeating cycles of return. Value moves outward and then back again, rather than being extracted and hoarded.

The real question is what happens when that same interdependence is organised not around a king, but around the community. ‘In the West, economies have evolved towards value extraction. Traditional African societies tended to have circular economies that did not extract; rather, the value was returned to its source of generation,’ Eglash told me.

Fractals alone do not create regenerative systems, but fractalised institutions provide avenues for citizens to take better action in economic and political activity. For the Arusha, reliance on a cluster for a settlement process worked to increase solidarity between groups. Where modern justice systems can harden people into repeat offenders, the Arusha’s approach worked to increase solidarity and repair relationships within the community.

‘In the same way, you need labour value to return to workers, and social value to return to communities,’ Eglash told me. Age-grade systems can help enable that. ‘If you look at the symbolic forms in age-grade rituals, you often see the cyclic-value pathways visualised as sand drawings, costume decorations and so on.’ In groups like the Igbo and the Chokwe, value did not centre only on money. It also took the form of knowledge, responsibility and participation, with important work distributed across social groups rather than hoarded at the top.

Modern economies tend to define value more narrowly, and to pull it upward. The recent AI boom offers a vivid example. Large language models such as ChatGPT are trained on vast datasets that include legally protected creative work, yet many creators receive nothing when their work is absorbed into these systems, a practice that has already triggered lawsuits.

In response, Eglash and a team of global creatives have built Ubuntu AI, a platform where African artists and designers can upload their work and get paid if companies want to use it to train AI. One of 10 OpenAI grant winners, Ubuntu AI is meant to democratise AI by giving African creatives ownership over the value they create.

‘We found out we were the only group trying to democratise the AI economy. Everyone else was just following OpenAI’s directive to have citizen input on AI policy,’ Eglash told me. But while there is nothing wrong with adding input to AI policy, it does little to create value for everyday people. And little to improve social cohesion among communities of creators and AI companies. ‘We pointed out that, at the local scale, you want community ownership of AI. How do you bring together the global and local? Fractal scaling of democracy.’

When local enterprises rely on outside platforms for essential services, money leaks out of the community

Ubuntu AI offers one example of what this can look like in practice. Instead of allowing value to be extracted from creators and absorbed by distant companies, it returns some of that value to the people who generated it in the first place. But fractal democracy can go further than payment alone. It can also shape how technologies spread through communities: not as tools imposed from above, but as resources organised through local clusters that keep value circulating close to its source.

A Detroit-based project led by Eglash and his team has pursued similar logic with Black-owned cooperatives, worker-owned businesses and other community ventures. Its premise is simple: when local enterprises rely on outside platforms for essential services – web hosting, delivery routing, payment processing, banking – money steadily leaks out of the community. Even when the business itself is local, the infrastructure beneath it may be extractive. The project’s aim is to rebuild some of that infrastructure so that the value generated by local work returns to local people.

To do that, the project partnered with clusters of organisations already rooted in their communities: farmers, designers and economic collectives whose work was tied to local repair and mutual support. It then used open-source tools to reduce the technical and financial barriers these groups faced. One participant, Deeply Rooted, ran a delivery service for urban farms in Detroit – something like a local version of Uber Eats. But each month, fees for hosting, routing and banking siphoned away money from the neighbourhoods producing the food and doing the work. So the project helped develop a worker-owned delivery platform instead. The difference was not only technical. It was economic and political. Instead of transaction fees flowing outward to outside firms, more of that money could circulate back to workers and the community itself.

That is the larger promise of fractal design in public life. The point is not simply to break large systems into smaller ones. It is to build nested, connected structures in which value can circulate back to the people and places that created it.

Building a more just future will require ideas drawn from many parts of the world. The fractal systems developed in Africa, both intuitively and by design, have much to offer. They suggest ways of organising society that preserve connection across scale without surrendering everything to a distant centre. Where the modern state society often excels at extraction, fractal systems point toward circulation, reciprocity and return. They show how complexity can be built without making ordinary people ever more remote from the value they produce.

That does not mean fractals are inherently liberating. Like any powerful design principle, they can be bent toward other ends. The danger is that fractal technologies will be absorbed into the very extractive systems they might have challenged. Credit card payments offer one example. Every time money moves through a card network or digital platform, fees can drain value away from the communities generating it. Even technologies once imagined as decentralised alternatives can be captured by large institutions and turned back into instruments of concentration rather than diffusion.

African fractals remind us that design is never neutral: the same recursive structure can be used either to hoard value or to return it. What matters are the values built into the system. Today, researchers and organisers are using Indigenous knowledge not to romanticise the past, but to imagine decolonised economies in the present. As Eglash put it to me at the end of our conversation: ‘We have focused a lot on the idea of developing decolonised economies: community-based, worker-owned, with sustainable unalienated labour, all guided by those Indigenous practices.’ If the future is to be fairer than the systems we have inherited, some of its most radical and useful blueprints may come from the precolonial past.

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Justice is geometric

Likam kyanzaire

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