The Fractals at the Heart of Indigenous African Architecture

The Fractals at the Heart of Indigenous African Architecture

Fractals are complex geometric shapes with fractional dimensional properties. They have emerged as swirling patterns within the frontiers of mathematics, information technology, and computer graphics. Over the last 30 years, these patterns have also become important modeling tools in other fields, including biology, geology, and other natural sciences. However, fractals have existed far beyond the birth of computers, and have been observed by anthropologists in indigenous African societies. One of which is Ron Eglash; an American scientist who presents the evidence of fractals in the architecture, art, textile sculpture, and religion of indigenous African societies. In his book, “African Fractals: Modern Computing and indigenous design”, the fractals in African societies are not simply accidental or intuitive but are design themes that evolve from cultural practices and societal structures.

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Although Africa is a continent with a great diversity of cultures, examples of fractal architecture and urban patterns can be found in many indigenous societies. These forms of urban and spatial patterns can be identified by basic characteristics, including recursion, scaling, self-similarity, infinity, and fractal dimension. They form the basis of the continuous looping character of these patterns across different scales that can project to infinity. While the terms used to describe fractal character often lie in mathematics and semiotics from nature, the urban patterns in African indigenous societies, which are a precursor to these terminologies, are drawn from cultural practices and societal norms.

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First Iterations of Fractal simulations by Ron Eglash and closer view of the Royal Isignia . Image © ArchDaily

An example of fractal urban design is the Indigenous city of Logone-Birni in Cameroon, founded by the Kotoko people. Aerial views of the city show continuous iterations of rectangular buildings forming a fractal pattern as urban design. These building complexes are local clay houses built by the Kotoko people and, as described by Eglash in his book, “an architecture of accretion”, where new rectangular enclosures grow by adopting and projecting from the preexisting walls of old buildings. The resulting urban pattern is one born from a patrilocal household culture and the city’s need for collective defense. “A man would like his sons to live next to him, and so we build by adding walls to the father’s house” was the architecture story told by descendants of this community. As the assembly of families grows, the fractal patterns emerge, collective buildings form a defensive enclosure and the scale of a building in the landscape is a testament to familial hierarchy.

The Ba-ila settlements of Southern Zambia provide another example. Aerial views reveal a series of circular enclosures arranged within a larger ring that houses the community, their houses, and livestock pens. Each circular enclosure contains a family dwelling, surrounded by a livestock pen to the front and a sacred altar to the back. The enclosures gradually reduce in size from the top to the bottom of the ring, revealing the hierarchy of each family in society. This unique fractal urban design reflects the societal structure of the Ila people, with the Chief of the community at the apex and new members at the base of the ring. Similar designs are found in other indigenous communities, such as Mokoulek in Cameroon and Labbenzanga in Mali.

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Ba-Ila Settlement of Southern Zambia. Image © Ron Eglash: African Fractals

Fractals are present not only in the urban planning of African indigenous architecture, but also in its building plans, art, fabrics, hairstyles, religious rites, children’s games, and other cultural elements. In his TED Talk, Ron Eglash highlighted the Royal Insignia, which is the palace for the king of Logone-Birni. The palace entails a recursion of rectangles as a spatial pattern. The spatial pattern reveals lobbies as rectangular spirals where, as one moves further into the enclosure, he is required to become more polite. These fractal spatial plans essentially map a social scale for people’s behavior. The recursion of these fractals also continues to smaller scales, such as how utensils are stacked within the house and the patterns that embellish the design of household objects.

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Fractals in the Cornrows hair styles of African cultures. Image © Richard Mellor

Consequently, the presence of fractals in various aspects of culture within indigenous societies suggests the existence of cultural algorithms within their ethos. For example, religious rites, such as the Bamana Sand Divination, are important fractal algorithms in West African societies. This divination, which is native to locals in Dakar, Senegal, uses a symbolic code of lines with 4-bit binary words as modes of seeking knowledge from the supernatural. Eglash notes in his talk that this divination not only influenced fractal patterns in West Africa but also binary codes and boolean algebra in the 1800s, which were used to create the digital computer.

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‘Sierpinsky Triangle’_deterministic fractal with self-similarity. Image © ArchDaily

Another cultural algorithm in precolonial African societies was the absence of political hierarchy and the presence of decentralized social groups. These societies presented a bottom-up approach to communal organization, which did not impose a fixed urban plan but rather societal ideals for architectural interpretations. These interpretations were explored with different iterations from individual families, and collectively they projected a pattern that was fractal. These patterns not only aided in design but were also celebrated and adopted as aesthetics of cultural practices within these communities. Essentially, the fractals at the heart of Indigenous African design were not an unconscious social dynamic but rather an abstract representation and practical technique for defining its socio-cultural structures.


  • Chétima, Melchisedek. “Beyond Ethnic Boundaries: Architectural Practices and Social Identity in the Mandara Highlands, Cameroon.” Cambridge Archaeological Journal 29, no. 1 (2019): 45-63.
  • Eglash, Ron. “Fractals in African settlement architecture.” Complexity 4, no. 2 (1998): 21-29.
  • Eglash, Ron. “African fractals: Modern computing and indigenous design.” (1999).
  • Eglash, Ron, and Toluwalogo B. Odumosu. “Fractals, complexity, and connectivity in Africa.” What Mathematics from Africa 4 (2005): 101-9.
  • Kitchley, Jinu Louishidha. “Fractals in architecture.” ARCHITECTURE AND DESIGN-NEW DELHI- 20, no. 3 (2003): 42-51.
  • Lorenz, Wolfgang E. Fractals and fractal architecture. na, 2002.

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