Many traditional African architectural layouts, textiles, and artworks show self-similar structure in which a motif repeats at progressively smaller scales, matching the formal definition of a fractal. This scaling is not incidental decoration but a consistent organizing principle across distinct cultures and media.
A fractal is a pattern generated by repeating a transformation at multiple scales, so the whole resembles its parts and detail persists as you zoom in. This can be measured by a fractional dimension that captures how the pattern fills space between the integer dimensions of line, plane, and volume.
The Ba-ila settlement in Zambia is laid out as a large ring of houses that itself contains a scaled-down ring at the rear (the chief's compound), and individual houses echo the same ring form. The aerial plan reproduces one shape at the levels of village, family enclosure, and single dwelling.
Eglash distinguishes fractal structure that practitioners consciously design and describe from patterns that emerge unintentionally, and he investigates which applies by interviewing the artisans themselves. Finding a fractal shape is not enough; the question is whether the makers have their own concepts and recursive procedures behind it.
Complex African fractal patterns can arise from simple rules applied repeatedly, such as a Bamana sand divination procedure that pairs marks to produce new rows, or scaling a drawn unit down and placing copies inside itself. The sophistication lies in iterating a modest operation rather than in a single elaborate blueprint.
Because these African designs embody genuine recursive and scaling mathematics, Eglash argues that labeling non-Western cultures as cognitively simpler or less developed is unfounded. The work resists both dismissing the patterns as accidental and romanticizing them as mystical, insisting instead on crediting indigenous mathematical reasoning.