I started collecting aerial photographs of Native American and South Pacific architecture; only the African ones were fractal. And if you think about it, all these different societies have different geometric design themes that they use. So Native Americans use a combination of circular symmetry and fourfold symmetry.

In this insightful quote, Ron Eglash, a mathematician and researcher known for his work on ethnomathematics, discusses his exploration of geometric patterns in traditional architecture across various cultures. He began by collecting aerial photographs of Native American, South Pacific, and African architecture, aiming to understand the underlying mathematical structures embedded in their designs. What stood out to him was that among these, only African architecture consistently displayed fractal geometry—a complex pattern characterized by self-similarity and recursion.

Eglash’s observation about fractal patterns in African design was groundbreaking because it challenged conventional views that complex mathematical thinking was exclusive to Western science. In African societies, these fractal structures appeared in village layouts, art, textiles, and even religious symbols, showing an intuitive grasp of mathematical concepts that had gone largely unrecognized in formal histories of architecture and mathematics.

He goes on to explain that other societies, like Native Americans, used different types of symmetry in their architectural and cultural expressions. Specifically, Native American design often blends circular symmetry—which reflects continuity and unity—with fourfold symmetry, symbolizing balance, direction, and harmony, frequently seen in sacred geometry and ceremonial structures. This suggests that each culture develops its own geometric vocabulary that reflects its worldview, values, and spatial understanding.

Ultimately, Eglash’s quote underscores the rich mathematical diversity in global architectural traditions. His research advocates for recognizing and respecting the cultural mathematics embedded in traditional design, showing that architecture is not only a physical or aesthetic practice, but also a mathematical and philosophical expression of cultural identity.