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. Last Updated: 07/27/2016

African Villages Have Fractal Pattern




In 1988, Ron Eglash was studying aerial photographs of a traditional Tanzanian village when a strangely familiar pattern caught his eye.


The thatched-roof huts were organized in a geometric pattern of circular clusters within circular clusters, an arrangement Eglash recognized from his former days as a Silicon Valley computer engineer. Stunned, Eglash digitized the images and fed the information into a computer. The computer's calculations agreed with his intuition: He was seeing fractals.


Since then, Eglash has documented the use of fractal geometry - the geometry of similar shapes repeated on ever-shrinking scales - in everything from hairstyles and architecture to artwork and religious practices in African culture. The complicated designs and surprisingly complex mathematical processes involved in their creation may force researchers and historians to rethink their assumptions about traditional African mathematics.


In contrast to the relatively ordered world of Euclidean geometry, fractal geometry yields less obvious patterns. These patterns appear everywhere in nature, yet mathematicians began deciphering them only about 30 years ago.


Fractal shapes have the property of self-similarity, in which a small part of an object resembles the whole object. "If I look at a mountain from afar, it looks jagged and irregular, and if I start hiking up it, it still looks jagged and irregular," said Harold Hastings, a professor of mathematics at Hofstra University. "So it's a fractal object - its appearance is maintained across some scales."


Eglash began studying tribal geometry when he came across an article about a group of Tanzanian women and their loss of autonomy in village organization. The author blamed the women's plight on a shift from traditional architectural designs to a more rigid modernization program.


Eglash was intrigued by what he read and asked the researcher to send him pictures of the village.


After detecting fractal patterns, Eglash sought to answer what property of fractals made them so widespread in the culture.


"Basically I just toured around looking for fractals, and when I found something that had a scaling geometry, I would ask the folks what was going on - why they had made it that way," he said.


In some cases Eglash found that fractal designs were based purely on aesthetics. In many cases, however, Eglash found that step-by-step mathematical procedures were producing these designs, many of them surprisingly sophisticated.


Eglash said the fractal design themes reveal traditional African mathematics may be much more complicated than previously thought.


"We used to think of mathematics as a kind of ladder that you climb," Eglash said. "And we would think of counting systems - one plus one equals two - as the first step andsimple shapes as the second step."


Recent mathematical developments like fractal geometry represented the top of the ladder in most Western thinking, he said. "But it's much more useful to think about the development of mathematics as a kind of branching structure and that what blossomed very late on European branches might have bloomed much earlier on the limbs of others.


"When Europeans first came to Africa, they considered the architecture very disorganized and thus primitive. It never occurred to them that the Africans might have been using a form of mathematics that they hadn't even discovered yet."