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Out of Africa: Using Fractals To Teach At-Risk Students

A fractal branching pattern
A fractal branching pattern, "la tress de fils," in the hairstyle of a woman in Yaounde, Cameroon. The corresponding simulation can be found at http://www.rpi.edu/˜eglash/eglash.dir/afmulti.cfm Photo credit: Ron Eglash

Fractal geometry is broadly evident throughout traditional African culture, according to Ron Eglash, an assistant professor of science and technology studies at Rensselaer Polytechnic Institute (RPI) in Troy, New York. He has documented fractal patterns in corn-row hairstyles, weavings and architecture of African villages, as well as in Santeria, the traditional religion of West Africa's Yoruba people and many forms of traditional African art. His research led to the publication last year of a book entitled, African Fractals: Modern Computing and Indigenous Design (Rutgers University Press, 1999).

Eglash completed an undergraduate degree in cybernetics and a master's degree in engineering at the University of California, Los Angeles and worked for a year at National Semiconductor on intelligent interface design. Intrigued by the prospect of gaining a more cultural perspective on what he terms "technosocial systems," he entered the History of Consciousness doctoral program at the University of California, Santa Cruz. "It had a reputation for allowing students the freedom to create their own interdisciplinary combination of courses," he says. "I was able to take classes in anthropology and graduate seminars in mathematics, and also work on computing models."

After completing his PhD, Eglash won a Fulbright scholarship and chose to do fieldwork in West and Central Africa. "I was looking for something that would combine both my technical and cultural interests," he says, and serendipitously came across an article on the relation between housing and women's autonomy in Tanzania. Traditional African settlements are self-organized, creating a self-similar, or fractal, structure, which provided greater social control for women, but the onset of modernization programs brought more rigidly structured cartesian grids to the village housing design.

"That got me thinking about the fractal/Euclidean contrast and I began studying aerial photos of indigenous architectures," says Eglash. When he scanned the photographs into the computer and analyzed them mathematically, he found that they were fractal in nature - and many, although not all, were based on explicit geometric algorithms. He also found numeric systems which employed recursion, similar to the pseudo-random number generation in computers. Nor are these fractal patterns characteristic of all indigenous layouts: a similar analysis of Native American and South Pacific villages did not reveal a fractal structure, making it a design theme culturally specific to Africa.

Eglash believes that such design themes could indicate that traditional African mathematics may be much more complicated than previously thought. In fact, his discovery could prove to be an effective teaching tool for instructing African-American students about their mathematical heritage. It might also lead to a novel approach to integrating information technology with Third World development. To increase awareness of his discovery among educators, he routinely speaks about his work with African fractal patterns at the annual meetings of the National Council of Teachers of Mathematics, and several teachers have reported positive results from using the material with their students. More recently he began to work with a local organization in Troy known as "The Ark", which sponsors educational programs for at-risk African-American students. His Web site features an interactive Java simulation that enables students to explore scaling models with relation to corn-row hairstyles, and he hopes to eventually create a CD-ROM math lab incorporating his fractal material.

Employing African fractal patterns and other forms of indigenous mathematical practices in the classroom could help offset a long-standing over-emphasis in the US on biological determinism, which Eglash believes creates a learning deterrent for students of all ethnic groups, including white students. He notes that certain cross-cultural studies revealed that while children, teachers and parents in China and Japan tend to view difficulty with math as a problem of time and effort, their American counterparts attribute differences in math performance to innate ability - which then becomes a self-fulfilling prophecy. "We need to be open-minded about the different ways in which different students can improve their mathematical performance, and find out how to accommodate those differences in the classroom," he says.

Read more about African fractal patterns and sample the new software at Ron Eglash's home page: http://www.rpi.edu/˜eglash/eglash.cfm.

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Editor: Alan Chodos
Associate Editor: Jennifer Ouellette