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> From: Jerry Becker
> Reply To: Kentucky K-12 Math Teachers Discussion List
> Sent: Friday, August 6, 1999 4:20 PM
> To: KYMATH
> Subject: [ME] Fractals in African Culture and Art
> [Note: Thanks to Corrie Bergeron for the following ...]
> From: "Steven D. Tripp" <tripp@U-AIZU.AC.JP>
> Subject: Fractals
> FOR IMMEDIATE RELEASE: 26 JULY 1999
> Contact: Ron Eglash, Ohio State University
> E-mail: Eglash.1
> Phone: (614) 292-2559
> Fractals provide unusual theme in much African culture and art
> Columbus, Ohio -- In everything from braided hairstyles to the design of
> housing settlements, the geometric structures known as fractals permeate
> African culture. In a new book, an Ohio State University scholar examines
> the unlikely pairing of this mathematical concept and the culture and art
> of Africa.
> "While fractal geometry is often used in high-tech science, its patterns
> are surprisingly common in traditional African designs," said Ron Eglash,
> senior lecturer in comparative studies in the humanities. Eglash is author
> of African Fractals: Modern Computing and Indigenous Design (Rutgers
> University Press, 1999).
> Eglash said his work suggests that African mathematics is more complex
> than previously thought. He also says using African fractals in U.S.
> classrooms may boost interest in math among students, particularly African
> He has developed a Web page to help teachers use fractal geometry in the
> Fractals are geometric patterns that repeat on ever-shrinking scales. Many
> natural objects, like ferns, tree branches, and lung bronchial systems are
> shaped like fractals. Fractals can also be seen in many of the swirling
> patterns produced by computer graphics, and have become an important
> new tool for modeling in biology, geology, and other natural sciences.
> In African Fractals, Eglash discusses fractal patterns that appear in
> widespread components of indigenous African culture, from braided
> hairstyles and kente cloth to counting systems and the design of homes and
> settlements. Other researchers have studied bits and pieces of African
> mathematics in areas such as art, architecture, and religious practices,
> but Eglash said this is the first attempt to describe the common theme of
> fractal geometry among several different African cultures. "There is no
> singular 'reason' why Africans use fractals, any more than a singular
> reason why Americans like rock music," Eglash noted in his book. "Such
> enormous cultural practices just cover too much social terrain."
> He began this research in the 1980s when he noticed the striking fractal
> patterns in aerial photos of African settlements: circles of circular
> houses, rectangles inside rectangles, and streets branching like trees.
> Eglash confirmed his visual intuition by calculating the geometry of the
> in the photos -- they were indeed fractal. At first he thought that only
> unconscious social dynamics were responsible. Later, however, he received
> a Fulbright grant for field work in west and central Africa, and found
> during his travels that fractals were a deliberate part of many African
> cultures' artistic expressions and counting systems, too.
> In one chapter, Eglash described an ivory hatpin from the Democratic
> Republic of the Congo that is decorated with carvings of faces. The faces
> alternate direction and are arranged in rows that shrink progressively
> toward the end of the pin. Eglash determined that the design matches a
> sequence of squares where the length of the line that bisects one square
> determines the length of the side of the following square.
> In another chapter, he illustrated how divination priests of the Bamana
> people in Dakar, Senegal, calculate fortunes using a recursively generated
> binary code. Eglash explained that diviners use base-two arithmetic, just
> like the ones and zeros in digital circuits, and bring each output of the
> arithmetic procedure back in as the next input. This produces a string of
> symbols that the priests then interpret as the client's fortune. This
> technique is similar to a kind of random number generation in computing,
> Eglash said, and the Bamana's technique can produce over 65,000 numbers
> before the sequence repeats.
> While fractals can be found in cultures on other continents -- Celtic
> knots are one example -- fractals are particularly prevalent in Africa.
> Eglash pointed out that this does not mean African mathematics is more
> complex than Western mathematics, or that African cultures are "closer to
> nature" because fractals are present in nature -- these sweeping
> conclusions are just plain incorrect, he said. "Creating a body of
> mathematics is about intellectual labor, not some kind of transcendental
> There are plenty of important components of European fractal geometry that
> are missing from the African version," Eglash said. On the other hand,
> Eglash maintained, his work does show that African mathematics is much
> more complex than previously thought.
> Knowing fractal geometry enables scientists to model complex processes in
> biology, chemistry, and geography on computer. It also helps generate
> realistic computer images of natural features such as rugged terrain or
> tangled tree branches. Still, most schools teach classical geometry -- the
> study of simple shapes like circles or squares -- not fractal geometry,
> Eglash said.
> In studies of African-American students' poor math performance,
> researchers have suggested that computer-based teaching methods or the
> presentation of real-world math applications might encourage students to
> learn more. According to Eglash, the use of African fractals in math
> classes could combine both solutions.
> Eglash's Web page contains links for obtaining both commercial products
> related to African fractals as well as free materials. For example, he has
> just written a program that allows students who visit the page to interact
> with a computer simulation of the patterns in cornrow hairstyles. Even
> without computers, Eglash said, students can still learn about Fractals
> using common school supplies.
> In his book he explained how to fold a piece of paper to demonstrate the
> geometry of a traditional African tie-dye method, for example. The Web
> page also has some materials that teachers can print out and use with
> their students. One lesson shows how students can derive fractal equations
> their own photos of cornrow braid patterns using a protractor and some
> simple calculations.
> Eglash cautioned that African-American students won't automatically be
> interested in fractals simply because they appear in African designs. He
> suggests that the most powerful potential of African fractal geometry
> comes from its opposition to biological determinism -- the assumption that
> ability is genetically determined. "Just think how often students are told
> by parents, 'Oh, don't worry
> about your bad scores, I was no good at math either.'" Such myths have
> their most devastating impact on minority children, Eglash said, but he
> makes a distinction between this kind of argument and more simplistic
> models of identity or self-esteem.
> For instance, when Eglash introduced fractal geometry to a class of
> 12-year-old African-American students at a 1996 urban youth conference,
> the students used traditional African fractals only as inspiration for
> creating new designs of their own.
> "The best thing we can do is give students the tools for constructing
> their own identities -- powerful new tools like African fractals -- and
> then just get out of the way," Eglash said.
> Jerry P. Becker
> Dept. of Curriculum & Instruction
> Southern Illinois University
> Carbondale, IL 62901-4610 USA
> Fax: (618)453-4244
> Phone: (618)453-4241 (office)
> E-mail: jbecker