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Topic: [ME] Fractals in African Culture and Art
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Jerry P. Becker

Posts: 16,576
Registered: 12/3/04
[ME] Fractals in African Culture and Art
Posted: Aug 6, 1999 4:20 PM
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<x-rich>[Note: Thanks to Corrie Bergeron for the following ...]


From: "Steven D. Tripp" <<tripp@U-AIZU.AC.JP>

Subject: Fractals


Contact: Ron Eglash, Ohio State University


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 Americans.

He has developed a Web page to help teachers use fractal geometry in
the classroom.



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

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 arrangements

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 fractal-like

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 revelation.

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 from

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 math

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)



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