Thursday, June 3, 1999

Now Important in Computer Modeling, Fractals Have a Rich History in African Design By BIANCA P. FLOYD An African woman's elaborate cornrow braids can be seen as more than a fashion statement or a cultural choice. The intricate pattern can also be useful in understanding fractals -- geometric patterns that are repeated on smaller and smaller scales to produce intricate designs outside the scope of classical geometry. BOOKMARK: A professor's Web site explores how fractals permeate all levels of African society, including art and architecture, religion, and politics. Ron Eglash, a professor of comparative studies at Ohio State University, demonstrates the principle with a tool on his Web site that allows students to create computer-generated graphics simulating the fractal branching patterns found in braided hairstyles. Mr. Eglash has also just published a book, African Fractals: Modern Computing and Indigenous Design (Rutgers University Press), that explores how fractals permeate all levels of African society, including art and architecture, religion, and politics. Although most people learn Euclidean geometry in school, few study fractal geometry, which plays an important role in the computer modeling of processes in biology, geology, and other natural sciences, Mr. Eglash explains. Meanwhile, fractal geometry has long been a theme in Africa, with a wide variety of local cultural associations -- in politics, religion, kinship, and labor practices, for instance. His research began in the 1980s, while he was studying settlement architecture in West and Central Africa. In taking aerial photographs of various settlement compounds, he noticed that many were composed of circular structures enclosed in other circles, or rectangles within rectangles, and that the compounds were likely to have street patterns in which broad avenues branched into tiny footpaths. From African Fractals "At first I thought it was just from unconscious social dynamics," Mr. Eglash says, "but during my fieldwork, I found that fractal designs also appear in a wide variety of intentional designs -- hairstyling, textiles, sculpture, painting, carving, metalwork -- and the recursive process of fractal algorithms are even used in African quantitative systems." Some of the most complex systems Mr. Eglash encountered were tied to religious activities, such as the sequence of symbols used in sand divination, a method of fortune telling found in Senegal. Other examples demonstrated the use of sophisticated mathematical ideas in everyday objects. Artisans in the arid region of the Sahel produce windscreens using a scaling design that gives them the maximum effect -- keeping out the wind-driven dust -- for the minimum amount of effort and material. When he returned from Africa, a colleague suggested that he focus on scaling patterns in black hairstyles. Students at Evergreen State University volunteered their programming skills to help create a multimedia lesson on African fractals. The Hairstyle Storyboard on his Web site uses a style called "the braids of threads," from Yaoundé, Cameroon, to explain branching fractals. The simulation guides students, step by step, through the creation of a three-dimensional fractal, beginning with the initial design and then mathematically determining the ratio of each iteration. The Web site also offers a bibliography of research on African fractals, examples of architecture that incorporate African fractals, and additional reference materials.