Ron Eglash, African Fractals: Modern Computing and Indigenous Design – New Brunswick NJ: Rutgers University Press, 1999

Abstract

, and religion. As Eglash explains, although most people learn Euclidean geometry in school, few study fractal geometry, which plays a significant role in the computer modeling process in the hard sciences. Meanwhile, according to Eglash, fractal geometry has long been a theme in Africa, with a wide variety of local cultural associations, including kinship, labor practices, politics, and religion. Eglash's research began in the 1980s while investigating settlement architecture in Central and West Africa. Aerial photographs of various settlement compounds revealed 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 very small footpaths. As Eglash notes, at first he thought it was just from unconscious social dynamics. But during his fieldwork, he found that fractal designs also appear in a wide variety of intentional designs-carving, hairstyling, metalwork, painting, textiles-and the recursive process of fractal algorithms are even employed in African quantitative systems. Eglash adds that in the design rationales and cultural semantics of many African geometric figures, as well as in indigenous quantitative systems (additive progression, doubling sequences, binary recursion) and symbolic systems (iconic symbols for feedback loops, equiangular spirals, infinity), there are abstract ideas and formal structures that closely parallel some of the fundamental aspects of fractal geometry. These results, Eglash concludes, are congruent with recent developments in complex systems theory, which suggest that pre-modern, non-state societies were neither utterly anarchic, nor frozen in static order, but rather utilized an adaptive flexibility that capitalized on the nonlinear aspects of ecological dynamics. While in Africa, Eglash encountered some of the most complex fractal systems that exist in religious activities, such as the sequence of symbols used in sand divination, a method of fortune telling found in Senegal. Some of his other findings include the use of sophisticated mathematical ideas in everyday objects. In the arid region of the Sahel, for example, artisans produce windscreens by utilizing a scaling design that gives them the maximum effect-keeping out the wind-driven dust-for the minimum amount of effort and material. When Eglash returned from Africa, one of his colleagues advised him to focus on scaling patterns in African hairstyles. An enthusiastic group of students at Evergreen State University volunteered their programming skills to help create a multimedia lesson on African fractals. The Hairstyle Storyboard Website (http://www.rpi.edu/~eglash/eglash.dir/afmulti.htm) that has been developed utilizes a style referred to as "the braids of threads", from Yaoundé, Cameroon, to explicate African branching fractals. The "fractal hairstyle" module guides users, 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 major goal is to eventually combine the images, software and video on African fractals. Given all this, at least two critical questions can be raised: (1) Since some scholars have found that all cities (historic, primitive and modern) are fractal precisely because they are complex natural systems, and other scholars have discovered that fractal tiling patterns exist on some of the oldest European tiled floors and in ancient Chinese art, what then does this say for the validity of Eglash's arguments concerning African fractals? (2) At what number of scales does self-similarity occur in African fractals and what method does Eglash employ to determine self-similarity? Eglash deals with these questions in several ways.