“It’s the same pattern at many different scales,” Ron Eglash explained about fractals in his 2007 TED Talk. To create one, you start with a seed shape and iteratively integrate smaller versions of the shape back into the design. It is a recursive process that leads to a shape of infinite length. Fractal shapes also mirror forms which we find everywhere in nature, suggesting that the process underlying their creation is equally ubiquitous. Although each seed shape unfolds into its own unique design, fractals collectively show us how complex patterns can emerge from simple, repeating interactions.
After explaining the basic history of fractals in mathematics, Eglash described the unexpected connection between fractal mathematics and African culture. He showed how fractals are “a shared technology in Africa,” informing the design of everything from the construction of villages to the strategy used in board games to the symbolic code of religious divination. Through his work and what it reveals, we get a greater sense the potential diversity of hidden knowledge embedded in both the natural and cultural dimensions of the world around us.
… in 1977, Benoit Mandelbrot, a French mathematician, realized that if you do computer graphics and used these shapes he called fractals, you get the shapes of nature … So nature has this self-similar structure. Nature uses self-organizing systems. Now in the 1980s, I happened to notice that if you look at an aerial photograph of an African village, you see fractals. And I thought, “This is fabulous! I wonder why?” And of course I had to go to Africa and ask folks why …
The fractals at the heart of African designs | Ron Eglash