Ferns, Fractals, and African Textiles

“Fractals are characterized by repetition of similar patterns at ever diminishing scales.”

By now most of us know that fractals are found throughout nature. Ferns, trees, and snowflakes are fractals, as well as lungs, branching river basins, and storm turbulence patterns. But who knew that traditional African culture uses fractals in village layouts, architecture, textile design, and divination methods?

That’s the topic of Ron Eglash’s book, African Fractals, Modern Computing and Indigenous Design. An ethno-mathematician, Eglash spent a year studying fractals in Africa after looking at an aerial photograph of a traditional settlement and noticing that it was laid out in a fractal.

Fractal model of Balla Village

What he discovered was a broad, sophisticated, and conscious use of fractal mathematics in many sectors of African life. Often the use of fractals extended beyond design, with social or religious concepts embedded in the complicated layouts.

Aerial — Palace of the chief in a city in Cameroon

For instance, in the palace depicted above, as one walks in toward the Chief’s chambers, increasing amounts of politeness are expected and signaled by the tightening spiral. In another exampled cited by Eglash, as young children in one village age, they are taught geometric patterns with increasing complexity, while simultaneously being taught the village’s myths (also incrementally).

blanket with fractal design

The use of sophisticated algorithms is not “merely intuitive”, or simply good design, Eglash explains, but a very deliberate use of self-similar structures. The divination method employed by the Bamana people (by making strike marks in the sand) provided the mathematical basis for the binary code, which leads to Eglash’s assertion that every digital circuit in the world is based on African mathematics.

African patterning style is NOT a design practice found generally among indigenous cultures, as many think upon learning about this  (and let’s be clear, to be so VERY shocked that a high level of mathematics is routinely, elegantly, and ritually employed by many African societies is plainly racist). Native American design, by contrast, plays with circular and four-fold symmetry.

On Eglash’s website, there are free applets that run in the browser where you can play with iterations of simple lines and watch their ever  increasing complexity.  What might be of interest to a quilter is how much the demonstration of the rectangular shape (representative of some traditional African settlements) looks like a log cabin quilt being made.

What traditional quilting patterns are fractals?  Changes in scale are required, as well as repetition, otherwise, MOST traditional quilts would be fractals. Are the patterns created by tie-dye and some shibori methods fractals? My guess is some are, yes. Celtic knots are fractals. The ferns emerging from the felt house are, and here they are nearly forming a heart as well.

Felt House, Day 11

Well, lest I’ve overly impressed you with my ability to restate ideas from  a 16 minute-lecture (2007 TED Eglash), let me end by saying it’s time to go watch American Idol —

which is to say, the show has been taping for at least 25 minutes, allowing me to skip 20 out of 21 words that Ryan Seacrest utters (some nights? it takes me 10 minutes to watch the show).

(And, BTW, I’m rooting for Crystal Bowersox or Lee Dewyze).

Quotes and images from Ron Eglash used with his permission.