Fire Walk With Me

Fractal geometry was well-integrated into African life by the time the Europeans showed up - which of course the Europeans didn’t understand, because they hadn’t discovered fractals yet.

“We used to think of mathematics as a kind of ladder that you climb, and we would think of counting systems – one plus one equals two – as the first step and simple shapes as the second step. Recent mathematical developments like fractal geometry represented the top of the ladder in most Western thinking. But it’s much more useful to think about the development of mathematics as a kind of branching structure and that what blossomed very late on European branches might have bloomed much earlier on the limbs of others. When Europeans first came to Africa, they considered the architecture very disorganized and thus primitive. It never occurred to them that the Africans might have been using a form of mathematics that they hadn’t even discovered yet.”

This is Ron Eglash, who wrote a book called African Fractals: Modern Computing and Indigenous Design From the book’s description:

Fractals are characterized by the repetition of similar patterns at ever-diminishing scales. Fractal geometry has emerged as one of the most exciting frontiers on the border between mathematics and information technology and can be seen in many of the swirling patterns produced by computer graphics. It has become a new tool for modeling in biology, geology, and other natural sciences.

Anthropologists have observed that the patterns produced in different cultures can be characterized by specific design themes. In Europe and America, we often see cities laid out in a grid pattern of straight streets and right-angle corners. In contrast, traditional African settlements tend to use fractal structure—circles of circles of circular dwellings, rectangular walls enclosing ever-smaller rectangles, and streets in which broad avenues branch down to tiny footpaths with striking geometric repetition. These indigenous fractals are not limited to architecture; their recursive patterns echo throughout many disparate African designs and knowledge systems.

Here he is giving a TED talk on the subject -  on of the subjects he mentions in this talk as an example of fractal geometry? Hair braiding. 

Here’s the traditional image used to illustrate fractals as a concept:

An example of African hair-braiding:

Here is the layout of a Ba-ila village, which is actually a fractal model (taken from this website on fractals) 

The iterations are as follows: The first image is of the layout of an individual house. This is the seed shape. The second interation shows the same configuration of a family compound. The third interation shows the layout of the entire village made up of several compounds.

An actual photo of a village with this layout:

(In your traditional mathematics/science textbook, Mandlebrot is credited with “discovering” fractals in 1975)