Many African designs are based on "fractals" -- patterns that repeat themselves at many scales (also called "scaling patterns"). To learn more you can order the book African Fractals by clicking here

African fractals: the TED video

Mathematicans in the 19th and early 20th century invented several fractal patterns.
One classic example is the Koch curve.

Later Benoit Mandelbrot showed the practical application to modeling natural objects:

This fern is classic, and many algae are good examples, as are lungs. I've looked at clouds from both sides now.

Fractal shapes abound in traditional African designs, from architecture to textiles.

One African fractal design that is also part of African American innovation in the U.S. is the scaling pattern of cornrow hairstyles.

Another scaling design from Africa is this Mangbetu ivory sculpture

You can build a paper model to explore scaling patterns in an African windscreen

Some examples of recursion in African material culture are numeric. The "marching formation" in the game of Owari offers insight into African concepts of iteration, self-organization, and related phenomena. Click here to experiment with these numeric patterns.