Please see here the poster for the women in Mathematics for social change and sustainable livelihoods conference in Naivasha, Kenya in July 2015.
Women in Mathematics for Social Change & Sustainable Livelihoods
About the Author: Jonathan Shock
I'm a lecturer at the University of Cape Town in the department of Mathematics and Applied Mathematics. I teach mathematics both at undergraduate and at honours levels and my research interests lie in the intersection of applied mathematics and many other areas of science, from biology and neuroscience to fundamental particle physics and psychology.
Interesting pictures of pattern of fractals illustrated by measuring scale and dimensions of a hair. It is just promoting mathematics in Africa as most African women shape their hair with different styles. It will also be attractive to study the pattern of a wool fractals.
The Eglash TED talk has lovely examples, but like all TED talks it is frustration because it skims so quickly over stuff. I can see the role he found for recursion, and he makes it clear that Africa seems much more advanced than the rest of the world in using recursive design at diminishing scales for all kinds of things, from personal adornment to buildings.
I am not so sure these patterns are fractal in the sense I am used to it. For instance, in the hairstyle above, is the idea that each of the curves continues down to infinitely small repeats of the basic T knot, and that there are infinitely many curves? And that there is a transformation that sends part of the pattern onto the whole? It rather seems to me that the African experience must include knowledge of how many scales to include, which I find a lot more interesting—scaling in nature also typically is over a limited range of scales.
A different aspect is the coverage of (part of) the sphere by what are basically long thin shapes. Of course it is known that any vector field on a sphere must have fixed points, and that if you interpret the trajectories on the vector field as hair, this means that to cover a sphere in hair you have to have whorls and crowns. Often said that a hairy sphere cannot be properly combed—that is, as you comb the hair you must get something that is not everywhere homeomorphic to parallel hair. Of course these hairstyles precisely do try to get rows that are locally homeomorphic to a set of parallel line segments. Do they nevertheless have to have some isolated points where this breaks down? Some of the styles collected by Eglash show such points, but on others it is less clear. Can a fractal design properly cover a sphere?