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If you take your thumb and your index finger and look right where they meet - go ahead and do that now - and relax your hand, you'll see a crinkle, and then a wrinkle within the crinkle, and a crinkle within the wrinkle. Right? Your body is covered with fractals.

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.

I started collecting aerial photographs of Native American and South Pacific architecture; only the African ones were fractal. And if you think about it, all these different societies have different geometric design themes that they use. So Native Americans use a combination of circular symmetry and fourfold symmetry.

The reason that Google was such a success is because they were the first ones to take advantage of the self-organizing properties of the web. It's in ecological sustainability. It's in the developmental power of entrepreneurship, the ethical power of democracy.

While fractal geometry is often used in high-tech science, its patterns are surprisingly common in traditional African designs.

There is no singular 'reason' why Africans use fractals, any more than a singular reason why Americans like rock music. Such enormous cultural practices just cover too much social terrain.

Creating a body of mathematics is about intellectual labor, not some kind of transcendental revelation. There are plenty of important components of European fractal geometry that are missing from the African version.

The best thing we can do is give students the tools for constructing their own identities - powerful new tools like African fractals - and then just get out of the way.

My assumption was that all indigenous architecture would be more fractal. My reasoning was that all indigenous architecture tends to be organized from the bottom up. As it turns out, though, my reasoning was wrong.

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.

Fractal geometry is everywhere, even in lines drawn in the sand. It's the cycle of life... You see fractals in plants, in flowers. Within the human lung are branches within branches.

Mathematicians didn't invent infinity until 1877. So they thought it was impossible that Africans could be using fractal geometry.

I just toured around looking for fractals, and when I found something that had a scaling geometry, I would ask the folks what was going on - why they had made it that way.

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