Africans can't possibly really be using fractal geometry, right?

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So I found myself, in other words, constructing a geometry, a geometry of things which had no geometry.

Here's a wonderful fractal.

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The Eiffel Tower has a fractal aspect.

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They were breathing those words with fractal lungs.

So here's a little fractal model for it.

Extract geometry from the images.

But painting for a long time had a fractal side.

They have a very rich, intertwined geometry.

I didn't put his name up here my colleague, Kerry, in Kenya, has come up with this great idea for using fractal structure for postal address in villages that have fractal structure, because if you try to impose a grid structure postal system on a fractal village, it doesn't quite fit.

The frilly crenulated forms that you see in corals, and kelps, and sponges and nudibranchs, is a form of geometry known as hyperbolic geometry.

We're just seeing the coarse scale geometry here.

The Greeks invented a theoretical model of geometry.

So in Manghetu sculpture, you'd see this recursive geometry.

This is exploring geometry and the rhythm of shape.

We use a modified inkjet printer, and we print geometry.

Geometry, fantastic. You know, quantum mechanics these are cool things.

So what is this hyperbolic geometry that corals and sea slugs embody?

This is the result of computational geometry, gesture recognition, and machine learning.

I saw this diagram drawn by a French architect, and I thought, Wow! What a beautiful fractal!

And primary visual cortex sees just simple geometry, just the simplest of shapes.

If geometry is the science of space, what is the science of time?

I started collecting aerial photographs of Native American and South Pacific architecture only the African ones were fractal.

But it's reassuring that at the heart of this mathematics is pure, beautiful geometry.

This sort of geometry revolutionized mathematics when it was first discovered in the 19th century.

Before hyperbolic geometry, mathematicians knew about two kinds of space Euclidean space, and spherical space.

And then I went in, and measured all the geometry because I figured, hey, biomimicry.

I saw my geometry teacher in high school, Mr. Rucell's wry smile under his handlebar mustache.

A Redwood is a fractal. And as they put out limbs, the limbs burst into small trees, copies of the Redwood.

The discovery of hyperbolic space ushered in the field of mathematics that is called non Euclidean geometry.

And where I was bad was algebra. And I was never allowed to take geometry or trig.

What physics tells us is that everything comes down to geometry and the interactions of elementary particles.

David Hughes at Ohio State University has written a primer on Afrocentric architecture in which he's used some of these fractal structures.

The first ingredient is materials and geometry, and that needs to be tightly coupled with the energy source.

And the power of mathematics is often to change one thing into another, to change geometry into language.

And a surprising aspect of it is that very often, the rules of this geometry are extremely short.

So they're mapping the social scaling onto the geometric scaling it's a conscious pattern. It is not unconscious like a termite mound fractal.