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Here's a wonderful fractal.

A little fractal generator

This power is called the fractal dimension of the fractal, and it usually exceeds the fractal's topological dimension.

The Eiffel Tower has a fractal aspect.

They were breathing those words with fractal lungs.

So here's a little fractal model for it.

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

Fractal art is a form of algorithmic art created by calculating fractal objects and representing the calculation results as still images, animations, and media.

But painting for a long time had a fractal side.

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.

This was an early example of what came to be known as a fractal.

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

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

A fractal is a natural phenomenon or a mathematical set that exhibits a repeating pattern that displays at every scale.

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

Another logarithm based notion of dimension is obtained by counting the number of boxes needed to cover the fractal in question.

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

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.

Brownian motion A path generated by a one dimensional Wiener process is a fractal curve of dimension 1.5, and Brownian motion is a finite version of this.

The features are interesting, for example, because they are very sharp, spatially intermittent (the distance between features is much larger than the features themselves), or have a fractal form.

Now, after I did the simulation, I realized the whole village kind of spirals around, just like this, and here's that replicating line a self replicating line that unfolds into the fractal.

Because of his access to IBM's computers, Mandelbrot was one of the first to use computer graphics to create and display fractal geometric images, leading to his discovering the Mandelbrot set in 1979.

So I tracked down one of the folks who makes these things, this guy in Mali just outside of Bamako, and I asked him, How come you're making fractal fences? Because nobody else is.

What you're seeing here is a hierarchical schematic development of the trunks of this tree as it has elaborated itself over time into six layers of fractal, of trunks springing from trunks springing from trunks.

'I am a mathematician, and I would like to stand on your roof.' That is how Ron Eglash greeted many African families he met while researching the fractal patterns he d noticed in villages across the continent.

At TED2010, mathematics legend Benoit Mandelbrot develops a theme he first discussed at TED in 1984 the extreme complexity of roughness, and the way that fractal math can find order within patterns that seem unknowably complicated.

The same fractal can be achieved by dividing a triangle into a tessellation of P2 similar triangles and removing the triangles that are upside down from the original, then iterating this step with each smaller triangle.

And in fact, what Murray was talking about yesterday in the fractal beauty of nature of having the descriptions at various levels be rather similar all goes down to the idea that the elementary particles are both sticky and standoffish, and they're in violent motion.

If you took the idea of fractal technology further, take a membrane, shrinking it down constantly like nature does that could be a seat for a chair it could be a sole for a sports shoe it could be a car blending into seats.

And so I finally got to this city, and I'd done a little fractal model for the city just to see how it would sort of unfold but when I got there, I got to the palace of the chief, and my French is not very good I said something like, I am a mathematician and I would like to stand on your roof.

Now, in the decade of Darfur and Iraq, a statement like that might seem somewhere between hallucinatory and obscene. But I'm going to try to convince you that that is the correct picture. The decline of violence is a fractal phenomenon. You can see it over millennia, over centuries, over decades and over years, although there seems to have been a tipping point at the onset of the Age of Reason in the sixteenth century. One sees it all over the world, although not homogeneously.