Hunting the Hidden Dimension -- Fractals

http://www.pbs.org/wgbh/nova/programs/ht/tm/3514.html?site=34&pl=qt&rate=hi&ch=1

5-Part series

NARRATOR: In 1978, at Boeing Aircraft in Seattle, engineers were designing experimental aircraft.


LOREN CARPENTER (Pixar Animation Studios): Exotic things, with two wings or two tails or two fuselages, and just weird stuff because, "who knows, it might work."

NARRATOR: A young computer scientist named Loren Carpenter was helping them visualize what the planes might look like in flight.

LOREN CARPENTER: I would get the data from them and make pictures from various angles, but I wanted to be able to put a mountain behind it, because every Boeing publicity photo in existence has a mountain behind it. But there was no way to do mountains. Mountains had millions and millions of little triangles or polygons or whatever you want to call it, and we had enough trouble with a hundred. Especially in those days when our machines were slower than the ones you have in your watch.

NARRATOR: Carpenter didn't want to make just any mountains. He wanted to create a landscape the planes could fly through. But there was no way to do that with existing animation techniques. From the time movies began, animators had to draw each frame by hand—thousands of them—to make even a short cartoon.

THUMPER (Bambi/Filmclip): That's why they call me Thumper.

NARRATOR: But that was before Loren Carpenter stumbled across the work of a little-known mathematician named Benoit Mandelbrot.

LOREN CARPENTER: In 1978, I ran into this book in a bookstore: Fractals: Form, Chance and Dimension, by Benoit Mandelbrot, and it has to do with the fractal geometry of nature. So I bought the book and took it home and read it, cover to cover, every last little word, including the footnotes and references, twice.

NARRATOR: In his book, Mandelbrot said that many forms in nature can be described mathematically as fractals: a word he invented to define shapes that look jagged and broken. He said that you can create a fractal by taking a smooth-looking shape and breaking it into pieces, over and over again.

Carpenter decided he'd try doing that on his computer.

LOREN CARPENTER: Within three days, I was producing pictures of mountains on my computer at work.

The method is dead simple. You start with a landscape made out of very rough triangles, big ones. And then for each triangle, break it into, into four triangles. And then do that again, and then again and again and again.

NARRATOR: Endless repetition—what mathematicians call iteration—it's one of the keys to fractal geometry.