Remembering the inventor of fractal geometry

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LISA MULLINS: Mathematician Benoit Mandelbrot died last week in Cambridge, Massachusetts. He was 85 years old. He was born in Poland, but his family fled to France in 1936. Later he came to the United States to study and conduct his research. Mandelbrot was a maverick mathematician. He challenged conventional math wisdom by developing a whole new way of measuring things that other academics deemed un-measurable. Peter Tyson is the editor in chief of NOVA Online.

PETER TYSON: We all learn Euclidean, that is classical, mathematics in school. And that deals with lines, circles, all of the things in a human environment that have straight lines that are very smooth. And what Mandelbrot discovered was that rough things like trees and clouds and coastlines can actually be measured using a new kind of mathematics called fractal geometry.

MULLINS: Now this is something that had eluded mathematicians for millennia basically. He's the one who said, see that craggy coastline, I can measure that using fractals. How do you define fractals?

TYSON: Fractals are � I found the best definition was really that it's somewhere between two and three dimensions. And the rougher something is, the higher its fractal dimension.

MULLINS: The rougher it is, the higher the fractal dimension? So, for instance, a cloud, I mean would that be considered rough?

TYSON: That would be considered rough and fractal. And a coastline is very fractal. Mathematicians before Mandelbrot would say that you couldn't measure a coastline because it all depends on your yardstick. Mandelbrot said you can actually measure it through its roughness. And this became a very precise way of measuring things like clouds and coastlines.

MULLINS: And so what did it make possible then, this discovery of fractal geometry?

TYSON: Well, it's informed all kinds of different scientific fields. Engineering, medicine. There's apparently a new kind of concrete that's designed using fractals. The sound barriers you see along the highway, they are apparently fractally designed. Antennas in your cell phone, those are fractal.

MULLINS: Those are fractal? They don't look rough, but you're saying they're based on fractal design that he identified?

TYSON: He didn't identify them, but somebody else did, realizing that antennas in cell phones could only get so small, but once they because fractal, in other words they started to bend the antenna in a certain way, they could not only make the antenna much smaller, but they could open it up to much wider band frequencies.

MULLINS: By the way, you're talking about things that have been manufactured, but does nature favor rough over smooth?

TYSON: Nature certainly seems to favor rough over smooth. We all say, there's not straight lines in nature and the fact is when you look at a cloud, a tree, these are all very rough, and yet measurable as Mandelbrot showed.

MULLINS: Well, in terms of what Mandelbrot has left us, one thing is the term called the Mandelbrot Set. What is that?

TYSON: The Mandelbrot Set kind of looks like the Michelin man tipped over, but it's an iconic image of a fractal that if you zoom in on it over and over again you see something that is distinctive of fractals, which is something called self-similarity, where the more you zoom in on this fractal, you see similar features that are exactly the same only smaller. And nature itself operates that way. Think of a fern and how the frond get ever smaller, but they still look largely the same.

MULLINS: And so in terms of the images that we see, and we should say that there are some posted on your website, the NOVA website, and we'll make a link through ours, TheWorld.org, but where do these images, some of which look very psychedelic, where do they fit in to fractal geometry?

TYSON: Well, I think they're made using fractal geometry, but now that you find them just everywhere, you type in �fractal� on the internet and look at images, and you'll see a million images that have come up of fractals. And these all arise because of Benoit Mandelbrot.

MULLINS: And you met him or at least talked to him on the phone, I guess, once.

TYSON: Yes, he once called me to make sure that I had received changed that he'd made to an interview I'd edited for our website. And I thought at the time, my God, I'm talking to an absolute icon here. And later he said, you know, since we both live in Cambridge, I hope we can meet one day. Unfortunately, that's no longer possible. I regret that. He was a great man.

MULLINS: Alright. Benoit Mandelbrot who died last week at the age of 85 in Cambridge, Massachusetts. Thanks very much for talking to us about him. Peter Tyson, editor in chief at NOVA online. Thanks Peter.

TYSON: You're welcome, Lisa.

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