Want to Paint Perfect Clouds? Use Math

The father of fractal geometry marvels that his work has led to computer renderings of natural shapes that are indistinguishable from the real thing.
  • Transcript


Question: How has computer technology impacted your work?

Benoit Mandelbrot: Well, the computer had been sort of spoken about since the early 19th century, even before.  But until the electronic computers came, which was in reality during World War II, or shortly afterwards.  They could not be used for any purpose in science.  They were just too slow, too limited in their capacity.  My chance was that I was myself a very visual person.  Again, a mathematician who had started a very unconventional career because my interest was both mathematics and in the eye.  And with IBM very primitive picture-making machines became available and we had to program everything.  It was heroic.  And my friends at IBM who helped me deserve a great thank you.  With these two, I could begin to do things which before had been impossible.  I could begin to implement an idea of how a mountain looked like.  To reduce a mountain, which is something most complicated to a very simple idea – how do you do it?  Well you make a conjecture, have positives about shapes of mountains, and you don’t think about the mathematics of it, you must make a picture of it. 

If the picture is – everybody to be a mountain, then there’s something true about it.  Or a cloud.  It was astonishing when at one point, I got the idea of how to make artifical clouds with a collaborator, we had pictures made which were theoretically completely artificial pictures based upon that one very simple idea.  And this picture everybody views as being clouds.  People don’t believe that they aren’t photographs.  So, we have certainly found something true about nature. 

And on the other side, the completely artificial shapes, the shapes that don’t exist in nature, which, for example, the Mandelbrot set, which was completely came out of the blue out of a very simple formula which is about one inch long and which gives us an endless, endless stream of questions and results.  There what happened is that to everybody’s surprise there’s a very strong inner resemblance between those shapes and the shapes of nature, which I have been studying.  And again, I spent half my life, roughly speaking, doing the study of nature in many aspects and half of my life studying completely artificial shapes.  And the two are extraordinarily close; in one way both are fractal.

Recorded on February 17, 2010
Interviewed by Austin Allen