Many painters had a clear idea of what fractals are. Take a French classic painter named Poussin. Now, he painted beautiful landscapes, completely artificial ones, imaginary landscapes. And how did he choose them? Well, he had the balance of trees, of lawns, of houses in the distance. He had a balance of small objects, big objects, big trees in front and his balance of objects at every scale is what gives to Poussin a special feeling.
Benoit MandelbrotI went to the computer and tried to experiment. I introduced a very high level of experiment in very pure mathematics.
Benoit MandelbrotBoth chaos theory and fractal have had contacts in the past when they are both impossible to develop and in a certain sense not ready to be developed.
Benoit MandelbrotPictures were completely eliminated from mathematics; in particular when I was young this happened in a very strong fashion.
Benoit MandelbrotBeing a language, mathematics may be used not only to inform but also, among other things, to seduce.
Benoit MandelbrotIf you look at coastlines, if you look at that them from far away, from an airplane, well, you don't see details, you see a certain complication. When you come closer, the complication becomes more local, but again continues. And come closer and closer and closer, the coastline becomes longer and longer and longer because it has more detail entering in.
Benoit Mandelbrot