Being a language, mathematics may be used not only to inform but also, among other things, to seduce.

Nobody will deny that there is at least some roughness everywhere

Both 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.

Everything is roughness, except for the circles. How many circles are there in nature? Very, very few. The straight lines. Very shapes are very, very smooth. But geometry had laid them aside because they were too complicated.

Some mathematicians didn't even perceive of the possibility of a picture being helpful. To the contrary, I went into an orgy of looking at pictures by the hundreds; the machines became a little bit better.

A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales...

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.