If 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.

I went to the computer and tried to experiment. I introduced a very high level of experiment in very pure mathematics.

Self-similarity is a dull subject because you are used to very familiar shapes. But that is not the case. Now many shapes which are self-similar again, the same seen from close by and far away, and which are far from being straight or plane or solid.

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

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

Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.

Beautiful, damn hard, increasingly useful. That's fractals.