The existence of these patterns [fractals] challenges us to study forms that Euclid leaves aside as being formless, to investigate the morphology of the amorphous. Mathematicians have disdained this challenge, however, and have increasingly chosen to flee from nature by devising theories unrelated to anything we can see or feel.

Think not of what you see, but what it took to produce what you see.

The straight line has a property of self-similarity. Each piece of the straight line is the same as the whole line when used to a big or small extent.

If one takes the kinds of risks which I took, which are colossal, but taking risks, I was rewarded by being able to contribute in a very substantial fashion to a variety of fields. I was able to reawaken and solve some very old problems.

I had very, very little training in taking an exam to determine a scientist's life in France.

The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.

The theory of chaos and theory of fractals are separate, but have very strong intersections. That is one part of chaos theory is geometrically expressed by fractal shapes.