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.

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.

A cloud is made of billows upon billows upon billows that look like clouds. As you come closer to a cloud you don't get something smooth, but irregularities at a smaller scale.

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.

When the weather changes and hurricanes hit, nobody believes that the laws of physics have changed. Similarly, I don't believe that when the stock market goes into terrible gyrations its rules have changed. It's the same stock market with the same mechanisms and the same people.

I had many books and I had dreams of all kinds. Dreams in which were in a certain sense, how to say, easy to make because the near future was always extremely threatening.