For much of my life there was no place where the things I wanted to investigate were of interest to anyone.

A formula can be very simple, and create a universe of bottomless complexity.

Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics

Asking the right questions is as important as answering them

I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and fragmented patterns around us, and leads to full-fledged theories, by identifying a family of shapes I call fractals.

If you look at a shape like a straight line, what's remarkable is that if you look at a straight line from close by, from far away, it is the same; it is a straight line.

I spent half my life, roughly speaking, doing the study of nature in many aspects and half of my life studying completely artificial shapes. And the two are extraordinarily close; in one way both are fractal.