Everybody in mathematics had given up for 100 years or 200 years the idea that you could from pictures, from looking at pictures, find new ideas. That was the case long ago in the Middle Ages, in the Renaissance, in later periods, but then mathematicians had become very abstract.

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.

Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline or a tree.

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

I didn't want to become a pure mathematician, as a matter of fact, my uncle was one, so I knew what the pure mathematician was and I did not want to be a pure - I wanted to do something different.

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.

I conceived, developed and applied in many areas a new geometry of nature, which finds order in chaotic shapes and processes. It grew without a name until 1975, when I coined a new word to denote it, fractal geometry, from the Latin word for irregular and broken up, fractus. Today you might say that, until fractal geometry became organized, my life had followed a fractal orbit.