An extraordinary amount of arrogance is present in any claim of having been the first in inventing something.

Engineering is too important to wait for science.

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.

Asking the right questions is as important as answering them

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

Some mathematicians didn't even perceive of the possibility of a picture being helpful. To the contrary, I went into an orgy of looking at pictures by the hundreds; the machines became a little bit better.