One couldn't even measure roughness. So, by luck, and by reward for persistence, I did found the theory of roughness, which certainly I didn't expect and expecting to found one would have been pure madness.

My fate has been that what I undertook was fully understood only after the fact.

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.

The Mandelbrot set is the most complex mathematical object known to mankind.

If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.

My life has been extremely complicated. Not by choice at the beginning at all, but later on, I had become used to complication and went on accepting things that other people would have found too difficult to accept.

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