It was astonishing when at one point, I got the idea of how to make artifical clouds with a collaborator, we had pictures made which were theoretically completely artificial pictures based upon that one very simple idea. And this picture everybody views as being clouds.

One of the high points of my life was when I suddenly realized that this dream I had in my late adolescence of combining pure mathematics, very pure mathematics with very hard things which had been long a nuisance to scientists and to engineers, that this combination was possible and I put together this new geometry of nature, the fractal geometry of nature.

If you assume continuity, you can open the well-stocked mathematical toolkit of continuous functions and differential equations, the saws and hammers of engineering and physics for the past two centuries (and the foreseeable future).

I claim that many patterns of Nature are so irregular and fragmented, that, compared with Euclid - a term used in this work to denote all of standard geometry - Nature exhibits not simply a higher degree but an altogether different level of complexity ... The existence of these patterns challenges us to study these forms that Euclid leaves aside as being "formless," to investigate the morphology of the "amorphous."

Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently.

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.

Although computer memory is no longer expensive, there's always a finite size buffer somewhere. When a big piece of news arrives, everybody sends a message to everybody else, and the buffer fills