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."

I went to the computer and tried to experiment. I introduced a very high level of experiment in very pure mathematics.

The straight line has a property of self-similarity. Each piece of the straight line is the same as the whole line when used to a big or small extent.

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.

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

When people ask me what's my field? I say, on one hand, a fractalist. Perhaps the only one, the only full-time one.

The beauty of what I happened by extraordinary chance to put together is that nobody would have believed that this is possible, and certainly I didn't expect that it was possible. I just moved from step to step to step.