If you look at coastlines, if you look at that them from far away, from an airplane, well, you don't see details, you see a certain complication. When you come closer, the complication becomes more local, but again continues. And come closer and closer and closer, the coastline becomes longer and longer and longer because it has more detail entering in.

Now that I near 80, I realize with wistful pleasure that on many occasions I was 10, 20, 40, even 50 years ahead of my time.

I had many books and I had dreams of all kinds. Dreams in which were in a certain sense, how to say, easy to make because the near future was always extremely threatening.

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).

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

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.

Self-similarity is a dull subject because you are used to very familiar shapes. But that is not the case. Now many shapes which are self-similar again, the same seen from close by and far away, and which are far from being straight or plane or solid.