After the story of z²+c proved to be so fruitful, it was natural for many people to go to study of z³+c or other such transformations. It turned out to be extraordinarily more complicated, not just a little more complicated, and what was so striking in the study of these simple transformations is that you had a stage that was totally elementary; a stage which is, how should I say, was very rich, but you could grasp it; and then - a total unknown. There is an image that I use for that purpose, which I think makes the point. In most sciences there's a core that is very simple, at least very simple to write. Anybody can understand gravitation, F = ^Gm₁m₂/_r², it's a formula that is very simple. As you go out and out and out it becomes more and more complicated. As you continue to go out it becomes more complicated again, more technical. But there's a big domain around the formula in which one doesn't encounter impossible difficulties. The study of fractals, of chaos in general - and I will say in a minute how it relates to chaos - is more like the situation of a very branching structure. There is a core that is very simple, which children can understand, which anybody can copy and implement, but in order to continue doing something doable you must follow a finger. If you go in a natural direction looking at natural questions, most likely you'll get into an abyss, which means some things that are extraordinarily difficult. Difficulty does not increase gradually as you go away from the simple core. And that is true of fractals in general. It's illegitimate as you look at the parts of fractal geometry that were written down for children to believe it's an easy subject, because the main constructions are like playing, the main early results are like play, and in general there's almost no effort needed to obtain them, or so it seems. Then people say it's an easy subject; it's far from true. If you follow very peculiar lines you again find easy considerations, but if you follow a natural line, which was a matter, for example, of the structure of the boundary of the Mandelbrot set, you very rapidly find things, which are beyond the most refined techniques we have.