Now I took the short path to tell you the story, but let me recount some more episodes. The Julia sets again are self-similar; each part is like any other part, but one of the observations made about the Mandelbrot set was the following: that a small corner of the Mandelbrot set looks in many ways like the Julia sets corresponding to it; therefore the Mandelbrot set included as parts of it reduced scale images of an immense variety of Julia sets; therefore it is not self-similar in that respect. It is self-similar in the sense that the islands are like the continent but slightly deformed; but not in a sense that the way in which the islands are arranged, the kind of strings that link them together are the same; in fact, they're different in every point. Therefore the complication of a set goes beyond fractals. Julia sets are self-similar, they are fractals by every definition and by intuition, except when they are just straight intervals which happens for some cases, in which case they are too simple to be fractal. The Mandelbrot set is a complication which includes a huge number of different fractals in its structure and is therefore beyond any fractal. It is a paradox of sorts that this has become the icon of fractality, whereas it does not fit the definition of the concept at all.