Anna Baron wrote: I'm curious to discover a really good explanation, in layman's terms, of what a *fractal* is - just a couple of sentences and no technical jargon. I don't know much about fractals myself: all I do is play around with Fractint a bit but formulas are a mystery to me. I've occasionally been asked what on earth these fractals are that grab part of my time, and I'm aware that whatever brief answer I've come up with was far from enlightening. I've no doubt any of you could do much better so I'd love to hear if anyone has a particularly good definition up his sleeve. (end of quotation) Dear reader, hallo Anna (this is a little bit more as a few sentences, I'm afraid) If you still think (have the feeling) you don't know what fractals are, maybe this will help you (and others): Did you ever make a description (definition) of a chair? Well, let's try: A thing you can sit on (but there are so many things you can sit on), with legs (but there are many chairs with no legs at all). Well, a new try: a thing, made with the intention to sit on (that exclude a horse for instance), often with legs, not too big, normally just only one person can sit on it (that excludes sofas and things like that). But how to exclude stools?.... You see, it is not easy and I think quit impossible to give a description of a chair in such a way you can always decide of a thing is a chair or not. Nevertheless, if I show you a chair, even if it is in the form of a z or such a plastic inflatable thing, you will say: "that's a chair" and if you are in a cafe and someone says let's sit down on a stool, you walk to a stool, not to one of the chairs. So you know perfectly what a chair is. Why is that so. I think because you have seen so many chairs and so often people who were with you have named things a chair. Because you have played a lot with fractint you have seen a lot of fractals, so you, for sure have a pretty good idea what fractals are. And if someone ask you: what are fractals? A description of what you have seen, for instance: pictures, which are very complex, abstract, colorful, often strange, sometimes beautiful, and with an incredible lots of details, so many that if you enlarges small parts of it you see new details, etc. , is really perfect. Remember that you are in the same situation as when someone ask you to give a description of a chair. Imagine you have to do that to a person who never saw a chair in his life. And: you can always end with: "if you really want to know, what fractals are, come with me and I show you some. But, Maybe you think: "but fractals are mathematical object. And you can describe (define) mathematical things exactly, with no ambiquity, can you?" I don't dare to give a yes or no on this question. For the moment let's look to the mathematical objects called fractals. As far as I know there is no definition of a fractal on which the "math society" agrees. I think it's far too early for that. But it's possible you find a definition in a (math) textbook and if you find several in different math textbooks they can be quite different. But those definitions (those made already and those from the future) will definitely not be about pictures, because (mathematical) fractals are NOT pictures and I never have seen such a thing and neither have you! Before you are going to think: "he's mad", please read on. To explain things, let's take a simple mathematical object: a square. If I gave you a piece of paper, a pair of scissors and something like a ruler and ask you to make a square, I'm sure you will make one. And I'm also sure that you know it must have straight parallel edges, and 4 angles of 90 degree. So look at your paper square. Are your edges really straight? Put them under a microscope. Do you see straight edges then? And your angles are they 90 degrees or maybe 89,9 degrees. And your square, is your paper flat? No. Your paper square is not a (mathematical) square. It is an image, a representation of a mental object, the mathematical square. And the nearer your angles are 90 degrees, how more flat your paper, etc. the better is your representation of a square. Nevertheless, people and also mathematicians will call you paper square a square. I suppose that all mathsman will realize that it's mere a representation, let's say a model of a mental mathematical object called square in much the same way that a picture of the Eiffeltower is not the Eifeltower itself. Well, with fractals it's the same. The pictures are models of mathematical objects called fractals. A very small model of the Eifeltower doesn't reveal many details, so we can say it's a poor model. A bigger and maybe better made drawings show more and more precise details, so that's a better model. In the same way there are pictures representing better or less good fractals. But I think all representations are very poor, because of the extreme complexity of the mental object "fractals". Even if you expand a picture of a fractal to one as big as the universe there still are details not visible. But the pictures of fractals are not only very poor, the situation is ever more bad. To explain that I must say something about how a picture of a fractal (at least with the most important method) is created. If you make a picture of the Eifeltower, you can do that not by coloring the Eifeltower itself, but by coloring what's around it. Most of the time that's the way fractals are created. The surroundings of what actually is (the representation) of the fractal are colored. Normally there is some rule so that a lot of colors are used. The coloring is in such a way that it "reflect" somehow the complexity of the fractal itself. So the surroundings of the fractal gives also complicated drawings. Now with a lot of drawings people call fractals two things are possible: The (representations) of the fractals exist of such small parts, that you only see "surrounding", or the drawing is actually only a part of the surroundings and no part of the fractal is in it. Honestly spoken I don't think those last examples has very much to do with (representations) of fractals, but never mind I think it's perfectly ok to call practically all images you create with fractint Fractals! There is much more to say about "what is a fractal". But if I go on I will need some math, although quite simple math. Then I would give some examples of (mathematical) fractals and how they are built. I think that's a good way to learn what fractals are (remember how you have learned what chairs are and witch things aren't.) P.s. I'm Dutchman, living in France, trying to write English. So don't blame me for mistakes, and for parts of the text, which are somewhat awkward. Thanks for reading, cheers jos hendriks