Subject-Was: Re: [Fractint] Mentor Needed - OT The most obvious kind of fractals are crystals, like frost. They observe simple rules to arrive at a complex and appealing result (even if programmers aren't required). By simple, I do not mean that it is easy to figure out what those rules are. Instead, I mean that the largest variety of fractal images seem to stem from the use of complex numbers that are composed of a real and an imaginary part. The imaginary part is called that, because it's multiplied by the square root of negative one, which isn't defined. That lack of definition didn't stop mathematicians from defining the arithmetic and trigonometric functions as they apply to complex numbers, though. That's no where near as silly as trying to go to Mars, but I guess that comment belongs in some other group like sci.physics. You should expect complex numbers crop up in subjects like non-linear dynamics, objects of non-integral dimension, and most generally, chaos (which is a much wider topic than fractals). Mathematical or computer art is typically called a fractal, but the numbers involved hav applications in Enjineering and Physics. Perhaps, because they hav a lot of interesting characteristics of the real world in that (to an arbitrary degree that I think someone estimated as the surface area of a sphere bounded by Pluto's distance in double-precision floating point math) they can be magnified and distorted by the lens you apply to them. In FRACTINT, these characteristics of the lens go in the parameter file (mostly). Now, as I said, "Chaos" is wider in scope than "Fractal". It covers things such as a television or FM radio station on an unused channel, the uniformly distributed pseudo-random number jenerators of use to cryptographers and statisticians, spelling errors that hav become rules, keyboard timing, deviance... Michael Barnsley has made some notable applications of fractal theory to imaje and sound compression (also more within the domain of Chaos than Fractals). FRACTINT and FDESIGN use a much less industrial strength version of this technology called Hyperbolic Iterated Function Systems. Theoretically, they can describe anything visual or auditory. Practically, they can achieve ratios of compression that beat JPEG in both quality and size -- but they demand a lot more power. Along similar, but harder to tap, lines of thot, are...lines, or L-systems -- rules that are a bit like the graphics known as turtle graphics. Cellular automata are another kind of graphic where rules are involved instead of equations and parameters. Of course, the ultimate kind of chaos in this context is just diving into a program that you don't understand, and when you're talking about computers today with gigabytes of disk space and megabytes of random access memory that has access to web pages that might number in the quadrillions...NO ONE REALLY UNDERSTANDS ALL THE STUFF ON THEIR COMPUTER, to do injustice to the possibility of understanding what is within reach. F1 is the best mentor you will find in FRACTINT if you don't understand what all the options under the zed key do. Beyond that, if you hav a problem that just doesn't seem to be satisfactorily answered on the web somewhere, there might be the groups this message is in, sci.fractals, and perhaps a few exemplary reading lists from the internet. Any old fractal programmer's wish list, perhaps -- perhaps it's in the library -- perhaps it's buried as a comment on FRACTINT's code like Fermat's Calculus Theorem -- three of his five major theorems hav been proven -- that's one of them, by the way. Now, where did my point go? Oh, yeah, it's at the top of my last paragraph. How silly. What's the usual help key in any DOS program?