Pretty simple. The details of the 2d set emerge when we apply different colors to the different iterations. We run into a problem when attempting to do this with a 3d set: we can only directly observe one layer of the 3d set at once, unless we slice it (which is not nearly as cool looking, not that anything I do is cool looking, unless you look at me when I am reallllllly hammered).
So we have to color it in a manner that shows the underlying structure (I could have said underlying mathematical structure... but I didn't). When we see the underlying structure (structure is a hard word to type, at certain periods of time, for various reasons, do not attempt to spell it without help) we.. see the underlying structure. Am I rambling? Yes. But this is not very important. The main point of the matter is this: the (or one of the) 3d Mandelbrot set is known, available, yet unacknowledged due to some esoteric reason that escapes me at the moment... pride? I don't know. Anyways, here is one of the simplest extensions of the Mandelbrot set into 3d, just a quick z^2, that doesn't really demonstrate the potential awesomeness, but will show you the true path to 3d almond bread cookies. (Mandelbrot... one of the best, simple cookie recipes in existence).
There are a lot more like this in another thread in this forum, but as I am not artistically inclined (rather, I am not inclined at all, unless I am on a slope), you might not enjoy it (or they) too much.
October 20, 2006, 06:40:26 PM
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