Google is giving props to chaos math today. they did an excellent job constructing their logo:
not only do they give the equation for the images they’re using… They even name the pic “Julia” when they could have gotten away with the more well known “Mandelbrot”. The equation they give is “Z=Z^2+C”. the subscript under the first “Z” indicates that this is an iterated equation. anyways, that eqation is what generates the Mandelbrot fractal. A Julia fractal is a similar image that is basically the inverse of the mandelbrot fractal at any given point (more specifically, for any value of C). The best way I can describe it is that you could “click” anywhere on the Mandelbrot fractal and get an image that’s quasi-similar to the original image. every point will generate a slightly different image.
One of the neat things about fractals is that they have infinite resolution. Given a computer with sufficient computing power, it could be zoomed in upon infinitely. the “chaos” comes in at the border between the frilly exterior, and the less exciting single-colored interior. the closer you zoom into the border between the two regions, the more complex the border gets. you can never actually see where the two regions meet. there’s no clear line no matter how far in you look.
The Mandelbrot set became fairly well popularized some time ago. The Julia set is much less well known. which is why it’s pretty cool of them to name the picture Julia instead of Mandelbrot. I guess someone in their ranks is a fractal junkie.
-IggDawg
I’ve got a fistful of fractal renderers on my comp. They’re fun, could never think of anything practical to do with them, besides make shitty Goa album covers, or desktops that give you headaches.
I remember back in the early 90s when just about any electronica album was guaranteed to have fractals of one sort or another on them. God forbid “the scene” would eat up something trendy.
wow, that’s amazing. you know, I used to hate math a couple of years ago but now I think it can be full of mystery, especially when you have to deal with such concepts as chaos in a fractal. crazy.
I used to hate math with the same sort of seething passion known only to religious fanatics. One day I actually found myself doing calculus in my head to figure out something. like, in the real world. so I put my hard-earned apathy aside and actually tried to do well at it.
Chaos math is interesting stuff. If you want a good read on it, pick up “Chaos” by James Gliek. It’s very light on the technical stuff, and gives a wonderful overview of all the different facets of it. it’s pretty cool stuff. and the math is easy :p.
glad i don’t know most of those words 🙂