I'd said before that weather was simple. And then said it wasn't. So that needs clarifying. Weather is, in a word, complex. Scientists have been working out ways to predict the weather for a looong time. And a pioneer of this field was a guy named Edward Lorenz. He started out trying to find patterns in meteorological data. As Lorenz studied weather patterns he began to realize that the weather did not always change as predicted. Minute variations in the initial values of variables in his twelve variable computer weather model would result in grossly divergent weather patterns. And that's only (yes, only) twelve variables. The man wasn't even close to predicting weather (Man still isn't). Instead, for all his effort, he got a graph that looks like this :
That is a part of the foundation of a subject now popularly known as chaos theory (At this point, the author would like you to understand that he has no idea what chaos theory is. He only rather fancies the Mandelbrot set, which he shall talk about in a bit). Chaos theory is the study of dynamical systems that are very sensitive to initial conditions. They never (ever ever) reach a steady state. Basically, there's no random element. Any state of the system can be calculated from the initial conditions, but the differences caused by a slight change in these conditions cause the system to change so wildly (exponentially) that it gives an appearance of chaos. This state is known as deterministic chaos.
Later on, another mathematician working in the field of dynamics came up with the Mandelbrot set. That man, was Benoit Mandelbrot. And this is the Mandelbrot Set :
Its what they call a fractal. It's not really related to the chaos theory anymore, but it was once. The beauty of this fella here is that it's the graph of a simple function. The brilliance is in the fact that the graph is infinitely complex. You can keep zooming in, and you'll keep finding beautiful patterns...
Well. Ya. We started with weather. But the idea was to come to the Mandelbrot set eventually... Beautiful isn't it?