I think another way of thinking about my original comment would be to imagine that you had an image of the Mandelbrot Set up on your monitor (assume you have drilled down a few times). If you knew the parameters that had generated that view you could write a very concise description suitable for transmission over a network. If you have forgotten the params and had to make due with a screen print saved to jpeg it would appear to contain more 'information'. Not only would the algorithmic version be shorter (so long as you hadn't drilled down to the point at which the numbers representing the view port had millions of degrees of precision) but you would be able to keep zooming in to view arbitrary detail. That is something you wouldn't be able to do with the jpeg. I guess what I'm driving at is that I don't understand how Information Theory is able to account for things like fractals without saying that either the Mandelbrot Set is random or that it contains infinite information. Am I looking at this problem correctly?