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Re:Procedural Building Generation in Unreal Engine 3 by jacques_chester on Monday December 13, 2010 @12:37AM (#1999480)
> 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?

This is (I think) the "coastline paradox": coast lines have different lengths depending on scale. Length grows with resolution, so in a sense the length of a coastline can be infinite.

I think the escape hatch is that the information conveyed is not the points on the screen, but the rule on how to generate those points. Going back to my other post this means that the city builder conveys no information about a particular city map.

Re:Procedural Building Generation in Unreal Engine 3 by partition on Monday December 13, 2010 @01:12AM (#1999563)
> I think the escape hatch is that the information conveyed is not the points on the screen, but the rule on how to generate those points. Going back to my other post this means that the city builder conveys no information about a particular city map.

Yep. The amount of information conveyed can be considered 'equivalent' to the length of the shortest algorithm used to get from one string to the other.

The field that is concerned about thinking about this problem in a disciplined manner is algorithmic information theory:

http://en.wikipedia.org/wiki/Algorithmic_information_theory

In particular, they show that the quantity is incomputable (the Komolgorov complexity).