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In my computational physics class we just learned about the correlation dimension. I know how to compute it, but don't quite know what it means.

I learned roughly that the correlation dimension of something is a measure of how well it covers the space, but I'm not too clear on the details.

For example, if I have a two dimensional space, and a plot with a correlation dimension of say 1.5, what does that mean? How about if it were 0.5? Does the meaning change if you are considering an infinite space, or a finite one? You can't have a correlation dimension higher than the dimension of the space you are in, right?

I need to learn this because our next assignment is all about correlation dimension, and I'd like to know what it is I'm computing, rather than just putting numbers in a formula (or writing a program to put numbers in a formula).

Thank you guys in advance for your help.