Does anyone know anything about fractals and specifically, the Haussdorff dimension and measure?

I'm going to write a small paper about this and I know the definition of the Haussdorff measure, but I would like some examples to learn from.

The Haussdorff dimension is a dimension defined so that the dimension of a set doesn't have to be an integer, for example the dimension of fractals often is of the form log(a)/log(b).