Hello Aaron,
I have not read Peters' work since about 1995 so am not sure what he uses to estimate the fractal dimension. In preparing the above blog post I used several references that were in agreement with the method I described above. However, I have also found other folks using an entirely different method to estimate the fractal dimension. So agreement here is not unanimous.
I think that the important point here is the concept of a fractal dimension. Namely, that the geometry we were taught is not entirely descriptive of real world phenomenon.
I hope this helps!
Jason