The limiting case, as n goes to infinity, has all points except for the boundary points equal to the average of the boundary values in harmonic functions. If we subtract a (zero-energy) constant function to make the average zero, then the level one energy, and hence all energies, is equal to the l^2 ("little L 2") measure of the function evaluated at the boundary points. The main problem with this measure is that it is not self-similar. We can't take energy at one level and write it as a weighted sum of energies at more refined levels.