I'm not sure I quite understand why systems with fractal systems show power-law behavior. My "gut" understanding is that the power-law index indicates the correct scaling factor for the system so that the original and scaled systems look "similar", and is indicative of the fractal dimension of the system. I'm still having difficulty seeing this physically; is there a good physical explanation of why fractal systems show power-law scaling? For example, in the famous coastline of Britain measurement, why does decreasing the length scale of my 'ruler' increase length as a power-law, and not say exponential, or some other crazy function? What is so special or universal about the power-law behavior ?