Nyquist noise in a fractal resistor network

The frequency-dependent impedance between two points separated by a distance r in an infinite fractal resistor network is calculated using general scaling arguments. The thermal noise is then calculated assuming a fluctuation-dissipation theorem. The power spectrum of voltage fluctuations scales as $r^{\mathrm{-}\alpha }$ at low frequencies, where α is the resistance exponent. At high frequencies the spectrum scales as &, where $d_w$ is the random-walk exponent. This disagrees with a recent calculation by Rammal, but implicitly agrees with other theoretical work.