Increasing erosion of the anode wall of a single-cathode F4 torch changes the fluctuation pattern of the plasma jet. Trajectories and temperature history of particles injected into the plasma become accordingly modified. In this work such fluctuations are characterised through spectral analysis of the torch voltage as well as of the light intensity of the jet outside the torch. Instead of considering the evolution of the main peaks in the frequency spectrum for both voltage and optical signals, the variation with increasing torch wear of the spectrum’s higher frequency fraction (above 20kHz) is focused on. The evolution of the fractal dimension in this high frequency range exhibits a reliable correlation with the erosion of the anode wall. This is confirmed further by the development of a simple stochastic model for the motion of the arc root along the anode wall. This model yields, depending on the probability for a pronounced arc root jump, a fractal dimension and an evolution just within the range observed in the measurements. Additionally, tracking the fluctuations at different locations outside the torch enables the isolation of the fluctuation dissipation due to jet viscosity and velocity.