Fractal Networks, Braiding Channels, and Voltage Noise in Intermittently   Flowing Rivers of Quantized Magnetic Flux
  We analyze the microscopic dynamics of vortex motion through channels that form river-like fractal networks in a variety of superconducting samples, and relate it to macroscopic measurable quantities such as the power spectrum. As a function of pinning strength, we calculate the fractal dimension, tortuosity, and the corresponding voltage noise spectrum. Above a certain pinning strength, a remarkable universal drop in both tortuosity and noise power occurs when the vortex motion changes from shifting braiding channels to unbraided channels. We compare our results with experiments. 
C. J. Olson, C. Reichhardt, and Franco Nori