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.