Anomalous diffusion of magnetic elements across the solar surface

Results are presented of observations of the random walks of concentrations of magnetic flux on the solar surface, giving a natural, macroscopic realization of anomalous diffusion with fractal dimension D = 1.56 +/- 0.08 and exponent of anomalous diffusion theta = 0.25 +/- 0.40. The results indicate that the random walk of magnetic flux in the solar photosphere is non-Euclidian and not two-dimensional diffusion. The results are entirely consistent with results from percolation theory for diffusion on clusters at a density below the percolation threshold.