Abstract
Recent observations have indicated that magnetic field elements are distributed on the Sun in fractal patterns with dimension D < 2. We suggest that the transport of magnetic field elements across the solar surface should be treated as diffusion on a fractal geometry. We review a semi-analytical, theoretical treatment of fractal diffusion. Comparison with observations of small-scale motions of solar magnetic flux concentrations indicates that fractal diffusion may be taking place with dimension in the range 1.3 to 1.8. It is shown that, compared to the predictions that would be made for two-dimensional diffusion, fractal diffusion in this range would lead to an increased level of in situ flux cancellation in decaying active regions by 7% to 35%. Other work in specialities outside of solar physics may be useful in explaining solar magnetic phenomena.
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