We generate, both analytically and numerically, artifical, two-dimensional images composed of a known self-similar, and thus multifractal measured with added Gaussian white noise. These are used to interpret observed, line-of-sight, solar magnetic field distributions noisy multifractals. The range of self-similar scaling of observed, distributions is extended beyond that of previous work. Our interpretation of the data is then used to confront theoretical models for the generation of small-scale solar magnetic fields. We investigate the multifractial structure of the field generated by two-dimensional, random cell dynamos and find that self-similarity is relatively enhanced for more intermittent distributions and strong correlations between cells. An optimum value of the intercellular diffusion coefficient maximizes the degree of intermittency. The simulated field from a linear, kinematic, fast dynamo with two-dimensional, chaotic, 'ABC' flow displays scaling properties resembling those of observed solar fields. We suggest that the chaotic element of this model is the crucial ingredient for the long-range correlations that lead to multifractal scaling.
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Cadavid et al. (1994) studied this question.