I work with atmospheric dynamics where large thermal upwellings (can be
100m) cause disturbances in the various layers of the atmosphere. These large disturbances create bands of turbulence where two layers move across each other. The turbulence is broken down into ever smaller disturbances according to a cascading power law ~L^-5/3 creating ever smaller disturbances until they reach a few mm and are dissipated as heat. Between the outer and inner scales, they are self-similar and can be considered a fractal population or distribution, i.e., if you look at any range of spatial frequencies between the two limits, the distribution of power in the various sizes of turbulence follows the same poser law. In the atmosphere's case, there are an infinite number of scales between the outer and inner scale.
I've always been partial to fractal clouds and using the law, you can make very realistic fractal clouds, because you are modeling the very nature of the clouds themselves. Marco
According to wikipedia, though, since it seems to contain no dense inner set (maybe it haz just been neatly excluded), it's not a fractal.