This article is from the sci.fractals FAQ, by Michael C. Taylor and Jean-Pierre Louvet with numerous contributions by others.
They are a Fractint fractal and are similar to fractal
mountains. Instead of a 2-d table of heights, the result is a 2-d
table of intensities. They are formed by repeatedly subdividing
Robert Cahalan has fractal information about Earth's Clouds including
how they differ from plasma clouds.
Fractal Clouds Reference by Robert F. Cahalan
Also some plasma-based fractals clouds by John Walker are available.
Fractal generated clouds
The Center for the Computation and Visualization of Geometric
Structures also has some fractal clouds.
Two articles about the fractal nature of Earth's clouds:
1. "Fractal statistics of cloud fields," R. F. Cahalan and J. H.
Joseph, "Mon. Wea.Rev." 117, 261-272, 1989
2. "The albedo of fractal stratocumulus clouds," R. F. Cahalan, W.
Ridgway, W. J. Wiscombe, T. L. Bell and J. B. Snider, "J. Atmos.
Sci." 51, 2434-2455, 1994