Observations show that molecular clouds in the interstellar medium are fractals with a dimensionality close to 2.35. A model for the formation of clouds from “cloudlets” ejected from stars is examined in this paper. It is shown that the motion of cloudlets in the interstellar medium is described by a model of generalized brownian motion, so that the resulting clouds should have a fractal structure. We examine the hypothesis that the fractal dimensionality of a cloud is completely determined by the way the mass of the cloudlets varies. The generalized brownian motion of an ensemble of particles is described as a random process with a time dependent parameter. The relationship among the growth of the cloudlet mass, the properties of the process by which the cloudlets move, and the fractal dimensionality of the structures resulting from this process is examined. It is shown that the fractal dimensionality of the formed clouds corresponds to the “natural” aggregation of mass assuming random cloudlet collisions.