In this paper the problem of the fractal dimension of the perimeter of self-organized vortices is investigated. Results from two numerical models (using the quasi geostrophic vorticity equation and the system of barotropic primitive equations, respectively) with initial fields where the total number of initial small-scale vortices is 72, and their intensities and locations are determined stochastically, indicate that the quasi-final kinetic energy fields have a power spectrum of the form E (k) ~ k-_, _ ≈ 1.0, and the fractal dimension of the perimeter of self-organized vortices falls near 4/3. An estimation of the fractal dimension using 77 cloud samples from cloud picture data is shown to be 1.30. The simulated fractal dimension here validates results previously computed based on satellite images (1.35), and is similar to results previously modeled by Large-Eddy-Simulation and indicated by the theory of relative turbulent diffusion.