Scaling laws in self-gravitating discs

The interstellar medium (ISM) reveals strongly inhomogeneous structures on every scale. These structures do not seem completely random since they obey certain power laws. Larson's (1981) law sigma proportional to R-delta and the plausible assumption of virial equilibrium justify the consideration of fractals as a possible description of the ISM. In the following we investi gate how self-gravitation, differential rotation and dissipation affect the matter distribution in galaxies. To this end we have performed 3D simulati ons for self-gravitating local boxes embedded in a larger disc, extending t he 2D method of Toomre and Kalnajs (1991) and Wisdom and Tremaine (1988). O ur simulations lead to the conclusion that gravitation, shearing and dissip ation can be dominantly responsible for maintaining an inhomogeneous and ev entually a fractal distribution of the matter.