Fractal Structures Driven by Self-Gravity: Molecular clouds and the Universe

In the interstellar medium, as well as in the Universe, large density fluctuations are observed, that obey power-law density distributions and correlation functions. These structures are hierarchical, chaotic, turbulent, but are also self-organizing. The apparent disorder is not random noise, but can be described by a fractal, with a deterministic fractal dimension. We discuss the theories advanced to describe these fractal structures, and in particular a new theory of the self-gravity thermodynamics, that could explain their existence, and predict their fractal dimension. The media obeying scaling laws can be considered critical, as in second order phase transitions for instance.