2005ApJ...625..849S

The interstellar medium seems to have an underlying fractal structure, which can be characterized through its fractal dimension. However, interstellar clouds are observed as projected two-dimensional images, and the projection of a three-dimensional fractal distorts its measured properties. Here we use simulated fractal clouds to study the relationship between the three-dimensional fractal dimension (D_f) of modeled clouds and the dimension resulting from their projected images. We analyze different fractal dimension estimators: the correlation and mass dimensions of the clouds and the perimeter-based dimension of their boundaries (D_per). We find the functional forms relating D_fwith the projected fractal dimensions, as well as their dependence on the image resolution, which allow us to estimate the ``real'' D_fvalue of a cloud from its projection. The application of these results to Orion A indicates in a self-consistent way that 2.5≲D_f≲2.7 for this molecular cloud, a value higher than the result D_per+1≃2.3 sometimes assumed in the literature for interstellar clouds.