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We study the distribution of stars, HII regions, molecular gas, andindividual giant molecular clouds in M33 over a wide range of spatial scales.The clustering strength of these components is systematically estimated throughthe fractal dimension. We find scale-free behavior at small spatial scales anda transition to a larger correlation dimension (consistent with a nearlyuniform distribution) at larger scales. The transition region lies in the range500-1000 pc. This transition defines a characteristic size that separates theregime of small-scale turbulent motion from that of large-scale galacticdynamics. At small spatial scales, bright young stars and molecular gas aredistributed with nearly the same three-dimensional fractal dimension (Df <=1.9), whereas fainter stars and HII regions exhibit higher values (Df =2.2-2.5). Our results indicate that the interstellar medium in M33 is onaverage more fragmented and irregular than in the Milky Way.

The fractal dimension of star-forming regions at different spatial scales in M33