A new geometric framework connecting scale distributions to coverage statistics is employed to analyze level sets arising in turbulence as well as in other phenomena. A 1-D formalism is described and applied to Poisson, lognormal, and power-law statistics. A d-dimensional generalization is also presented. Level sets of 2-D spatial measurements of jet-fluid concentration in turbulent jets are analyzed to compute scale distributions and fractal dimensions. Lognormal statistics are used to model the level sets at inner scales. The results are in accord with data from other turbulent flows.