and the density in the model distribution continues to drop below this value. []{data-label="DensitySlices"}](f1b.png){width="50.00000%"}

Initial gas configuration - clumpy models {#ClumpySetup}
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It has long been predicted on theoretical grounds that the dusty gas surrounding an accreting SMBH will not be smoothly distributed, but will instead form clumps [@Krolik1988]. This prediction has been supported by observations such as the variability of x-ray absorbing column densities in type 2 Seyferts [@Risaliti2002] as well as IR spectroscopy [@Mason2006; @Honig2010a; @Deo2011]. A vast literature exists concerning radiative transfer through clumpy torus models, with many prescriptions for generating clumpy density distributions from an underlying smooth density model and comparing the results to observations [@Nenkova2002; @Elitzur2004; @Honig2006; @Schartmann2008; @Stalevski2012; @Heymann2012].

Our method for generating the clumpy gas distributions most closely resembles those of @Honig2006 and @Schartmann2008. We use a three dimensional grid and spherical-polar $(r,\theta, \phi)$ coordinates, with logarithmic spacing in the radial coordinate and linear spacing in the angular coordinates. Our resolution is 128 radial zones, 96 $\theta$ zones for all $\theta$ ranging between $0$ and $\pi$, and 192 $\phi$ zones for all $\phi$ ranging from $0$ to $2 \pi$. The density of each clump in a given simulation is the same, and a 