We present a Chandra study of surface brightness fluctuations in the diffuse intracluster medium of the Perseus Cluster. Our study utilizes deep, archival imaging of the cluster core as well as a new mosaic of 29 short $, 5,$-ks observations extending in eight different directions out to radii of $r_{500} sim 2.2, r_{2500}$. Under the assumption that the distribution of densities at a given radius is log-normally distributed, two important quantities can be derived from the width of the log-normal density distribution on a given spatial scale: the density bias, that is equal to the square root of the clumping factor C; and the one-component turbulent velocity, vk,1D. We forward-model all contributions to the measured surface brightness, including astrophysical and particle background components, and account for the Poisson nature of the measured signal. Measuring the distribution of surface brightness fluctuations in 1 arcmin2 regions, spanning the radial range $0.3rm {-}2.2, r_{2500}$ ($7.8rm {-}57.3,$ arcmin), we find a small to moderate average density bias of around $3{{ rm per cent}}$ at radii below $1.6, r_{2500}$. We also infer an average turbulent velocity at these radii of V1D < 400 km s-1. Direct confirmation of our results on turbulent velocities inferred from surface brightness fluctuations should be possible using the X-ray calorimeter spectrometers to be flown aboard the XRISM and Athena observatories.
