We present a multiwavelength morphological analysis of star forming clouds and filaments in the central ($< 50$ kpc) regions of 16 low redshift ($z<0.3$) cool core brightest cluster galaxies (BCGs). New Hubble Space Telescope (HST) imaging of far ultraviolet continuum emission from young ($sim 10$ Myr), massive ($> 5$ Msol) stars reveals filamentary and clumpy morphologies, which we quantify by means of structural indices. The FUV data are compared with X-ray, Ly$alpha$, narrowband H$alpha$, broadband optical/IR, and radio maps, providing a high spatial resolution atlas of star formation locales relative to the ambient hot ($sim10^{7-8}$ K) and warm ionised ($sim 10^4$ K) gas phases, as well as the old stellar population and radio-bright AGN outflows. Nearly half of the sample possesses kpc-scale filaments that, in projection, extend toward and around radio lobes and/or X-ray cavities. These filaments may have been uplifted by the propagating jet or buoyant X-ray bubble, or may have formed {it in situ} by cloud collapse at the interface of a radio lobe or rapid cooling in a cavitys compressed shell. The morphological diversity of nearly the entire FUV sample is reproduced by recent hydrodynamical simulations in which the AGN powers a self-regulating rain of thermally unstable star forming clouds that precipitate from the hot atmosphere. In this model, precipitation triggers where the cooling-to- freefall time ratio is $t_{mathrm{cool}}/t_{mathrm{ff}}sim 10$. This condition is roughly met at the maxmial projected FUV radius for more than half of our sample, and clustering about this ratio is stronger for sources with higher star formation rates.
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