  Brightest cluster galaxies (BCGs) are usually quiescent, but many exhibit
star formation. Here we exploit the opportunity provided by rest-frame UV
imaging of galaxy clusters in the CLASH (Cluster Lensing and Supernovae with
Hubble) Multi-Cycle Treasury Project to reveal the diversity of UV morphologies
in BCGs and to compare them with recent simulations of the cool, star-forming
gas structures produced by precipitation-driven feedback. All of the CLASH BCGs
are detected in the rest-frame UV (280 nm), regardless of their star-formation
activity, because evolved stellar populations produce a modest amount of UV
light that traces the relatively smooth, symmetric, and centrally peaked
stellar distribution seen in the near infrared. Ultraviolet morphologies among
the BCGs with strong UV excesses exhibit distinctive knots, multiple elongated
clumps, and extended filaments of emission that distinctly differ from the
smooth profiles of the UV-quiet BCGs. These structures, which are similar to
those seen in the few star-forming BCGs observed in the UV at low redshift, are
suggestive of bi-polar streams of clumpy star formation, but not of spiral arms
or large, kpc-scale disks. Based on the number of streams and lack of culprit
companion galaxies, these streams are unlikely to have arisen from multiple
collisions with gas-rich galaxies. These star-forming UV structures are
morphologically similar to the cold-gas structures produced in simulations of
precipitation-driven AGN feedback in which jets uplift low-entropy gas to
greater altitudes, causing it to condense. Unobscured star-formation rates
estimated from CLASH UV images using the Kennicutt relation range up to 80
solar masses per year in the most extended and highly structured systems. The
circumgalactic gas-entropy threshold for star formation in CLASH BCGs at
z~0.2-0.5 is indistinguishable from that for clusters at z < 0.2.
