We present new deep, high-resolution, 1.5 GHz observations of the prototypical nearby Perseus galaxy cluster from the Karl G. Jansky Very Large Array. We isolate for the first time the complete tail of radio emission of the bent-jet radio galaxy NGC 1272, which had been previously mistaken to be part of the radio mini-halo. The possibility that diffuse radio galaxy emission contributes to mini-halo emission may be a general phenomenon in relaxed cool-core clusters, and should be explored. The collimated jets of NGC 1272 initially bend to the west, and then transition eastward into faint, 60 kpc long extensions with eddy-like structures and filaments. We suggest interpretations for these structures that involve bulk motions of intracluster gas, the galaxy's orbit in the cluster including projection effects, and the passage of the galaxy through a sloshing cold front. Instabilities and turbulence created at the surface of this cold front and in the turbulent wake of the infalling host galaxy most likely play a role in the formation of the observed structures. We also discover a series of faint rings, southeast of NGC 1272, which are a type of structure that has never been seen before in galaxy clusters.