In the ipsocentric formulation of the response of a molecular charge cloud to an external magnetic field, each point is taken as its own gauge origin. Orbital contributions to induced current density can then be defined in both localized and delocalized pictures of electronic structure, and the mapping of these contributions exposes a physical criterion for the localizability of orbitals. It is found that intrinsically localized orbitals support local, closed-loop circulations, whereas attempts to impose localization on intrinsically delocalized orbitals yield unphysical, open-ended flowlines. This distinction is illustrated by current density maps for benzene, naphthalene, anthracene, tetracene, coronene, pyracylene, and borazine computed at the ab initio, coupled Hartree-Fock, CTOCD-DZ (continuous transformation of origin-diamagnetic zero) level. The computed maps recover the chemical intuition of a polycyclic aromatic hydrocarbon as comprising an intrinsically delocalized pi-system atop a localized a-valence system. When maximal localization is enforced, the local forms of pi orbitals in the hydrocarbons all display open flowlines that build up into complex global patterns such as the counter-rotating ring currents in circulenes and the leaky perimeter circulations of the linear acenes. In contrast, the pi system of borazine displays islands of closed circulation and is well represented by localized orbitals.