Abstract: There is a niche body of work on limiting shapes, i.e., asymptotic Newton polyhedra, of symbolic generic initial systems considered for polynomial rings in characteristic zero (e.g., by my academic sister Sarah Mayes-Tang, and separately by Dumnicki, Szemberg, Szpond, and Tutaj-Gasinska, a quartet of Polish mathematicians). In particular, in one joint paper the latter four authors compute the limiting shape for ideals defining zero-dimensional star configurations in projective space--star configurations turn out to be a steady source of a lot of interesting "ALGECOM" phenomenology. In this talk, we discuss work-in-progress to generalize their computation to the case of ideals defining zero-dimensional configurations in projective space determined by hypersurfaces of a common fixed degree. Along the way, we draw connections to a 2015 investigation (published in Transactions of the AMS in 2017) of select homological and asymptotic properties of hypersurface and matroidal configurations by Geramita, Harbourne, Migliore, and Nagel. I'll aim to close the talk by indicating how we might see--or "hear"--select asymptotic numerical invariants in the limiting shape: Waldschmidt constants, asymptotic Castelnuovo-Mumford regularity, and resurgences for homogeneous polynomial ideals