Based on a stratification of quartics by the Betti table of their apolar ideal, I will discuss waring rank and cactus rank on quarternary quartics, their varieties of sums of powers, and to what extent these apolar ideals are artinian reductions of arithmetic Gorenstein varieties. This is a report on a collaboration with Grzegorz and Michal Kapustka, Hal Schenk, Mike Stillman and Beihui Yuan.