where Σ has the bounds -1 ≤ Σ ≤ 1, and captures the nature of the anisotropy by a non-zero value. Oblate shapes have Σ < 0 and prolates have Σ > 0. We plot the average prolateness Σ as a function of M bb for a number of values of M sc in Figure (b), and can directly compare to the asphericity observations in Figure (a). There is a similar trend in the overall values, with an approach to spherical Σ → 0 at a similar M bb at the same point as in ∆ and values that approach the linear chain predictions at high M bb . All of the chains exhibit prolate geometries, including the linear chain; the latter is expected from both the theoretical and simulation literature. These established measures of molecular shape provide information that is consistent with experimental observations, and provide further insight by confirming their interpretation. Furthermore, these shape measures provide a quantitative measure to reinforce the observation of individual simulation snapshots; namely, as a bottlebrush backbone increases in length, it transitions from a spherical star-like conformation, to a short cylinder, and finally to a flexible cylinder that exhibits the limiting behavior of a semiflexible coil. This will be useful as the architecture or chemical nature of the brush becomes more complicated, and molecular shapes become more complicated.