Animations 1 and 2 show the effect of inclination on the s₄ moment signature of a peanut-shaped bulge in two simulations (referred to as B1 and B3 in Debattista, et al. 2005). In each case only a single time snapshot is used and this is projected onto the sky plane as indicated at the top. Both simulations include a classical bulge such as would form via mergers. Model B1 did not form a peanut while a strong peanut formed in model B3.

In model B1, the system has no peanut and s₄ does not show the characteristic double minimum along the bar's major axis up to an inclination of 30°. Negative s₄ on the bar major axis occurs for some orientations, but this is not a signature of a peanut. At an inclination of 40° with the bar close to the minor axis, shallow minima in s₄ unrelated to a peanut are evident. At the same inclination, when the bar is close to the major axis, the s₄ diagnostic is still viable.

In model B3, the peanut is evident as a prominent double minimum in s₄ along the major axis of the bar. As the inclination increases, the double minima become unequal as the bar's orientation approaches the minor axis, but can still be recognized. At an inclination of 40°, the peanut can no longer be recognized when the bar is close to the disk's minor axis, although it can when the bar is close to the major axis.

Animation 3 shows the buckling of a bar. The animation consists of four panels with time indicated at bottom right. The top right panel shows the system face-on as seen in the observer's frame. The bottom left (main) panel shows the system face-on in the bar's rest frame. The contours show the density while colors indicate the mean height of particles, with 0.05 being the rms thickness of the initial system. The top left and bottom right panels show the edge-on views, side-on and end-on, respectively. The side on view develops a clear peanut shape after buckling and the end-on view shows the extent to which the center thickens. The animation starts shortly after the bar forms and shows three strong episodes of bending. The paper describing this simulation is Debattista, et al. (2006).

Animation 4 shows an unpublished disk+(classical) bulge system seen from different positions.

Animation 5 shows the non-rigid rotation of nuclear bars inside a large scale bar. The paper describing this simulation is Debattista & Shen (2007).