Show how things have shifted throughout a given period. This would be really nice to combine with a line chart that gets drawn bit by bit. This data would tell a story. Also allow pausing/resuming at any given moment with a button or spacebar. For example, the play/pause button could be shown between the prev/next buttons.
Thanks @christiangebel for the idea!
One way to implement this could be to press and hold the prev/next buttons. The functionality would be quite hidden, but it would make the UI minimalistic visually simple.