The Law of Common Fate from Gestalt psychology states that visual objects moving with the same velocity along parallel trajectories will be perceived by a human observer as grouped. However, the concept of common fate is much broader than mere velocity; in this paper we explore how common fate results from coordinated changes in luminance and size. We present results from a crowdsourced graphical perception study where we asked workers to make perceptual judgments on a series of trials involving four graphical objects under the influence of conflicting static and dynamic visual factors (position, size and luminance) used in conjunction. Our results yield the following rankings for visual grouping: motion > (dynamic luminance, size, luminance); dynamic size > (dynamic luminance, position); and dynamic luminance > size. We also conducted a follow-up experiment to evaluate the three dynamic visual factors in a more ecologically valid setting, using both a Gapminder-like animated scatterplot and a thematic map of election data. The results indicate that in practice the relative grouping strengths of these factors may depend on various parameters including the visualization characteristics and the underlying data. We discuss design implications for animated transitions in data visualization.