Introduction
Movement and implication of movement can improve the ability of readers to identify patterns being displayed but can also damage that ability if not mindfully implemented. Understanding the gestalt principles related to movement and implied movement is critical to well-crafted data visualization. The basic symbols in use throughout these examples are simply lines and circles but how they move and their angle and their visual relationship with each other will produce different visual structures.
Even in charts that don't utilize motion, these principles are important. Graphical primitives such as lines have slope, a sort of visual potential energy, and can mean one kind of relationship in the context of a line chart and a very different kind in the context of a dendrogram or network visualization. Well-designed charts account for unintended disruption of knowledge transmission due to the graphics being interpreted in one way when the chart utilizes them in another.
Common Fate
Of the traditional gestalt principles, common fate stands out because it refers to visual structure apparent in animated graphics. When we see shapes moving, we group together the shapes that are moving in the same direction and speed.
In the case of this example, this signal is accurate. If you examined the code, you'd see there are two groups of circles being called and animated. If it were the case that the movement of circles is accidentally aligned, or external factors not relevant to the data caused shapes to be moved as a group, then this would be a false (and strong) visual signal being sent to a reader.
Parallelism
If we draw the paths of the animated circles, we see another principle available for mis/use. Parallelism can be thought of as the fossilized animation of elements, as lines with the same or very similar slopes are visually associated as being part of the same group. Here we see two groups, mirroring the same two groups from the common fate example.*
Charts using lines in a traditional way--to show time series--see parallelism always working in their favor. Shared slopes are a meaningful grouping, as it indicates a shared pattern of increase or decrease over time. It's particularly prominent in slopegraphs, which rely on parallelism as their main grouping method. If this were a slopegraph, then we would see three things decreasing in value at the same rate while two things increase in value at the same rate, and those groups would be more meaningful than the fact that two of the datapoints share almost the same destination (the third and fourth lines).
But parallelism is also a key principle to account for in other methods of data visualization. That's because so many charts use lines to indicate relationships between elements. In these cases, a line is a topological indicator, showing that two elements are explicitly connected.
* We might also see a triangle with radiating bars (an unfortunate side effect of the size of the example). The ability to visually shift between two groups of three parallel lines and the triangle with radiating bars points to the importance of multistability in data visualization, a more complex topic for a later time.
Connectedness
To undestand this better, we need to save our lines and bring back our circles and now bring a few more circles for the ends of the lines that are lacking circles. This effectively merges the two lines and three circles in the lower middle of the screen via the principle of connectedness.
There now exist four shapes, three of which are made up of two circles and a line and one shape that is made up of three circles and two lines. This could be a very simple network diagram showing people connected to friends. Or it might be a diagram showing where minerals are extracted and where they're refined. In either case, the strong signal coming from the layout of the lines and circles makes a reader want to assume that circles near each other are somehow related and that those connected by similarly sloped lines are related.
For this reason, unless there's an unambiguous directionality to a visualization of connectedness, the elements are typically not laid out in discrete steps like this. A genealogical chart, for example, would make sense having steps such as these. For data visualization of networks where there are no obvious steps, a force-directed network layout is a common choice.