Why the balls always line up
Every lane makes a whole number of trips in one cycle. If one lane makes 3 trips and the next makes 4 in the same 30 seconds, both are back on the start line at 30 seconds. With twelve lanes making 3 to 14 trips, all twelve are back at the same instant.
In between, the differences between neighbouring lanes add up steadily. That steady drift is what draws the waves, the groups and the spirals. Nothing is animated between those shapes; they are what twelve steady tempos look like over time.

