This is one of my favorite music videos, and a fantastic example of what you can do with a simple split screen. Director Michel Gondry uses a single stream of video that plays in opposite directions within the two subframes. As summarized on the Director File page for Sugar Water:
Essentially “Sugar Water” is a one-take video, told on two sides of the screen... By performing only one take, Gondry bases the video in real-time. Yet Gondry flips you around by having the story explained both forwards (on the left side of the screen) and backwards (on the right side).
Gondry is not overly precise with the visually patterned elements in the two subframes. For example, there is often imperfect synchronization between the two band members, in terms of their onscreen size, location, action and speed of movement. To me, the slightly loose construction adds to the puzzle-like aspect of the video: it nudges the viewer to pay closer attention as things seem to drift in and out of the presumed pattern. Additionally, a kind of relative timebase emerges, as elements slide in and out of sync with each other, like dancers who keep in rhythm with both the score and each other. David Bordwell once referred to the formal patterning in Yasujiro Ozu's films as "rigorous but not rigid", and the same statement may apply here. Personally, in my own split-screen work, I have a habit of wanting to make things precise with every detail I can think of. It's good to remind myself of the difference between rigorous and rigid - between beauty rooted in formal structure and precision for its own hollow sake.