In this video
, we show an example of a synchronized splay state. This is the k=7 state - in other words the phase differences
between nearest-neighbors is 7π/4. Splay states are also known as 'rotating wave' states because the phase travels around the ring. Here, the phase
travels in a counter-clockwise direction. This state has a 8-fold twisted rotational symmetry. This twist is given by the k number, and represents
the amount of phase rotation that must accompany the spatial ring rotation. Since phase tracks time, by running forward time, we can run forward phase.
As an example, a phase rotation by 7π/4 is accompanined by a spatial rotation of the ring by pi/4. To see this we run forward time by 7/8 of a cycle,
after which, we now see the ring has indeed rotated by one oscillator, or pi/4.