I wanted to create an effect of pulsating lines moving back and forth across the monoliths, but still wanted the effect to loop nicely. It took a couple of experiments to get to the mask texture that I use now, that uses the R channel for the direction and speed of the effect, and the B channel as a mask. The lines animate using the a sine wave.

The pulse that travels across the entire surface of the objects uses the world position (y) in the pixel shader, distorted by a noise map.