This is a good question. The "directions" you mention would, in our system, typically be considered to depend on the nature of the drive. For instance, if you repeatedly rotate the magnetization by 180 degrees, you can imagine the magnetization going up-down-up-down-... repeatedly, whereas if you instead used rotations of 181 degrees, it would take a long time for the state to come back around to pointing along its exact original orientation.

The proposed signature of a "discrete time crystal" was to observe the magnetization point up-down-up-down-... even when you used e.g. 181 degree rotations, if you allow dipole-dipole interactions to act for long enough between rotations. This is what we observe: "wrapped" magnetization when we use imperfect rotations with short nuclear spin interaction times, then locked up-down-up-down-... magnetization when we use imperfect rotations with longer nuclear spin interaction times.

A last subtelty when comparing to traditional oscillating systems is that the response is not at the same frequency as the drive, but will have a period determined by both the drive period T and the symmetry of the dipole interactions. Our system's interactions have 2 symmetric states, so the response period is at 2T. Other systems have other symmetries; for instance, the research team at Harvard showed oscillations at 3T using a spin system with different interaction symmetries.