Trajectory
The path a system travels through time — the route across the map.
A trajectory is the ordered sequence of states a system passes through over time. It is, in other words, a particular structure of unfolding — the path the system traces through its phase space.
The states are defined by the variables used to describe the system. If those variables are used as the axes of a phase space, the trajectory can be embedded in that space and made visible as a line. Where the phase space contains every conceivable state, the trajectory shows the states the system has actually assumed — not the possibility, but the history.
The shape of an unfolding
It is worth pausing on what a trajectory can make visible. A path that keeps circling a fixed point points to a stable equilibrium; a path that repeats in a loop, to a rhythm or cycle; a path that never quite follows the same route and yet stays within a bounded region, to chaos in the strict sense. The shape of the unfolding thus carries information that cannot be read from isolated snapshots.
For clinical practice this connects closely to idiographic thinking: what matters is not the average patient, but this person and the path he travels through time. Two people with the same diagnosis may describe entirely different trajectories — and it is precisely in that path, to our impression, that more treatment-relevant information often lies than in a single score.