Trajectory
The path a system travels through time: the route across the map.
A trajectory is the ordered sequence of states that 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 determined by the variables with which the system is described. 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 which states the system has actually assumed, and thereby something of its 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 suggests a stable equilibrium; a path that repeats itself in a loop, a rhythm or cycle; a path that never follows exactly the same route and yet stays within a bounded region, 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 with idiographic thinking, which is concerned not with the average patient but with this one person and the path he or she travels through time. Two people with the same diagnosis may describe very different trajectories, and in our impression it is precisely that path that often holds more treatment-relevant information than a single score.