Phase space
The imaginary space of all the states a system can assume.
The phase space, also called state space, is the imaginary space of all possible states in which a system can find itself, laid out along the dimensions that matter for that system.
The idea is simpler than it sounds. Take the quantities that describe a system, for a person for instance mood, tension and sleep, and make each of them an axis. Every state a person is in at a given moment is then a single point in that space. When the state changes over time, the point traces a path: the trajectory. One could think of the phase space as the map, and of the trajectory as the route travelled across it.
Why this image helps
The phase space can make patterns visible that remain hidden in an ordinary time series. A system that keeps returning to the same region points to an attractor; a system that suddenly jumps to another region points to an order transition. What is hard to distinguish in separate measurements takes on a form in this spatial representation, a Gestalt, as it is called in synergetics.
For clinical practice this is more than a mathematical nicety. The image helps us to see a patient not as a collection of separate symptom scores, but as a system moving through a space of possible states, visiting some regions often and avoiding others. The question then shifts from "how high is this score" to "where in the state space is this person, and in which direction are they moving".