A state space (or, which is roughly equivalent, *phase space*)
is the set of all possible states of a
Dynamical
System; each state of the system corresponds to a unique point in
the state space.

Describing a system in its state space means switching from a simple space (with 3 dimensions) and complex things (made out of N elements) to a complex space (3^N dimensions) and simple things (points in that space).

A system’s development over time, i.e. its
System
Dynamics is equivalent to a *trajectory* in its state
space. All possible trajectories in the space can be expressed as
vectors; their aggregation is called the *phase portrait* of the
state space.

The regions of the state space in which a system stays or to which it returns (i.e. in which it is stable) are the system’s Attractor regions.

An Attractor Landscape is the abstraction of a state space to what is relevant, i.e. interesting to us – attractors and possible trajectories between them.

## References

- Abraham & Shaw (1995):
*Dynamics: The Geometry of Behavior* - DeLanda (2002):
*Intensive Science and Virtual Philosophy* - Terman & Izhikevich (2008): “State space“