  Stochastic dynamics is generated by a matrix of transition probabilities.
Certain eigenvectors of this matrix provide observables, and when these are
plotted in the appropriate multi-dimensional space the phases (in the sense of
phase transitions) of the underlying system become manifest as extremal points.
This geometrical construction, which we call an
\textit{observable-representation of state space}, can allow hierarchical
structure to be observed. It also provides a method for the calculation of the
probability that an initial points ends in one or another asymptotic state.
