An Orthogonal organized finite state machine (OOFSM), proposed in [1], is a discrete state space abstraction of the evolutionary behavior of dynamic systems. A lattice partitioning applied to a continuous state space discretizes the state space. A discrete vector field that abstracts the intersection of trajectories with the boundaries of the discretized state space provides for the abstraction of the evolutionary behavior of the discretized system and thereby, of the original continuous dynamic system. The resulting model conceptually describes an orthogonal organized group of states with transitions defined between neighboring states, hence, a spatially organized finite state machine of possibily high dimensions. The OOFSM model is extended in [2] to represent observable data, say as acquired from a sensor network. Applications such as gradients, contouring and the determination of the discrete trajectory path from timestamped data observations are considered.

The OOFSM model itself has geometric properties and hence, may also serve as a visualization model. Low-dimensional OOFSMs (dimensions of three or less) are suitable for direct visual manipulation in a 3D renderer. Examples of such visualizations appear in [1, 2]. However, visualizations of higher dimensional OOFSMs suffer the usual issues of higher dimensional data visualiation. Moreover, it may be important to understand the evolutionary behavior of complex dynamic systems, say, those prone to cascading failure conditions. To address these issues, a TransDimension Visualization Model (TDVM) for complex dynamic system visualizations is proposed in [3]. The TDVM includes multiple imagery and animation elements in a metaphor-based environment that facilitates heightened understanding of the evolutionary behavor of high dimensional dynamic systems.