State space visualization

We have developed a new state-space visualization of moderately turbulent flows

The idea:

State of fluid - the 3D velocity field at every point of the cell is a point in a state space, always approximated by a finite-dimensional computer mesh. Our solutions are accurate to single precision accuracy; requires 61,506 coupled ODEs or more.

Construct a state space coordinate system in which a few coordinates capture most of these recognizable structures?