Fig. 1. (a) White noise texture; (b) 2D vector field; (c) LIC: white noise texture filtered according to the vector field.

Fig. 2. OLIC: LIC with sparse texture and ramp-like kernel-function.

Fig. 3. (a) LIC image of circular flow; (b) OLIC image with clockwise flow; (c) OLIC image with counterclockwise flow.

Fig. 4. A discrete sampled trajectory in parallel coordinates (left) and a three-dimensional extruded surface defining the same trajectory (right).

Fig. 5. Extruded parallel coordinates illustrate three trajectories of a five-dimensional system.

Fig. 6. Two-dimensional base trajectory with two wings (for the third and fourth dimension) linked to it.

Fig. 7. (a) Linking with wings of an econometric model; (b) Hedge-hog visualization of a four-dimensional data set.

Fig. 8. Three-dimensional parallel coordinates.

Fig. 9. (a) A six-dimensional stacked predator–prey model with simple linkage; (b) Complex linkage with highlighted time interval for the trajectory of a chaotic attractor.

Fig. 10. Two examples of streamsurfaces with stream arrows.

Fig. 11. Spot (enlarged) and the resulting spot-noise texture.

Fig. 12. (a) Streamsurface with anisotropic spot-noise texture; (b) Stream arrows shifted out of the stream surface and anisotropic spot noise.

Fig. 13. An illustration of the Poincaré map definition.

Fig. 14. (a) Poincaré map visualized with directed strokes; (b) addition of spot-noise, streamlines and streamsurface.

Fig. 15. (a) A texture on the Poincaré section (b) is distorted after repeated applications of Poincaré map P.

Fig. 16. (a) A typical trajectory of the Dynastic Cycle; (b) A chaotic trajectory of the Dynastic Cycle.

Fig. 17. (a) Wonderland model with critical manifolds (escape scenario); (b) particle system visualizes flow close to a critical manifold.