Visualizing the behaviour of higher dimensional dynamical systems

In recent years scientific visualization has been driven by the need to visualize high-dimensional data sets within high-dimensional spaces. However most visualization methods are designed to show only some statistical features of the data set. The paper deals with the visualization of trajectories of high-dimensional dynamical systems which form a L/sub n//sup n/ data set of a smooth n-dimensional flow. Three methods that are based on the idea of parallel coordinates are presented and discussed. Visualizations done with these new methods are shown and an interactive visualization tool for the exploration of high-dimensional dynamical systems is proposed.

[1]  Herman Chernoff,et al.  The Use of Faces to Represent Points in k- Dimensional Space Graphically , 1973 .

[2]  G. W. Furnas,et al.  Generalized fisheye views , 1986, CHI '86.

[3]  Austin Henderson,et al.  Rooms: the use of multiple virtual workspaces to reduce space contention in a window-based graphical user interface , 1986, TOGS.

[4]  Georges G. Grinstein,et al.  Iconographic Displays For Visualizing Multidimensional Data , 1988, Proceedings of the 1988 IEEE International Conference on Systems, Man, and Cybernetics.

[5]  Alfred Inselberg,et al.  Parallel coordinates for visualizing multi-dimensional geometry , 1987 .

[6]  Matthew O. Ward,et al.  Exploring N-dimensional databases , 1990, Proceedings of the First IEEE Conference on Visualization: Visualization `90.

[7]  G. David Kerlick,et al.  Moving iconic objects in scientific visualization , 1990, Proceedings of the First IEEE Conference on Visualization: Visualization `90.

[8]  Georges G. Grinstein,et al.  Perceptualization of scientific data , 1990, Other Conferences.

[9]  Ted Mihalisin,et al.  Visualization and analysis of multi-variate data: a technique for all fields , 1991, Proceeding Visualization '91.

[10]  Haim Levkowitz,et al.  Color icons-merging color and texture perception for integrated visualization of multiple parameters , 1991, Proceeding Visualization '91.

[11]  Andrew J. Hanson,et al.  Interactive visualization methods for four dimensions , 1993, Proceedings Visualization '93.

[12]  Jarke J. van Wijk,et al.  A Probe for Local Flow Field Visualization , 1993, IEEE Visualization.

[13]  F. W. Schneider,et al.  Mixed-mode and quasiperiodic oscillations in the peroxidase-oxidase reaction , 1993 .

[14]  G. Feichtinger,et al.  The geometry of Wonderland , 1996 .

[15]  Werner Purgathofer,et al.  Animating flow fields: rendering of oriented line integral convolution , 1997, Proceedings. Computer Animation '97 (Cat. No.97TB100120).