Graph drawing by force-directed placement
Software—Practice & Experience
Computational mechanics of cellular automata: an example
Proceedings of the workshop on Lattice dynamics
Tracking scalar features in unstructured datasets
Proceedings of the conference on Visualization '98
SC '97 Proceedings of the 1997 ACM/IEEE conference on Supercomputing
Vortex tracking in scale-space
VISSYM '02 Proceedings of the symposium on Data Visualisation 2002
A case study in selective visualization of unsteady 3D flow
Proceedings of the conference on Visualization '02
VISSYM '03 Proceedings of the symposium on Data visualisation 2003
Causal architecture, complexity and self-organization in time series and cellular automata
Causal architecture, complexity and self-organization in time series and cellular automata
Visualization of turbulent flow with particles
VIS '93 Proceedings of the 4th conference on Visualization '93
Tracking of Vector Field Singularities in Unstructured 3D Time-Dependent Datasets
VIS '04 Proceedings of the conference on Visualization '04
Accelerated Unsteady Flow Line Integral Convolution
IEEE Transactions on Visualization and Computer Graphics
Volume Tracking Using Higher Dimensional Isosurfacing
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Efficient Visualization of Lagrangian Coherent Structures by Filtered AMR Ridge Extraction
IEEE Transactions on Visualization and Computer Graphics
Efficient Computation and Visualization of Coherent Structures in Fluid Flow Applications
IEEE Transactions on Visualization and Computer Graphics
Generalized Streak Lines: Analysis and Visualization of Boundary Induced Vortices
IEEE Transactions on Visualization and Computer Graphics
Pathline predicates and unsteady flow structures
The Visual Computer: International Journal of Computer Graphics
Data, Information, and Knowledge in Visualization
IEEE Computer Graphics and Applications
Topology-based visualization of time-dependent 2D vector fields
EGVISSYM'01 Proceedings of the 3rd Joint Eurographics - IEEE TCVG conference on Visualization
Path line oriented topology for periodic 2D time-dependent vector fields
EUROVIS'06 Proceedings of the Eighth Joint Eurographics / IEEE VGTC conference on Visualization
Automatic detection and visualization of distinctive structures in 3D unsteady multi-fields
EuroVis'08 Proceedings of the 10th Joint Eurographics / IEEE - VGTC conference on Visualization
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The visualization of unsteady scientific data is still a challenging problem. Most techniques rely on the animation of individual time-steps. In this paper we propose a steady visualization of the dynamics in fluids using @e-machines. @e-machines are a concept from computational mechanics and can be thought of as finite state machines that can be visualized as directed graphs. The nodes are the causal states of the process. Given a local past of a position, causal states comprise all the information needed to predict the future of this position. As causal states stem from information theory, it can be shown that they are the most compressed representation of local dynamics that still allows for this prediction. Edges in the graph indicate transition probabilities between causal states in successive time-steps. Hence, the visualization of the @e-machine graph provides a concise and highly compressed steady visualization of the system's dynamics that still allows for an in-depth examination. In this paper we describe the construction and visualization of @e-machines and how interaction mechanisms with the physical domain allow for a detailed analysis of data sets describing fluid dynamics.