## Visualization of Complex Dynamical Systems | |
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NDimViewer: Visualization of High-Dimensional Dynamical Systems
(1998-1999)NDimViewer is a web-based visualization system for numerical solutions of dynamical systems and representation of the calculated data using one out of three techniques: Extruded Parallel
Coordinates, Linking With Wings, or Three-Dimensional
Parallel Coordinates.
It is specialized for high-dimensional dynamical systems with a
dimension count up to 25, depending on the chosen technique.
The implementation itself is separated into a calculation and a
visualization part, which are treated independently. (more)
| |

Color-table animation for vector fields
(1997-1998)FROLIC is a fast variant of Line Integral Convolution (LIC) and illustrates 2D vector fields by approximating streamlets by a set of disks with varying intensity. Color-table animation is a very fast way of animating FROLIC images. Various color-table compositions are investigated. When animating FROLIC images visual artifacts (pulsation, synchronization) must be avoided. Several strategies in this respect are dealt with. | |

Visualizing Dynamical Systems near
Critical Points
(1996-1998)The visualization of dynamical systems, e.g., flow fields, already provides quite a reasonable number of useful techniques. Many approaches seen so far either facilitate the visualization of the abstract skeleton of flow topology, or directly represent flow dynamics by the use of integral cues, such as stream lines, stream surfaces, etc. In this paper we present two visualization techniques which feature both approaches and demonstrate that combining both techniques, synergetic advantages are gained. | |

Enhancing the Visualization of
Characteristic Structures
in Dynamical Systems
(1997-1998)We present a thread of streamlets as a new technique to visualize dynamical systems in three-space. A trade-off is made between solely visualizing a mathematical abstraction through lower-dimensional manifolds, i.e., characteristic structures such as fixed point, separatrices, etc., and directly encoding the flow through stream lines or stream surfaces. Bundlers of streamlets are selectively placed near characteristic trajectories. An over-population of phase space with occlusion problems as a consequence is omitted. On the other hand, information loss is minimized since characteristic structures of the flow are still illustrated in the visualization. | |

Visualizing the Behavior of Higher
Dimensional Dynamical Systems
(1996-)The project deals with various techniques to visualize trajectories of high-dimensional dynamical systems. | |

The Virtual Ink Droplet Method
(1997)The virtual ink droplets method is an efficient visualization technique for two-dimensional dynamical systems. It is based on a physical model of smearing ink over a sheet of paper. Due to this intuitive metaphor images of flow fields can be easily understood and interpreted. | |

Java Exploration Tool for Dynamical Systems (1997)Various texture-based techniques to visualize 2D analytical dynamical systems are implemented as Java-applet. These techniquese include LIC, OLIC, FROLIC, etc. | |

Animating Flowfields: Rendering of Oriented Line Integral
Convolution (1997)Oriented Line Integral Convolution: Texture based flow visualization to illustrate direction and orientation of flow (extension of Line Integral Convolution). | |

Collaborative Augmented Reality: Exploring Dynamical Systems
(October 1996 - March 1997)In this paper we present collaborative scientific visualization in Studierstube. Dynamical systems are investigated in a multi user setting by the use of augemented reality. | |

Visualizing Poincaré Maps together with
the underlying flow
(June 1996 - March 1997)Advanced visualization techniques for 2D Poincaré maps embedded within standard visualization techniques for the underlying 3D flow. | |

Hierarchical Streamarrows for the Visualization of
Dynamical Systems
(April 1996 - March 1997)Hierarchical streamarrows are an extension to the streamarrows technique. It is not affected by problematic cases as, e.g., such of high divergence or convergence. | |

Examples for Visualization using
DynSys3D (1996 -)DynSys3D: A workbench for developing advanced visualization techniques in the field of three-dimensional dynamical systems under AVS. | |

Streamarrows -- Results (1996 - 1997)Streamarrows are a novel technique developed to illustrate multiple layers of streamsurfaces. Arrow shaped portions of a streamsurface are rendered semitransparently to make portions of phase space structures perceivable which would otherwise have been occluded. Streamarrows are well suited for, e.g., highly curled streamsurfaces as produced by the above mentioned mixed-mode oscillations. | |

Visualization of Mixed Mode Oscillations (1995 - 1997)Mixed-mode oscillations are a phenomenon quite often encountered in chemical systems. They owe their name to the alternating large and small amplitude heights in the observed time series. Another characteristic feature of mixed-mode oscillations are the alternating chaotic and periodic responses as a parameter is varied. | |

A Guided Tour to Wonderland: Visualizing the Slow-Fast
Dynamics of an Analytical Dynamical System (1994 - 1996)The Wonderland model is an oeconometric model which describes the interaction between population size, economic activity and environmental implications. Various visualization techniques were taken to illustrate the phase space behaviour of this nonlinear system. | |

Visualization of the Dynastic Cycle (1994 - 1995)The Dynastic Cycle is an oeconometric model which was designed to model the periodic alteration of the society between despotism and anarchy in ancient China. Thereby a three-class society of farmers, bandits and soldiers is considered. We give some phase-space visualizations to illustrate the long term behaviour of the model which is characterized by a pronounced slow-fast dynamic. | |

Graphical Nonlinear Time Series Analysis (1994 - 1995)With Graphical Nonlinear Time Series Analysis a user investigates time series in phase space that may have originated from underlying nonlinear systems. The program enables the user to quickly focus on interesting portions of his data. In a following step he may then use numerical tools for further analysis. | |

Nonlinear Iterated Function Systems (1993 - 1994)Iterated Function Systems describe (typically fractal) objects by a set of contractive affine transformations. Nonlinear Iterated Function Systems are defined by contractive nonlinear functions. Thus the modeling flexibility of Iterated Function Systems is greatly increased. We have done some work on modeling and rendering of 3D Nonlinear Iterated Function Systems. Furthermore interactive programs for the specification of 2D (Nonlinear) Iterated Function Systems have been implemented. | |

Visualization of Strange Attractors (1993 - 1994)The Visualization of Strange Attractors facilitates the understanding of the long term behavior of chaotic dynamical systems. Typically a simple one-dimensional trajectory is used in phase space to approximate a strange attractor. We have investigated more complex visualization techniques for both illustrating the global and local properties of strange attractors. | |

Editor for Strange Attractors (1993)An Editor for Strange Attractors allows an interactive and intuitive specification and modification of dynamical systems defined by differential or difference equations. | |

Institute of Computer Graphics
/
Visualization and Animation Group
/
Research

This page is maintained by **Helwig Hauser**. It was last updated on **November 8, 1999**.

If you have any comments, please send a message to helwig@cg.tuwien.ac.at.