2.1. IntLenPins

This was the implementation of the first step on the way to the more complex visualization techniques described in the next two subsections. It is the most abstract of the three techniques.

Here a sphere is placed around the fixed point, that shall be visualized, so that the fixed pont itself represents the center of the sphere. The radius of the sphere can be chosen interactively. On the surface of the sphere an interactively chosen number of startpoints is stochastically distributed. These startpoints are the startpoints of an integration, calculated over some fixed time (also chosen by the user), which has to be done either in positive or in negative time, so that the integration is done in the opposite direction from where the fixed point is. The spatial length of this integration is then shown by drawing straight lines for each startpoint, which are perpendicular to the surface of the sphere. The length of these straight lines is equal to the length of the respective integration.

In the following some results of this technique are shown:

In these two pictures above the same fixed point is visualized by the two possibilities, that this method is capable of. In the first picture, the length of the integration is visualized by giving the streamlets different colors. Brigther means the integration over a constant time was longer in spatial distance, darker means the integration length was shorter.



In the two above pictures, the three fixed points of the Lorentz system have been visualized using the IntLenPins approach. Notice, that when using too much streamlets (integrating from too many startpoints) usually not improves the understanding of the behavior, as more and more details are hidden and the overlapping decreases the threedimensional appearance.



Finally these two pictures show a combination of this fixed points visualization method with the colored Streamline approach of visualizing the global behavior of the system around the fixed points. The colored Streamline is presented in a later section.