2.5. PlotXYZ

This visualization technique, that can also be used for the visualization of fixed points, but not only for these, is the most abstract of the five here presented methods, that were developed during this project.

This method is not only useful for the purpose of fixed points visualization, but more generally a visualization method, that goes very well along with the well known streamlines visualization technique. With this method one can plot the X-, Y-, and Z-axis over time for a calculated Streamline, so that the behavior of a streamline over time can be investigated (in an abstract way).

The graphs for the X-, Y-, and Z-axis are either in red, green, and blue, respectively, or the original color of the colored streamline is taken for each of the graphs, so that one can also see the mapping on each of the graphs for the X-, Y-, and Z-values.

How can this technique be used, to visualize the behavior of fixed points?

If a trajectory (streamline) is attracted by a fixed point, than this can be seen, as the X-, Y-, and Z-values after some time, when the fixed point is (nearly) reached, wont change anymore over time.

In this picture a colored streamline and a part of the three ploted function graphs for X, Y, Z over the time are shown. The colormapping for the colored streamline shows the velocity (blue is low velocity, red is high velocity).
In the two following pictures again a colored streamline and a part of the three ploted function graphs for X, Y, Z over the time are shown, in the first one by giving the functions plots new colors, in the second one by preserving the original color of the streamline as described earlier. Here we can clearly see, that most of the time is spent in the low velocity areas of the streamline.