Visualization Methods

Two or three of the system's n dimensions can be selected and the evolution of the system in these emphasized variables may be visualized directly. To minimize the loss of information, at least some of the remaining variables can be mapped onto visual attributes of the visualization, like color or texture. Often the evolution of the system in some of the variables is of more interrest than in others, so this approach is sufficient.

Most of the visualizations in this work have been generated using this method. Three of the system's four dimensions were mapped directly to the axes of the viewing space, the fourth variable was either not depicted or mapped to the saturation of the color.

Another possibility of depicting the behavior of a dynamical system in more than three dimensions, is to decompose the visualization into several views of a lower and easier to handle dimension. A simple and powerful approach are parallel coordinates, [InDi]. Each of the n variables is mapped onto one of n parallel coordinate axes, depicted within the same image. A point in n-D is represented as a polyline connecting the n coordinate values of the point.

To avoid overcrowding of images when depicting large amounts of points (for example curve segments) with parallel coordinates, extruded parallel coordinates [WeLö97] may be used.