Enhancing the Visualization of Characteristic Structures in Dynamical Systems

Abstract

We present a thread of streamlets as a new technique to visualize dynamical systems in three-dimensional space. A trade-off is made between solely visualizing a mathematical abstraction through lowerdimensional manifolds, i.e., characteristic structures such as fixed points, separatrices, etc., and directly encoding the flow through stream lines or stream surfaces. Bundles 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.