**project duration:** 1993

** ESA **(Editor for Strange Attractors) is an interactive program to display the long-term behavior of nonlinear, dynamical systems. ESA projects these systems into 2D or 3D space. Camera position and viewing parameters can be specified interactively. Bifurcation diagrams and Poincare sections are included in the functionality of ESA.

ESA displays the following types of data: trajectories of dynamical systems given by differential or difference equations and time series which are resulting from (nonlinear) dynamical systems. The user specifies and modifies the differential equations interactively and determines the allocation of variables of the differential equations to coordinate axes of the 2D or 3D plot. One or more trajectories are either displayed as point sets or polylines. Furthermore the visualization of simple sets of initial points (cube, tetrahedron, pyramid) is possible. Up to three windows may be defined simultaneously. Geometric operations include rotation, translation, scaling and zooming. Parameters of the differential equations, initial points of the trajectories and number of points to be displayed are all definable by the user.
Bifurcation diagrams illustrate the long term behavior of a whole class of systems. One parameter of the set of defining equations is taken as bifurcation parameter and is varied along the horizontal axis. On the vertical axis the long term behavior of one of the state variables is plotted. Varying the bifurcation parameter only slightly may produce vastly differing behavior (periodic or chaotic attractor). ESA includes the following interactive operations: selection of a bifurcation parameter, modifications of the set of equations, zoom, translation, selection of range.
A simple analysis of 2D and 3D time series is possible in ESA as well. ** WINESA **, a preliminary implementation of the system in MS-Windows, is available as well. Several different systems and several windows of the same system can be investigated simultaneously.

To download the software either press ESA (PC, Dos, german user interface, uncompress with pkunzip, sample data included) or WINESA (PC, Windows, uncompress with pkunzip, sample data included). Further information is given in the following technical reports:

- Application of Visualization Techniques to Complex and Chaotic Dynamical Systems
- Interactive Exploration of Dynamical Systems

This page is maintained by **Eduard Gröller**. It was last updated on **November 20, 1998**.

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