Visualizing 3D chaotic systems
Preface
This site contains the visualizations of the 3D chaotic systems described in the book Elegant Automation: Robotic Analysis of Chaotic Systems by Sprott (2023).
Each chapter contains the description and visualizations of one chaotic system. There are two modes of visualization specified: pre-computed visualization, and real-time simulation.
The pre-computed visualization for each system was made with a java-based creative coding language called Processing. It contains the 3D trajectory computed for each system for a simulation time of 103 seconds. The trajectory is colored based on the values of local Lyapunov exponent, it visualizes how predictable or unpredictable the each portion of the trajectory.
The real-time simulation was made using another creative coding language called P5.js. It is based on the interpreter language called javascript. The P5.js was used due to being interactive and having html embedding capability. An online editor for P5 is also available here. Because of its interpreter nature, P5.js has caused the following limitations and cautions.
Due to the high computational cost and processing delays, the calculation of local Lyapunov exponents and the corresponding color-coding were omitted in the real-time simulations. Consequently, the trajectories in these simulations are displayed in a uniform solid color.
Running real-time simulations for extended durations may cause the web browser to slow down or become unresponsive. Therefore, it is recommended to limit the simulation time to the predefined duration within the browser.
However, the source code for all simulation files has been made open-source, with links provided in the summary section. Interested readers may download the code and run the simulations locally to achieve improved performance and longer simulation times.