Chaotic Systems in VR

This site is a set of WebXR experiments to show phase portraits of Chaotic Systems in VR.

Experiments

Lorenz System 'Butterfly' Strange Attractor	Modified Chua System (Tang et al. 2001) 4-scroll Attractor
Rössler System Rössler Attractor

Controllers

Click trigger on right hand controller to restart the simulation from a random point.

HUD

There is a fixed position HUD attached to every phase portrait. It shows:

• h: step size
• e: maximum error at ODE solver (RKF45) at current step size
• st: simulation time (equals h multiplied by N below)
• rt: real time (wall time) since simulation started
• N: number of simulation steps passed and also number of points currently shown on display

Display

• Red-Green-Blue lines shows X-Y-Z axes.
• The position of the camera and the length of XYZ axes lines are dynamically adjusted.
• Simulation restarts automatically after some seconds when what is to be shown is displayed.

Why this site ?

One of the courses I enjoyed the most at my university back in early 2000 was "Non-Linear Circuits and Systems" and the course book was Strogatz's Nonlinar Dynamics and Chaos. Although I have not used the things I learned in that course day to day basis, I never forgot the basics. An important thing was to visually represent the behavior of such systems, and I think it is a very good match for VR, and that is why I created this site.

If you want to learn more about nonlinear systems and chaos...

If you are here, most probably you already know about the topic, but if not, I highly recommend either or both:

• The book I mentioned above: Nonlinear Dynamics and Chaos
• The Nonlinear Dynamics and Chaos course given by Prof. Strogatz at Cornell available on youtube.

Technical Information

• This is a pure javascript frontend application with no backend.
• The VR 3D environment in frontend (web pages) is coded using A-Frame web framework.
• The points are rendered using a custom A-Frame component using BufferedGeometry and Points of three.js.
• Math is rendered using MathJax outputting SVG (because that can be displayed by the browser in VR headset as well).
• Runge-Kutta-Fehlberg (RKF45) ODE solver (custom implementation) is used.
• This app is hosted at Netlify and tested on Oculus Go and Quest.
• I use Glitch during development, and export it to Github and when merged to master this is deployed to Netlify.

Contact

Please send an email to: info at metebalci.com