Lorentz 3D Applet

This applet demonstrates the numerical solution of the Lorentz equations, allowing full 3D viewing, mouse rotation and zooming, and animation of the equation parameters. A simplified version of the Java source code is available.

The Lorentz Equations

The Lorentz Equations form a system of 3 coupled, non-linear differential equations corresponding to diffusionless convection. In this application the variables x, y and z represent convective flow, horizontal temperature and vertical temperature respectively. The constant terms A, B and C represent the Prandtl number, the Rayleigh number and the ratio of the vertical to horizontal size respectively.

dx/dt = A(y - x) dy/dt = Bx - x - xz dz/dt = xy - Cz

In this version of the software, the solution is found numerically using a 4th order Runge-Kutta method, and the colouring is derived from the iteration counter.

Lorentz Equations Applet

Running the Applet

To view this applet, you will need a recent (Java J2SE 6 or later) version of Java. Webstart will allow you download the latest version if necessary. Click on the screen shot of the applet to run the application.

You can click and drag with the mouse to interact with the 3D view of the solution:

  • left click and drag to rotate the view
  • right click and drag to translate the view
  • middle click and drag up / down to zoom the view

Ticking the Animate checkboxes will sweep the specified parameter through a range of values controlled by the amplitude and origin values. Each of the three parameters may be animated independently.