POV-Ray is is a high-quality, free software tool for creating three-dimensional graphics. Available for download here: http://www.povray.org/
The Lorenz attractor is a simplified model of convection of a gas within a confined space. This very simple model results in some very interesting motion, an example of deterministic chaos. A chaotic system is very sensitive to initial conditions and the system rapidly diverges.
The system is described by three coupled non-linear differential equations:
dx / dt = a (y - x)
dy / dt = x (b - z) - y
dz / dt = xy - cz
where a is the Prandtl number representing ratio of fluid viscosity to thermal conductivity b is the Rayleigh number representing the difference in temperature between the top and bottom of the box c is the ratio of the width to height of the box
Commonly used constants are a = 10, b = 28 and c = 8/3.
This repository contains the POV-Ray code for rendering the Lorenz attractor, and producing an animation of the attractor building up over time to show the chaotic behaviour.
A video of the rendered animation can be found here (the video has a much slower, smoother framerate than the gif below):
https://www.youtube.com/watch?v=SBTiyolNGfw
