hesigh/zeeman

Dr. Zeeman's Catastrophe Machine

Zeeman's Catastrophe Machine Simulation

This repo is a simple C++ program that uses OpenGL and GLUT for simulating the famous mechanical device named after mathematician Cristopher Zeeman (1925 – 2016). It is a simple example of a dynamical system with catastrophe behavior.

How to use

Program can be simply compiled using make command. Some commands:

• s - Show projection of a catastrophe curve on the control space (plane)
• 1 - Turn on vertical oscillation
• 2 - Turn on circular oscillation
• q - Quit

Catastrophe free oscillation

Catastrophe oscillation

Some details

In some way such phenomena are quite counter intuitive, since it shows that it's possible that a smooth change of input of a differentiable dynamical system can cause singularity in output. This effect can be explained geometrically looking at the equilibrium surface of a given system. For more, feel free to contact and see the reference:

• Arnol'd V.I. - Catastrophe Theory, 2nd Edition [Springer-Verlag, 1986]

Main OpenGL reference:

• Angel E., Shreiner D. - Interactive Computer Graphics: A Top-Down Approach with Shader-Based OpenGL, 6th Edition [Addison Wesley, 2011]