Скачать или смотреть Pendula gaining energy

This comes from a magnetic pendulum simulator that I wrote in c++ using OpenGL. Here we get some nice circulation around magnetic sources. Dynamical systems like this are chaotic, which means that slight variations in initial conditions can lead to arbitrarily large divergences in long term dynamics - for example, the pendulum bobs starting at almost the exact same location, and having what appears to be totally uncorrelated position and velocity at future times. Each colour corresponds to a different moving pendulum bob, with a trail showing you its previous position, so you can more easily see how far apart some of the neighbours have become.

Each of the coloured blurry blobs is a magnetic attractor. In most configurations the magnetic sources are placed symmetrically, with no outside forces enabled to move the sweeping pendulums out of a symmetric motion.

Since damping is negative, the particles gradually gain energy, rather than losing it. This allows them to slowly climb out of what would otherwise be stable orbits, or weakly trapping regions. Discord:   / discord