Wigner crystal simulation

This is fun little a Wigner crystal simulation. It minimizes the energy of a bunch of electrons (which repel each other due to electromagnetic forces) in a radial quadratic potential (i.e. something like V(x,y) = x^2 + y^2). It works by simulating the dynamics with damped forces. The electron-electron repulsion is accelerated through the Barnes-Hut algorithm.

For visualization, the Delaunay triangulation of the points is computed; points having degree 5 are marked red, points with degree 7 are marked blue (both are considered to be defects of the crystal), others are black.

The UI in the upper-left corner controls some simulation parameters:

• Count is the number of electrons in the simulation. Higher values mean slower & less stable simulation, but more interesting effects.
• Step is the time step size. Smaller values lead to slower simulation, larger values lead to instabilities.
• Damping is the velocity damping factor (i.e. the parameter C in v' = -Cv). Smaller values mean hotter simulation (more movement & wiggliness), larger values mean colder simulation (behaves more like gradient descent on energy).
  
• Precision is the parameter for Barnes-Hut algorithm. Smaller values lead to imprecise electron-electron force calculations & instabilities, larger values increase precision at the expense of slower simulation.

I've no idea how useful that is, but at least it's fun to watch, so I figured I'd share it. If you enjoyed it, please let me know, I'll be more than happy :)

The full code for this project is here. It uses my own C++ game engine (which is used for most other projects I've released here as well).

This project was inspired by John Carlos Baez's post on mastodon about Wigner crystals.