Recreational Mathematical Physics (RMP)
Have fun with mathematical physics!
Random crystal corner
A crystal of size L×L×L is fully filled with atoms. From one corner, atoms are removed under the constraint that if a cube is missing then all cubes deeper into the corner must also be missing. The missing region therefore forms a 3-dimensional Young diagram (a plane partition). Monte-Carlo sampling generates typical thermal crystal corners.
Radial KPZ / Eden Growth
Start from either a random closed curve or a regular polygon, then let the interface grow outward according to different stochastic rules. In the isotropic case the macroscopic envelope tends toward a circle, while anisotropic rules can produce kinetic Wulff-like shapes.
Conway’s Game of Life on a Torus
Conway’s Game of Life is a classic cellular automaton in which each cell is either alive or dead, and the entire pattern evolves by simple local rules. Here the lattice has periodic boundary conditions in both directions, so the square is topologically a torus: cells leaving one edge re-enter from the opposite edge. Click or drag on the board to draw your own initial state.
Lianliankan (连连看)
A periodic-boundary version of the classic tile-matching game. Two identical tiles vanish if they can be connected through empty space by an axis-aligned path with at most two turns. Here the board lives on a torus, and an empty padding ring is always present.
New behavior:
PBC (torus) + one empty padding row/column is always present.