Exact every frame
Only the independent balls are stored. Every rotation, reflection, glide and lattice translate is applied again while drawing each frame.
A live hard-disc gas on a wallpaper quotient
Symmetric Brownian motion
Choose one of the seventeen wallpaper groups. Random kicks and near-elastic impacts move a handful of independent balls; the group rebuilds every other ball on every frame, so the symmetry is exact while the motion remains unpredictable.
Selected group
Loading the wallpaper groups…
Motion and optimizer settings
Density
The optimizer is preparing a start.
Brownian, not scripted
A damped random force continuously perturbs velocity. The motion is generated live and does not repeat; the seed in the address reproduces its optimized starting state.
Symmetric impacts
Collisions are solved against nearby group images. The equal and opposite impulse is carried back through the same isometry, preserving both the bounce and the wallpaper symmetry.