Six interactive essays on what a grid keeps and what it throws away when a simulation replaces continuous space and time with discrete steps.
Most simulations of continuous physics run on a lattice: space becomes a grid of sites and time becomes a sequence of steps. The continuum laws are symmetric under every rotation and conserve energy exactly. A grid has only a handful of rotations, and a time step has no reason to conserve anything. Each essay here asks which symmetry of the continuum survives the discretisation, and what goes wrong when it does not.
The first two parts cover the two discretisations, space and time. The other four put rules on the grid: Life, which keeps the square's symmetries; two lattice gases, one anisotropic on the square and one isotropic on hexagons; lattice Boltzmann, which recovers isotropy on the square by choosing weights; and the Ising model, whose rule keeps a symmetry that its cold state breaks.