Scalar Field on a Lattice

Classical field theory treats space as filled everywhere with a field — a number (or set of numbers) defined at every point — rather than with discrete particles moving through empty space. This simulation puts a scalar field on a finite lattice and evolves it with the Klein-Gordon wave equation, so you can watch a disturbance spread as a wave across the grid. Raise the mass term and the wave stops spreading freely and instead clumps into short-lived, localized lumps — a hands-on picture of why a massive field's excitations behave like particles while a massless field's excitations behave like radiation.