Same physics as the 3D version, viewed top-down as a colour heatmap instead of a tilted height field. The scalar field φ lives only at discrete lattice sites and every site obeys the Klein-Gordon field equation using only its immediate neighbours:
∂²φ/∂t² = c²∇²φ − m²φ − γ·∂φ/∂t
- Wave speed c — how fast a disturbance propagates outward from one lattice site to its neighbours before reflecting off the fixed (φ=0) boundary.
- Mass² term — at m²=0 the field is a pure massless wave (like light); raising m² adds a restoring force at every site that suppresses long-wavelength ripples and favours short-lived, localized "lumps" — the classical picture of why massive fields describe particles while massless fields describe radiation.
- Damping γ — dissipates energy so a struck field eventually settles rather than ringing forever.
Toggle "Show quanta" to mark every lattice site where |φ| is a local maximum above threshold with a bright dot — the field-vs-particle picture in miniature: nothing exists there but the continuous field itself, yet a large localized bump behaves like a particle.