A hot cylinder presses on a thin plate. Watch temperature spread by the 2D heat equation while the lattice atoms jiggle harder where it is hot.
The plate starts pre-heated for the picture; press Reset for a cold start (the race table needs a cold start).
The science
Heat equation. For a thin plate: ∂T/∂t = α ∇²T + s(x,y) − 2h(T − T∞)/(ρ c d) with thermal diffusivity α = k/(ρ c). Here the heater source s is a Gaussian footprint normalised to the chosen power P.
Fourier's law. Heat flux q = −k ∇T: it points from hot to cold; the yellow arrows are drawn from this gradient.
Diffusion length. Heat reaches roughly √(4 α t) after time t; time to cross a plate of size L is about L²/α. Copper (α ≈ 1.2·10⁻⁴ m²/s) is about 25 times faster than stainless steel (≈ 4·10⁻⁶).
Numerics. Explicit FTCS on a 64 × 64 grid, stable for Δt ≤ Δx²/(4α); we use 0.8 of that bound. Insulated edges use mirrored ghost nodes; cooled edges are fixed-temperature (Dirichlet).
Lattice picture. In an insulator heat is carried by lattice vibrations (phonons); in metals mostly by electrons. The sphere lattice is a visual aid: vibration amplitude grows with the local temperature, but it is not a molecular-dynamics calculation.
Material values (k, ρ, cp) are typical handbook numbers typed from memory [verify against a source such as the CRC Handbook or Incropera]. Real plates also lose heat by radiation and convection, which are lumped into the single coefficient h.
Safety. Educational model, not a design tool. Do not touch hot surfaces in real life.