# HEAT SIMULATION

The rules for how heat spreads are some of the simplest in physics, but they can still lead to fascinating phenomena.

### CONTROLS

Click and drag to add heat

## HOW IT WORKS

Heat spread is governed by an equation unceremoniously titled the heat equation. It may look confusing, but its meaning is actually highly intuitive.

### THE HEAT EQUATION

The heat equation doesn't exactly tell us what the heat should be. Instead, it tells us how the heat should change as time goes on. This might make more sense if you've taken calculus, but if you know something should change at every moment in time, you can construct a perfect image of it just by combining all of the little changes.

Specifically, the equation tells us that the change in heat, *du/dt*, is equal to the *Laplacian* of the heat, Δ*u*. The Laplacian tells us how much the value at a certain point differs from its neighbors, which should make sense: if the heat in a certain area is really different from its neighbors, it should change a lot. If it's the same as its neighbors, it shouldn't change at all.