Theoretically, we're solving Laplace's Equation (a special case of the Poisson Problem). In practice, we're just doing repeated neighborhood averaging:

new temperature (x,y) = 0.25 * (temperature(x-1,y) + temperature(x+1,y) + temperature(x,y-1) + temperature(x,y+1));

Typically boundary elements, which have no neighbor on one side, are computed in a totally different way, such as:

- Imposing a fixed value, like an inside or outside temperature
- Copying over a value from the interior, making an insulating boundary