gdd.md

@@ -28,6 +28,27 @@ Add a tick counter as a UI element.
 Diffusing should use 'pull' operations; tiles should pull values from surrounding tiles.
 This is an attempt to think forwards to parallelising computation of diffusiong - ideally using the GPU.
 
+#### Diffusion Algorithm
+
+Diffusion is modelled as two-dimensional steady-state heat conduction.
+This means that the amount of a value does not change between the start and end of the computation of the diffusion step.
+The value at one 2D location is calculated based on the values of itself and its neighbours in the previous step.
+A diffusion coefficient controls the rate of diffusion.
+
+[Video explanation](https://www.youtube.com/watch?v=RGbV7T_iWT8)
+[Derivation](https://www.tec-science.com/thermodynamics/heat/heat-equation-diffusion-equation/)
+
+Implementation:
+
+```cs
+private float TransferHeat(float t0, float alpha, float nx, float ny, float px, float py)
+{
+    float d2tdx2 = nx - 2 * t0 + px;
+    float d2tdy2 = ny - 2 * t0 + py;
+    return t0 + alpha * (d2tdx2 + d2tdy2);
+}
+```
+
 ### Tile Types
 
 Tiles start as wild tiles.