Cellular Automata From First Principles 11: Diffusion as Local Exchange

Mon, 10 Aug 2026 18:40:00 +0100

Until now most cells have stored discrete state:

0 / 1
empty / tree / fire
road / car

Now let each cell store a continuous quantity.

For diffusion:

state[y, x] = concentration

The local transition is no longer birth, death or movement.

It is local exchange.

Start with a pulse

import numpy as np

size = 121

grid = np.zeros(
    (size, size),
    dtype=np.float64,
)

grid[
    size // 2,
    size // 2,
] = 1.0

At the beginning one cell contains all the concentration.