Cellular Automata From First Principles 50: Vectorize the Update Loop

Mon, 10 Aug 2026 20:53:00 +0100

Cellular Automata From First Principles 50: Vectorize the Update Loop

A cellular automaton is local.

That does not mean we should update it cell by cell in Python.

For dense grids, the same local rule is applied everywhere. That regularity is exactly what array programming is good at.

Start with the obvious implementation

def life_step_slow(grid):
    height, width = grid.shape
    next_grid = np.zeros_like(grid)

    for y in range(height):
        for x in range(width):
            total = 0
            for dy in (-1, 0, 1):
                for dx in (-1, 0, 1):
                    if dx == 0 and dy == 0:
                        continue
                    total += grid[(y + dy) % height, (x + dx) % width]

            alive = grid[y, x] == 1
            next_grid[y, x] = (
                total == 3 or (alive and total == 2)
            )

    return next_grid

This is useful because it states the mechanism clearly.

Vectorization on Programmer.ie: Modern AI programming

Cellular Automata From First Principles 50: Vectorize the Update Loop

Cellular Automata From First Principles 50: Vectorize the Update Loop

Start with the obvious implementation