Task 1 of 5

The Neighbor Census

A cellular automaton is a world of cells, each one dead (0) or alive (1), where every cell's next state depends only on its immediate neighborhood. That makes it embarrassingly parallel: 256 cells, 256 threads, and no thread needs to know what any other thread is doing — only what the grid looked like.

Every rule in this module starts with the same question: how many of my eight neighbors are alive? This world is a torus — walk off the right edge, reappear on the left — and wrapping costs one modulo: (x + dx + 16) % 16. The + 16 is not decoration: JavaScript's % can go negative while the GPU's cannot, and adding the width first keeps both operands positive so CPU mode and GPU mode tell the same story.

sum the 3×3 block, subtract yourself — and the torus has no edges

Goal: make the kernel return, for every cell, the number of live cells among its eight neighbors — with the edges wrapped around.

Requirements

Visit the 3×3 block around this cell with nested dy/dx loops from −1 to 1
Wrap every coordinate: (this.thread.x + dx + 16) % 16 (and the same for y)
Don't count yourself — a cell is not its own neighbor

Hint 1 — the loop bounds

Two statically bounded loops: for (let dy = -1; dy < 2; dy++) around for (let dx = -1; dx < 2; dx++). Nine visits per cell.

Hint 2 — the subtract-self trick

Skipping the middle of the 3×3 block needs no if: sum all nine cells, then subtract grid[this.thread.y][this.thread.x] at the end. If you're dead you subtract 0; if you're alive you take yourself back out.

Hint 3 — the whole loop body

const yy = (this.thread.y + dy + 16) % 16;
const xx = (this.thread.x + dx + 16) % 16;
count += grid[yy][xx];

— then

return count - grid[this.thread.y][this.thread.x];

Same idea elsewhere

Reading a fixed window around your own coordinate is the stencil pattern, and it dominates real GPU workloads: CUDA stencil kernels tile the grid into shared memory with a one-cell "halo" so neighbors are read once, and WebGPU compute shaders do the same with workgroup memory.

All tasks in Cellular Automata

This page is an interactive exercise — the editor, the GPU runner and your saved progress need JavaScript. The text above is the full brief.