Interactive · the narrow band

Change the rule. Find the band.

One grid, one rule. A cell is born with exactly three neighbours — you decide at which neighbour counts it survives. Click through the numbers and watch the system react live: most rules make it collapse or clog. Only a narrow band carries structure.

Generation 0

A cell is born with exactly 3 neighbours. It survives at these neighbour counts:

Survives at these neighbour counts — click to toggle

Click a number on or off — the rule changes instantly, no restart. Birth stays fixed at 3.

born at 3 · survives at 2, 3
living cells 0 · 0.0 % of the grid
too littlethe narrow bandtoo much
persists · stablechanges · moving

Why this matters

Try it: pull the window tighter than 2–3 and the system dies out. Pull it wider and it clogs until nothing is moving any more. Only a few rules — around “2 or 3” — carry patterns that stay stable and move at the same time.

That is what “the narrow band” means: a working system is not robust against its rules, it is highly sensitive to them. A small change decides whether order emerges or everything collapses — and the very efficiency that makes it valuable amplifies whatever rule you give it. That is why quality is not optional.