Life Without Death
B3/S012345678 — cells are born as usual, and never die
Cells are born normally but never die, so the pattern grows into a permanent maze of corridors and dead ends.
How it works
In plain English, before the notation
Births follow Conway’s rule exactly: three neighbours and a dead cell comes alive. But the survival list contains every possible neighbour count, so once a cell is on it stays on forever. The result is a growing structure that can only ever add to itself, and it grows into thin corridors rather than solid blocks — because filling a region in solidly removes the three-neighbour conditions that growth depends on.
Grow a labyrinth
- Open Presets and load "Maze Growth" — a very sparse scattering of seeds.
- Press Play and let it run until the growth stops. Turn on Grid Lines (G) to see that the corridors are one cell wide.
- Press Clear (C) and draw a short diagonal line with the Pencil. A single line is enough to start a structure that spreads across the whole grid.
Starting configurations
Loads straight into the simulatorTry any rule
The catalogue covers a few dozen rules. Here you can run any of the 262,144 two-state grid rules, or any of the 256 one-dimensional rules, including ones nobody has written up.
Well-known rules
Where it came from
The rule was studied in the mid-1990s by David Griffeath and Cristopher Moore, who were interested in what happens when you remove death from Life. Their answer was that the rule stays computationally interesting: some structures behave like wires carrying signals, and predicting the outcome is provably hard.
The rule, precisely
What each cell looks at
The 8 cells touching it, including diagonals (the Moore neighbourhood)
What a cell can be
Two states per cell — 0 (dead) and 1 (alive) — on a square grid
The update
next = 1 if state = 1 or n = 3; otherwise 0
B3/S012345678. The survival set lists every count from 0 to 8, which is the notation’s way of saying that survival is unconditional.
Ladders, corridors and permanent structure
Because nothing is ever erased, the whole history of the pattern stays on screen:
- Growth is confined to the boundary; the interior freezes as soon as it is filled.
- Certain configurations form "ladders" — narrow structures that extend in a straight line at a constant speed, behaving much like wires.
- A ladder that runs into existing structure can stop, turn, or start new growth, which is what makes signal-carrying constructions possible.
- Sparse random starts grow the longest. Dense starts choke themselves off quickly, because a filled neighbourhood cannot host a three-neighbour birth.
Provably hard to shortcut
Moore and Griffeath showed that predicting the state of a cell in Life Without Death is P-complete. In practice that means there is no known way to jump ahead — to find out what happens, you have to run it.
Accretion and irreversible growth
Processes where material is added and never removed — frost on glass, mineral deposits, dendritic crystals — produce the same kind of branching, self-blocking structure for the same reason: growth is only possible where there is still an exposed edge.
Things to try
- Try a single diagonal line versus a single horizontal line. The two produce very different structures.
- Because nothing dies, this rule is worth watching at 60 fps in Settings — the interesting part is the shape it settles into, not any individual step.
- Press Clear (C) and draw two seeds far apart. Watch what happens where their growth fronts meet.