Maze
B3/S12345 — Conway’s birth rule with much more generous survival
Generous survival conditions let a few seed cells sprawl outwards into branching corridors one cell wide.
How it works
In plain English, before the notation
Births work exactly as in Conway’s rule, but a live cell now survives with anywhere from one to five neighbours. That extra tolerance means structures persist long enough to keep extending, and what they extend into is a network of one-cell-wide corridors — which is why the rule is called Maze.
Grow corridors from a few seeds
- Press Soup (R) — the default density here is a sparse 8%.
- Press Play and watch corridors extend from each seed and knit together.
- Turn on Grid Lines (G) to confirm the corridors really are one cell wide.
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
Maze comes from Mirek Wójtowicz’s MCell rule collection, which catalogued and named a large number of Life-like rules in the 1990s. A close relative, Mazectric (B3/S1234), produces noticeably longer straight corridors — dropping the 5 from the survival set is the only difference.
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 = 0 and n = 3) or (state = 1 and n in {1,2,3,4,5}); otherwise 0
B3/S12345. Compare with Conway’s B3/S23: the birth condition is identical and only the survival set has been widened.
Corridors and junctions
The characteristic output is a maze-like network that grows and then locks:
- Corridors are consistently one cell wide, because a wider corridor puts interior cells over the survival limit.
- Growth continues until every corridor end is blocked by other structure.
- The resulting network is genuinely maze-like — connected, with dead ends and loops — though it is not generated by any maze algorithm.
- Very sparse starts produce the largest and most legible mazes; dense starts jam almost immediately.
Not studied for computation
This rule is used for its output, not for what can be built inside it.
Procedural generation
Cellular automata of this kind are used in practice to generate cave systems and dungeon layouts, because they produce connected, organic-looking structures from a random seed and a handful of parameters.
Things to try
- Change Soup density: 2% gives long sweeping corridors, 15% gives a dense tangle.
- Pause once growth stops, then use the Pencil to add three cells at a dead end and restart growth from there.
- Set Cell Scale to 3px or lower to fit a maze large enough to look at as a whole.