34 Life
B34/S34 — briefly proposed as a rival to Conway’s rule
Grows aggressively and squares itself off, filling the space with rectangular blocks that jostle at their borders.
How it works
In plain English, before the notation
Birth and survival use the same condition: three or four neighbours. That symmetry sounds elegant, and in the early 1970s it was suggested as a cleaner alternative to Conway’s rule. It turned out to grow far too aggressively — patterns expand into blocky rectangular masses instead of settling into the mix of stable and moving structures that makes Life worth watching.
See why it was set aside
- Press Clear (C) and use the Pencil to draw a small blob of five or six cells.
- Press Play. Instead of settling, it expands outwards and squares off.
- Switch the rule to Conway’s Game of Life and draw the same blob for comparison.
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
34 Life was among the alternatives considered in the years after the Game of Life appeared, when people were still testing which neighbour counts gave the most interesting behaviour. Its explosive growth is precisely the failure mode Conway had been tuning B3/S23 to avoid.
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 n in {3, 4}; otherwise 0
B34/S34. Because the birth and survival sets are identical, the next state depends only on the neighbour count and not at all on the cell’s current state — an unusual property called outer-totalistic degeneracy.
Expansion with square geometry
The rule is dominated by growth, but the growth has a definite shape:
- Small clusters expand into rectangular regions rather than round or diamond ones.
- Region borders remain active indefinitely, even once the interior is stable.
- Because the cell’s own state is irrelevant, the rule is unusually easy to reason about — but that same property is why it produces so little variety.
- Some oscillators exist, but they are far outnumbered by expanding structure.
Too expansive to build with
Constructing logic requires patterns that can sit next to each other without interfering. In 34 Life almost everything expands into its neighbour.
A useful negative example
34 Life is worth keeping in the catalogue as a control: it shows that a symmetric, tidy-looking rule is not automatically an interesting one, and that Conway’s specific choice of neighbour counts was not arbitrary.
Things to try
- Draw a straight line of ten cells and watch the ends behave differently from the middle.
- Reduce Soup density to 5% — even at that density the grid fills quickly.
- Turn on Grid Lines (G) and use Step (.) to see how the block edges advance one cell at a time.