2×2
B36/S125 — a rule that preserves block structure
Patterns made of 2×2 blocks stay made of 2×2 blocks, which gives the whole grid a coarse, modular look.
How it works
In plain English, before the notation
This rule has a property no other rule here shares: if your starting pattern is made entirely of 2×2 blocks aligned to a grid, every later step will be too. The automaton effectively runs on a coarser grid, four cells at a time, which gives everything a chunky, modular appearance.
Test the block property
- Press Clear (C), open the Stamp picker, and place several "Block" stamps aligned to the same 2-cell spacing.
- Press Play. Everything that happens stays on the block grid.
- Now place a single cell with the Pencil to break the alignment, and watch the constraint disappear.
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 2×2 rule is a standard example of block emulation: one cellular automaton behaving, on a restricted set of inputs, exactly like a different and simpler automaton on a coarser grid. It also has replicators, which is why it appears alongside HighLife in discussions of self-copying rules.
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 in {3,6}) or (state = 1 and n in {1,2,5}); otherwise 0
B36/S125. The block-preserving property is a theorem about this specific pairing of sets, not something visible from the notation alone.
Coarse-grained dynamics
On block-aligned starts the rule behaves like a much simpler automaton:
- Aligned 2×2 blocks are preserved indefinitely, so the effective grid is half the resolution in each direction.
- Replicating patterns exist, as in HighLife.
- Starts that are not block-aligned behave like an ordinary Life-like rule with no special structure.
- The visual effect is distinctive: everything looks built out of the same modular units.
Emulation rather than construction
The interesting computational fact about this rule is that it contains a simpler automaton inside itself, which is a different kind of result from building logic gates.
Coarse-graining
Physics regularly replaces a fine-grained model with a coarser one that reproduces the same large-scale behaviour. This rule is a clean, exact instance of that idea rather than an approximation.
Things to try
- Turn Grid Lines on (G) and set Cell Scale to 8px — the block structure is hard to see at smaller scales.
- Place blocks at deliberately misaligned offsets and compare the result with the aligned case.
- Press Soup (R): random starts are not aligned, so the special behaviour will not appear.