Day & Night
B3678/S34678 — the rule reads the same if you swap on for off
Swap every live cell for a dead one and the rule behaves identically, so the same structures work in sparse space and in solid matter.
How it works
In plain English, before the notation
This rule has an unusual property: if you invert the whole grid, turning every live cell dead and every dead cell alive, the pattern evolves in exactly the mirrored way. That means anything that works in empty space also works, inverted, inside a solid block. The screen tends to split into light regions and dark regions, each running the same physics.
See the symmetry directly
- Press Soup (R) — the default density here is 35%, higher than most rules, because this rule needs company on both sides.
- Press Play and let it settle into light and dark regions.
- Look at a structure inside a dark region and find its counterpart in a light one. They are the same object with the colours exchanged.
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
Found by Nathan Thompson in 1997, in a search specifically for a rule that is symmetric under inversion. Such rules are rare, and Day & Night is the best-known example that also produces interesting behaviour rather than immediately saturating or dying.
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 {3,6,7,8}) or (state = 1 and n in {3,4,6,7,8}); otherwise 0
B3678/S34678. The self-complementary property comes from a specific relation between the two sets: a rule is symmetric under inversion when survival on k corresponds to birth on 8−k, and vice versa.
Two backgrounds, one set of physics
Every structure comes in a pair — one version drawn in live cells on empty space, and its inverse drawn in empty cells inside a solid region:
- The grid separates into large light and dark domains with active, structured boundaries.
- Spaceships and oscillators exist on both backgrounds, and a spaceship can in principle cross from one to the other.
- Because both backgrounds support structure, the boundary between them is where most of the activity happens.
- Low-density starts behave very differently from high-density ones, which is not true of most Life-like rules.
Rich enough to build with
Day & Night supports gliders, guns and reflectors, and a substantial pattern catalogue has been assembled for it.
Phase separation
The way the grid divides into two competing regions, each stable in its interior and active only at the shared border, resembles what happens when a mixture separates into two phases. The analogy is about the geometry of the boundary, not the underlying thermodynamics.
Things to try
- Use the Eraser inside a dark region to carve a shape, then watch it evolve as though it were a live pattern on empty space.
- This rule is one of the few where changing Soup density substantially changes the outcome. Try it well below and well above 50%.
- Set Cell Scale to 2px for a large grid — the domain structure is much clearer at scale.