OpenWorldLab
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Life-like rules Two-state rule on a square grid, 8 neighbours

Seeds

B2/S — nothing survives its own turn

Nothing survives its own turn, so every pattern is pure chain reaction. Small clusters explode into branching sparks.

How it works

In plain English, before the notation

The survival list is empty, so every live cell dies at the end of every step, without exception. Anything you see on the second step was born on the first. Because a dead cell needs only two live neighbours to be born, this does not lead to extinction — it leads to a chain reaction that races outwards and leaves nothing standing behind it.

Every live cell dies at the next step. There are no exceptions and no still lifes.
A dead cell with exactly two live neighbours becomes alive.
Two neighbours is a very easy condition to meet, so most starting patterns expand rather than die out.

Start a chain reaction

  1. Open Presets and load "Seeds Chain Reaction", or press Clear (C) and draw two adjacent cells with the Pencil.
  2. Press Play. Two cells alone produce a small pattern that travels; a slightly larger cluster usually explodes.
  3. Open Settings and switch Grid Boundaries to Solid walls, then watch the expanding front stop at the edge instead of wrapping round to the other side.

Starting configurations

Loads straight into the simulator

Try 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.

B2
B
Toggle:
Snone
S
Toggle:
B2/S Likely: chain reactions only
Birth: A dead cell becomes alive with 2 live neighbours.
Survival: No live cell survives its own turn — every live cell dies at every step.

Well-known rules

Where it came from

The rule is credited to Brian Silverman and was popularised through Mirek Wójtowicz’s MCell rule collection in the 1990s. It is the standard example of a rule with an empty survival set that nonetheless does something.

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 = 2); otherwise 0

B2/S. Nothing appears after the S because the survival set is empty — no neighbour count lets a live cell reach the next step.

Everything moves, because nothing can stand still

With no survival, the only stable behaviour is motion, and Seeds has a lot of it:

  • Small spaceships travel at the maximum possible speed of one cell per step — the theoretical limit for any rule of this kind.
  • Most random starts expand as an irregular front, filling the grid within a few hundred steps.
  • A handful of very small seeds do the opposite and vanish within a few steps. Which of the two happens is extremely sensitive to the starting arrangement.
  • There are no still lifes at all, which makes Seeds one of the few Life-like rules where the debris field is always empty.

Explosive rather than complex

Seeds sits well past the point where localised structures can survive next to each other; almost any interaction spreads.

No universality proof is known. In Wolfram’s classification the behaviour is Class 3 — chaotic and expansive rather than computationally structured.

Fronts that consume their own fuel

Combustion frontsDielectric breakdownExcitable media

The shape of the expanding front — branching, irregular, never doubling back — resembles a spark discharge or a flame in a thin sheet of fuel, both of which move forwards because the material behind them is spent. The resemblance is qualitative; Seeds has no notion of energy or concentration.

Things to try

  • Density matters more here than anywhere else. Anything above about 5% fills the grid immediately; 1–2% lets you watch individual fronts.
  • Reduce Speed to around 10 fps in Settings — at 30 fps most of what happens is over before it registers.
  • Draw a diagonal wall of cells and fire a small pattern into it to see how the front reorganises.

Frequently Asked Questions

No. The survival set is empty, so every live cell is guaranteed to die at the end of the step. Any apparently stationary pattern is really a small oscillator being rebuilt in place.

References

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