Diamoeba
B35678/S5678 — survival requires a crowd
Needs dense company to survive. Random starts collapse into solid diamond-shaped blobs with restless, rippling edges.
How it works
In plain English, before the notation
A cell needs at least five live neighbours to survive, which is a lot — an isolated cell has no chance and even a small cluster falls apart. What survives is bulk. Random starts contract into solid blobs that square themselves off into diamonds, with edges that keep shifting without ever settling down.
Find the survival threshold
- Press Soup (R) at the default 40% density and press Play. Most of the field dies back, and what remains contracts into diamonds.
- Press Clear (C) and use the Pencil with Brush Size 5 (in Settings) to draw a solid square. Watch whether it grows or shrinks.
- Repeat with progressively smaller squares to find where the behaviour flips.
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
Named and catalogued by Dean Hickerson. Diamoeba is best known for an open question: whether the rule has a spaceship at all. A substantial reward was offered for finding one, and as of writing none has been reported.
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 {3,5,6,7,8}) or (state = 1 and n in {5,6,7,8}); otherwise 0
B35678/S5678. The high survival threshold is the defining feature — most Life-like rules allow survival at 2 or 3 neighbours.
Bulk survives, detail does not
Almost everything interesting happens at the boundary of a blob:
- Random starts above roughly 30% density contract into one or more diamond-shaped regions.
- Starts below that threshold usually die out completely within a few dozen steps.
- The diamond edges never stop moving, so the pattern is stable in outline but never actually still.
- Whether Diamoeba has any spaceship is an open question and has been for decades.
Little is known
Without spaceships there is no obvious way to carry a signal from one place to another, which is the usual starting point for building logic in a Life-like rule.
Surface tension
A rule that rewards being surrounded and punishes being exposed produces something that behaves like a liquid drop: it minimises its boundary, resists being broken up, and merges when two regions touch.
Things to try
- Draw two separate blobs close together and watch them merge — the merge is faster than either blob’s own boundary motion.
- Try Soup (R) at 25% and again at 45%. The difference between "dies out" and "forms diamonds" is sharp.
- Increase Speed to 60 fps in Settings; the blob outlines take a while to stabilise.