HighLife
B36/S23 — Conway’s rule plus one extra way to be born
Conway’s rule plus one extra birth condition, which is enough to make a small pattern that copies itself every twelve steps.
How it works
In plain English, before the notation
HighLife is Conway’s Game of Life with a single change: a dead cell also comes to life when it has exactly six live neighbours. Almost everything from Life still works here — gliders, blocks, blinkers. But the extra rule makes one new thing possible that Life cannot do naturally: a small pattern that builds a copy of itself.
Watch a pattern copy itself
- Open Presets and load "Self-Copying Pattern".
- Press Play. After 12 steps there are two copies; after 24 there are four.
- Let it run for a few hundred steps and step back from the screen — the copies do not fill space evenly, they leave triangular gaps.
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
Nathan Thompson found the rule in December 1994 while searching outer-totalistic rules for one that supported self-reproduction without an elaborate engineered mechanism.
The point of the discovery was that self-reproduction did not need to be designed. Von Neumann’s self-replicating machine required a carefully constructed universal constructor; HighLife’s replicator is twelve cells that someone stumbled across.
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 {2, 3}); otherwise 0
B36/S23. The added 6 in the birth set is what separates this rule from Conway’s B3/S23; every other transition is identical.
The replicator and its consequences
HighLife inherits Life’s still lifes, oscillators and gliders, and adds patterns built on repeated copying:
- The replicator is a 12-cell pattern that becomes two copies of itself after 12 steps.
- Copies of copies arrange themselves in the same way a Sierpiński triangle does, so the population grows roughly as t^1.58 rather than t².
- Two replicators sent at each other can annihilate, or leave behind gliders and other debris, depending on the offset.
- The bomber is a naturally occurring spaceship with a period of 48 that sheds debris as it travels.
Has the ingredients, less thoroughly explored
HighLife supports gliders, glider guns and reflectors — the components normally used to build logic in a Life-like rule — and constructions using the replicator have been assembled.
Self-reproduction without a blueprint
The replicator is often cited in discussions of the origin of self-copying systems, because it shows that reproduction can fall out of a rule rather than being engineered into it. The analogy to biological reproduction stops there: the replicator has no genome and copies nothing but its own shape.
Things to try
- Load the replicator preset, pause, and use the Pencil to add a single cell next to it. Small perturbations usually destroy the copying behaviour.
- Switch the rule to Conway’s Game of Life while the replicator is on screen — the same pattern settles into a small oscillator, which shows how much rests on that one extra birth condition.
- Press Soup (R) at 20% density and compare the settled debris with Conway’s. HighLife leaves noticeably more of it.