Variants and other worlds

Life-like rules

A rule is "Life-like" if it uses the same board as Life - two states, square grid, Moore neighbourhood - and differs only in which neighbour counts cause birth and survival. Every rule in this table can be run in the Lab: pick it from the Rules panel, or type the rule string directly.

Changing the board

The bigger jumps come from changing something other than the digit list.

Different neighbourhoods

The von Neumann neighbourhood uses only the four edge-adjacent cells, which produces diamond-shaped growth instead of square. Larger than Life extends the radius to 5, 10 or more cells and replaces the digit lists with numeric ranges; as the radius grows, the behaviour converges on continuous automata. Hexagonal lattices give each cell six neighbours and remove the awkward distinction between edge and corner adjacency entirely.

More states

Generations rules add a decay chain: a dying cell passes through several intermediate states before becoming empty, which produces trails and travelling waves. Brian's Brain is the minimal case - three states, one refractory generation - and it produces a world where almost nothing stands still. Try Brian's Brain.

Purpose-built automata

WireWorld was designed backwards from the intended result. Its four states - empty, copper wire, electron head, electron tail - and its one interesting rule (wire becomes a head if exactly one or two neighbours are heads) were chosen to make electronics easy to build rather than to be mathematically minimal. It works: people have built adders, displays and a prime-number sieve. Try WireWorld.

Agents instead of fields

Langton's Ant and the wider family of turmites put a moving read-write head on the grid rather than updating everything at once. With two colours and the turn sequence RL you get the famous highway. Other turn strings produce symmetric growths, spirals, or chaos that never resolves. Try Langton's Ant.

Giving the grid a state of its own

Every variation above changes the cells. A less-explored move is to give the squares a state that the cells depend on. Antiot's Field - a rule written for this site rather than taken from the literature - does exactly that: each square holds a quantity of fertility, a living cell grazes the square beneath it every generation, and empty squares recover slowly. Birth requires fertile ground as well as the right neighbour count.

The consequence is that a still life eats its own patch and starves, and so does an oscillator, because it keeps returning to the same squares. Only patterns that travel reach fresh ground indefinitely. Run a random soup under it for ten thousand generations and the population falls from around seven thousand cells to exactly ten: two gliders, and nothing else at all. Run Antiot's Field.

Continuous automata

SmoothLife (Stephan Rafler, 2011) generalises Life to continuous space, continuous time and continuous states, replacing the neighbour count with an integral over a ring-shaped kernel. The gliders survive the transition, arriving as smooth blobs that slide rather than step.

Lenia (Bert Wang-Chak Chan, 2019) pushes this further with arbitrary kernels and growth functions, and has yielded hundreds of distinct self-organising "species" - things that swim, rotate, split and repair themselves. Later work made the whole system differentiable, so the rules themselves can be learned by gradient descent. Neural cellular automata take that to its conclusion: a small neural network as the transition rule, trained so that a pattern grows into a target image and regenerates when damaged.

More dimensions

Three-dimensional Life-like rules exist - Carter Bays established a framework in the 1980s and found rules such as 5766 that support gliders in 3D. They are harder to look at than to define, which is largely why they have received less attention.

Why bother with variants

Partly for the same reason people climb hills. But the survey also makes a real point: Life's richness is not an accident of B3/S23 alone, nor is it common. Most of the 262,144 Life-like rules produce either a dead board or grey mush within a hundred generations. Only a thin band produces anything worth watching, and that band is exactly the one where local structures can persist and interact. Complexity is rare, but it is not unique - and every rule in that band produces its own zoo, with its own gliders, its own still lifes, and its own community of people cataloguing them.