List of Life-like cellular automata

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The following is a list of notable Life-like cellular automata.

Outer-totalistic rules

Rulestring Name Description
B0123478/S01234678 AntiLife
B012345678/S34678 InverseLife
B1/S012345678 H-trees
B1/S1 Gnarl A simple exploding rule that forms complex patterns from even a single live cell.
B1357/S02468 Fredkin A rule in which, like Replicator, every pattern is a replicator. Also known as "Replicator 2".
B1357/S1357 Replicator A rule in which every pattern is a replicator.
B2/S Seeds An exploding rule in which every cell dies in every generation. It has many simple orthogonal spaceships, though it is in general difficult to create patterns that don't explode.
B2/S0 Live Free or Die An exploding rule in which only cells with no neighbors survive. It has many spaceships, puffers, and oscillators, some of infinitely extensible size and period.
B234/S Serviettes An exploding rule in which every cell dies every generation (like seeds). This rule is of interest because of the fabric-like beauty of the patterns that it produces. Also known as "Persian Rug".
B25678/S5678 Iceballs
B3/S012345678 Life without death An expanding rule that produces complex flakes. It also has important ladder patterns. Also known as "Flakes" or "Inkspot".
B3/S023 DotLife An exploding rule closely related to Conway's Life. The B-heptomino is a common infinite growth pattern in this rule, though it can be stabilized into a spaceship.
B3/S12 Flock Patterns tend to quickly settle into dominos, duoplets and period 2 oscillators. There is a common period 14 shuttle oscillator involving the pre-beehive.
B3/S1234 Mazectric An expanding rule that crystalizes to form maze-like designs that tend to be straighter (ie. have longer "halls") than the standard maze rule.
B3/S12345 Maze An expanding rule that crystalizes to form maze-like designs.
B3/S1237 SnowLife
B3/S124 Corrosion of Conformity
B3/S13 LowLife
B3/S23 Conway's Life A chaotic rule that is by far the most well-known and well-studied. It exhibits highly complex behavior.
B3/S238 EightLife Also known as "Pulsar Life".
B3/S45678 Coral An exploding rule in which patterns grow slowly and form coral-like textures.
B34/S34 34 Life An exploding rule that was initially thought to be a stable alternative to Conway's Life, until computer simulation found that most patterns tend to explode. It has many small oscillators and simple period 3 orthogonal and diagonal spaceships.
B34/S456 Bacteria
B345/S2 Blinkers
B345/S4567 Assimilation A very stable rule that forms permanent diamond-shaped patterns with partially filled interiors.
B345/S5 Long Life A stable rule that gets its name from the fact that it has many simple extremely high period oscillators.
B3457/S4568 Gems An exploding rule with many smaller high-period oscillators and a c/5648 spaceship.
B34578/S456 An exploding rule with many smaller high-period oscillators and a c/2068 spaceship.
B35/S234578 Land Rush
B3567/S15678 Bugs
B35678/S4678 Holstein
B35678/S5678 Diamoeba A chaotic pattern that forms large diamonds with chaotically oscillating boundaries. Known to have quadratically-growing patterns.
B357/S1358 Amoeba A chaotic rule that is well balanced between life and death; it forms patterns with chaotic interiors and wildly moving boundaries.
B357/S238 Pseudo Life A chaotic rule with evolution that resembles Conway's Life, but few patterns from Life work in this rule because the glider is unstable.
B36/S125 2x2 A chaotic rule with many simple still lifes, oscillators and spaceships. Its name comes from the fact that it sends patterns made up of 2x2 blocks to patterns made up of 2x2 blocks.
B36/S235 Blinker Life An exploding rule where the T-tetromino is a blinker puffer, appropriate because it evolves into traffic light in Life, also made of blinkers.
B36/S23 HighLife A chaotic rule very similar to Conway's Life that is of interest because it has a simple replicator.
B367/S125678 Slow Blob
B3678/S235678 Stains A stable rule in which most patterns tend to "fill in" bounded regions. Most nearby rules (such as coagulations) tend to explode.
B3678/S34678 Day & Night A stable rule that is symmetric under on-off reversal. Many patterns exhibiting highly complex behavior have been found for it.
B368/S238 LowDeath HighLife's replicator works in this rule, albeit with a different evolution sequence due to the result of B38/S23's pedestrian effect.
B368/S245 Move A rule in which random patterns tend to stabilize extremely quickly. Has a very common slow-moving spaceship and slow-moving puffer. Also known as "Morley".
B37/S1234 Mazectric with Mice
B37/S12345 Maze with Mice
B37/S23 DryLife An exploding rule closely related to Conway's Life, named after the fact that the standard spaceships bigger than the glider do not function in the rule. Has a small puffer based on the R-pentomino, which resembles the switch engine in the possibility of combining several to form a spaceship.
B378/S012345678 Plow World
B378/S235678 Coagulations An exploding rule in which patterns tend to expand forever, producing a thick "goo" as it does so. Suprisingly, Coagulations actually has one less birth condition than Stains.
B38/S23 Pedestrian Life Has a number of natural elementary (5,2)c/190 knightships.
B38/S238 HoneyLife
B45/S12345 Electrified Maze
B45678/S2345 Walled cities A stable rule that forms centers of pseudo-random activity separated by walls.
B4678/S35678 Vote 4/5 A modification of the standard Gérard Vichniac voting rule, also known as "Anneal", used as a model for majority voting.
B5678/S45678 Vote Standard Gérard Vichniac voting rule, also known as "Majority", used as a model for majority voting.

Non-totalistic rules

Also see Non-totalistic Life-like cellular automaton and Hensel notation for more information.
Rulestring Name Description
B3/S2-i34q tlife T-tetromino is a common c/5 orthogonal spaceship in this rule, giving it its name. Possibly the best-explored 2-dimensional 2-state non-totalistic cellular automaton.
B3-n/S23 DLife
B34ek5ak/S2-c34z GlideLife Has many small c/4 diagonal spaceships.
B36/S2-i34q tHighLife Has an orthogonal replicator sharing some traits with HighLife's diagonal replicator. A cross between tlife and HighLife.
B367/S2-i34q SilverLife A rule extremely rich in exotic speeds, including a p91 flamingoship.
B37/S2-i34q tDryLife Not explosive, unlike DryLife. Has a small 2c/23 orthogonal, a high-period diagonal pond puffer, and a ship camelpuffer, both of which have been stabilised. A cross between tlife and DryLife.
B2i34c/S2-i3 Salad Also has multiple small spaceships.
B3/S2-in34iw hlife3 R-pentomino is a common c/14 diagonal spaceship in this rule.
B2ae4i/S1e2in cb2 An unusual example of a non-exploding (i.e. eventually regularizes) rule with the transition B2a.
B3/S234iw alife There are common c/42 diagonal and 2c/7 diagonal spaceships.
B2c3ae4ai56c/S2-kn3-enq4 Allows for arbitrary spaceships speeds of c/n where n is an even number and greater than 3.
B2c3aj4nrt5i6c78/S1c23enr4aet5-iq67 Allows for arbitrary spaceships speeds of c/n where n is an odd number and greater than 4.