List of Life-like cellular automata

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The following is a list of Life-like cellular automata. A more up-to-date and complete list can be found on Catagolue.

Rulestring Name Description
B0123478/S01234678 AntiLife The black/white reversal of Conway's Game of Life.
B0123478/S34678 InverseLife A rule by Jason Rampe, showing similar oscillators and gliders to Conway's Game of Life. The black/white reversal of B3678/S23.
B1/S012345678 H-trees An exploding rule where H-shaped branches grow from pattern borders.
B1/S1 Gnarl A simple exploding rule by Kellie Evans that forms complex patterns from even a single live cell.
B1357/S1357 Replicator A rule in which every pattern is a replicator.
B1357/S02468 Fredkin A rule in which, like Replicator, every pattern is a replicator. Also known as "Replicator 2".
B2/S Seeds An exploding rule by Brian Silverman 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[1] An exploding rule in which every cell dies in 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 Small masses of solid living cells flicker in and out of existence. Some reach a critical mass and begin to slowly grow. Also known as "Ice nine".
B3/S012345678 Life without death An expanding rule that produces complex flakes, featuring dense wickstretchers named "ladder". 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/S0248 Star Trek
B3/S12 Flock Patterns tend to quickly settle into dominoes, 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 A rule similar to Mazectric but without S3. A slow burn from almost any starting pattern, resulting in a rusting away of the local continuum.
B3/S128 EightFlock
B3/S13 LowLife
B3/S2 This rule has 6 small still lifes, the tub, the hive, the aircraft carrier, the loaf, the mango, and the pond. However, there are no still lifes with more than 8 and less than 20 cells. There are also a few common oscillators, including the blinker and the toad, and lots of rare ones.
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/S4567 Lifeguard 2
B3/S45678 Coral An exploding rule in which patterns grow slowly and form coral-like textures.
B34/S34 3-4 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[2]
B345/S2 Blinkers
B345/S4567 Assimilation A very stable rule that forms permanent diamond-shaped patterns with partially filled interiors. Like in 2×2, patterns made of blocks will permanently remain made of blocks.
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 Gems Minor An exploding rule with many smaller high-period oscillators and a c/2068 spaceship.
B35/S234578 Land Rush Expanding chaos organizing itself into plowed fields.
B3567/S15678 Bugs[2]
B35678/S4678 Holstein[3] A rule symmetric under on-off reversal. Black regions are surrounded by froth and tend to eventually collapse starting from the corners, but can be stabilized in various ways by oscillators on their boundaries. There are also three known spaceships.
B35678/S5678 Diamoeba A chaotic pattern that forms large diamonds with chaotically oscillating boundaries. Known to have quadratically-growing patterns. Like in 2×2, patterns made of blocks will permanently remain made of blocks.
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.
B3578/S24678 Geology A very well-balanced and chaotic rule that forms large "continents" of live cells surrounded by chaos at a roughly 50% density, but they eventually erode away into smaller "islands". It is symmetric under on-off reversal.
B36/S12 HighFlock
B36/S125 2×2 A chaotic rule with many simple still lifes, oscillators and spaceships. Its name comes from the fact that it sends patterns made up of 2 × 2 blocks to patterns made up of 2 × 2 blocks.
B36/S128 IronFlock
B36/S23 HighLife A chaotic rule very similar to Conway's Life that is of interest because it has a simple replicator.
B36/S234578 Land Rush 2 An exploding rule that got confused with Land Rush, likely due to a typo. It does contain a period 4 orthogonal c/2 ship.
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/S238 IronLife
B36/S245 Logarithmic replicator rule Name comes from a dirty orthogonal replicator.
B367/S125678 Slow Blob
B367/S23 DrighLife
B3678/S1258 2x2 2
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/S128 LowFlockDeath
B368/S236 Life SkyHigh
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 Morley 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 "Move".
B37/S012345678 DryLife without Death
B37/S12 DryFlock
B37/S1234 Mazectric with Mice Some "mice" run back and forth in the halls of the maze.
B37/S12345 Maze with Mice Similar to B37/S1234, Some "mice" run back and forth in the continually-stretching halls of the maze.
B37/S23 DryLife An exploding rule closely related to Conway's Life, named after the fact that standard spaceships bigger than the glider do not function in the rule. Has a small 9c/28 orthogonal 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/S012345678 Pedestrian Life without Death
B38/S12 Pedestrian Flock
B38/S128 HoneyFlock
B38/S23 Pedestrian Life A close Life variant with a number of distinctive natural growth patterns and (5,2)c/190 oblique spaceships.
B38/S238 HoneyLife
B45/S12345 Electrified Maze
B45/S1235 Oscillators Rule[4] Random patterns shrink to tiny oscillators, with periods anywhere between 1 ("still lifes") and 16. Larger periods are rare.
B45678/S2345 Walled cities A stable rule by David Macfarlane that forms centers of pseudo-random activity separated by walls.
B45678/S5678 Majority[2]
B4678/S35678 Vote 4/5[5] A modification of the standard Gérard Vichniac voting rule, also known as "Anneal", used as a model for majority voting.
B48/S234 Lifeguard 1
B56/S14568 Rings 'n' Slugs
B5678/S45678 Vote[5] Standard Gérard Vichniac voting rule, also known as "Majority", used as a model for majority voting.

See also


  1. "Andreas Rejbrand’s Website:The “Persian rugs” cellular automaton Rule". Retrieved on September 5, 2022.
  2. 2.0 2.1 2.2 Interesting Rules at Fano Experimental Web Server (archived copy)
  3. "Paul Rendell's Holstein Cellular Automata Page". Retrieved on September 5, 2022.
  4. "Cool Universes in the Cosmos of Cellular Automata:Oscillators Rule". Retrieved on September 5, 2022.
  5. 5.0 5.1 "Cellular Automata Laboratory:Cellular Automata Theory-Vote and Other Totalistic Rules". Retrieved on September 5, 2022.

External links