List of Life-like cellular automata
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The following is a list of notable Life-like cellular automata. A more up-to-date and complete list can be found on Catagolue.
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 | 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. 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/S2 | This rule has 6 small still lives, the tub, the hive, the aircraft carrier, the loaf, and the mango, and the pond. However, there are no still lives 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. No still lives with more than 8 cells have appeared in B3/S2/C1. | |
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 | 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 | |
B345/S2 | Blinkers | |
B345/S4567 | Assimilation | A very stable rule that forms permanent diamond-shaped patterns with partially filled interiors. Like in 2x2, 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 | |
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. Like in 2x2, 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. |
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 oblique spaceships. |
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. |