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
References
- ↑ "Andreas Rejbrand’s Website:The “Persian rugs” cellular automaton Rule". Retrieved on September 5, 2022.
- ↑ ^{2.0} ^{2.1} ^{2.2} Interesting Rules at Fano Experimental Web Server (archived copy)
- ↑ "Paul Rendell's Holstein Cellular Automata Page". Retrieved on September 5, 2022.
- ↑ "Cool Universes in the Cosmos of Cellular Automata:Oscillators Rule". Retrieved on September 5, 2022.
- ↑ ^{5.0} ^{5.1} "Cellular Automata Laboratory:Cellular Automata Theory-Vote and Other Totalistic Rules". Retrieved on September 5, 2022.
External links
- Cellular Automata rules lexicon
- Interesting Rules at Fano Experimental Web Server (archived copy)
- University of Groningen Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence: Cellular Automata Lab - Game of Life