List of Life-like rules
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The following is a list of Life-like rules. 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. | |
B028/S0124 | Invertamaze | A strobing rule which makes mazes that invert themselves each generation (SEIZURE WARNING). | |
B08/S4 | Neon Blobs | A strobing rule in which patterns become neon-like explosive patterns. | |
B1/S012345678 | H-trees | An exploding rule where H-shaped branches grow from pattern borders. | |
B1/S014567 | Fuzz | An exploding rule in which solid patterns appear. | |
B1/S1 | Gnarl | A simple exploding rule by Kellie Evans that forms complex patterns from even a single live cell. | |
B1/S134567 | Snakeskin | A rule in which patterns explode and form snake-like patterns. | |
B12678/S15678 | Solid islands grow amongst static | A rule in which patterns grow exponentially and form solid patters inside static-like patterns. | |
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". | |
B1358/S0247 | Feux | An explosive rule where patterns turn into replicators and flash in and out of existence. | |
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. | |
B2/S13 | B2/S13 | An exploding rule, one of the few B2 life-like rules that has a replicator. | |
B2/S2345678 | B2/S2345678 | An exploding rule, with still lifes that may form indestructible barriers to growth, which can be used as casing for single-use wires, with which logic gates can be constructed.^{[1]} | |
B234/S | Serviettes^{[2]} | 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". | |
B25/S4 | B25/S4 | An exploding rule, it has a one-dimensional asymmetric replicator. | |
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 | 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/S35 | Dance | ||
B34/S456 | Bacteria^{[3]} | ||
B345/S0456 | Never happy | An explosive rule where patterns slowly form diamond-like shapes and slowly explode. | |
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. | |
B34568/S15678 | Spiral and polygonal growth | A rule with "plow" structures that move along an edge of a polygon, increasing its size (turning corners and thickening it as they go), corner-extenders that create these in their wake, and nontrivial interactions based on these (such as a 16-cell methuselah that takes 12127116559 generations to become a period-2 oscillator)^{[4]} | |
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/S23 | Grounded Life | A stable rule "one outer-totalistic condition away from Life", where neither of the standard spaceships works, and the most common spaceship is an orthogonal 2c/5 spaceship called "Glider 3736". | |
B35/S234578 | Land Rush | Expanding chaos organizing itself into plowed fields. | |
B35/S236 | B35/S236 | An exploding rule explored by Dean Hickerson and David Eppstein.^{[5]} | |
B3567/S15678 | Bugs^{[3]} | ||
B35678/S34567 | Cheerios | An explosive rule where patterns explode while "cheerios" form in the chaotic mess. | |
B35678/S4678 | Holstein^{[6]} | 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 | Sqrt replicator rule | Name comes from a dirty orthogonal replicator. | |
B367/S125678 | Slow Blob | ||
B367/S23 | DrighLife | A mix between DryLife and HighLife | |
B3678/S1258 | 2x2 2 | ||
B3678/S135678 | Castles | A rule where patterns almost explode into castle-like stable patterns. | |
B3678/S23 | B3678/S23 | Black/white reversal of InverseLife. | |
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/S12578 | B368/S12578 | An exploding 2x2-like rule with a small 4c/13o replicator, of which guns and W110 unit cells had been constructed ^{[7]} | |
B368/S128 | LowFlockDeath | ||
B368/S236 | Life SkyHigh | A rule that is similar to HighLife but adds a B8 and S6 to the rulestring, hence, the name "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 | An explosive rule, some of the patterns can turn into wickstretchers. | |
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 | A mix between Pedestrian Life and 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^{[8]} | 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^{[3]} | ||
B4678/S35678 | Vote 4/5^{[9]} | 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 | A rule in which patterns stabilize into "Rings" and "Slugs". | |
B5678/S45678 | Vote^{[9]} | Standard Gérard Vichniac voting rule, also known as "Majority", used as a model for majority voting. |
See also
References
- ↑ Genaro J. Martínez, Andrew Adamatzky, Harold V. McIntosh, Ben De Lacy Costello, Computation by competing patterns: Life rule B2/S2345678, 2008
- ↑ "Andreas Rejbrand’s Website:The “Persian rugs” cellular automaton Rule". Retrieved on September 5, 2022.
- ↑ ^{3.0} ^{3.1} ^{3.2} Interesting Rules at Fano Experimental Web Server (archived copy)
- ↑ Dean Hickerson, "B34568/S15678"
- ↑ D. Eppstein. "B35/S236".
- ↑ "Paul Rendell's Holstein Cellular Automata Page". Retrieved on September 5, 2022.
- ↑ D. Eppstein. "Replicators: B368/S12578".
- ↑ "Cool Universes in the Cosmos of Cellular Automata:Oscillators Rule". Retrieved on September 5, 2022.
- ↑ ^{9.0} ^{9.1} "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