Within the Conway's Game of Life community, any rules other than B3/S23 are referred to as "other cellular automata" (OCA), a topic which has its own section on the ConwayLife.com forums and also its own namespace on the site's wiki. Some of these cellular automata have been chosen due to the similarity of their ruleset to Conway's Game of Life, while potentially having drastically different behavior. Others have been chosen due to having drastically different rules, while bearing a striking similarity to Life in terms of how they ultimately evolve. Although they pale in comparison to the original Life, many of these variants have received enough attention from the community to be listed here:
- The oldest and most well known Life variants come in the form of "outer-totalistic" rules, i.e. ones where a cell's state in the next generation is a function of (a) its current state and (b) the number of living neighbors it has:
- 2x2 (B36/S125) is somewhat lacking in specific patterns it has in common with B3/S23, but its general character is reminiscent of that of Life, in that it tends to eventually stabilize into a collection of still lifes, oscillators, spaceships, and occasional infinite linear growth. Its most notable feature, however, is that any pattern made entirely of an array of (correctly aligned) 2x2 blocks will evolve into another pattern of 2x2 blocks, thus emulating a "block cellular automaton" using the Margolus neighborhood.
- 3-4 Life (B34/S34) was first considered shortly after the invention of Conway's Game of Life, with some issues of the newsletter Lifeline dedicating a section to it in the early 1970s. It was initially assumed that patterns in this rule would tend to eventually stabilize, as with Life, but the advent of computers revealed that the rule was "explosive" in nature, with sufficiently large patterns tending to perpetually expand.
- Day & Night (B3678/S34678) is also extremely popular due to being an example of a "self-complementary" rule, i.e. toggling the state of every cell on the board will result in the pattern evolving the same way but with the cell states flipped. The rule is also quite rich with oscillators and spaceships of numerous distinct periods.
- Diamoeba (B35678/S5678) features large diamonds of live cells with an oscillating border. These diamonds tends to contract and expand in a somewhat organic way like amoebas, as the rule name implies, and overall larger soups tend to be very slowly explosive, while smaller soups die out. A few spaceships are known, as well as some examples of regular infinite growth in the form of wickstretchers and spacefillers.
- DotLife (B3/S023) allows for a lone cell to exist as a still life, hence the name. The addition of the S0 survival condition also results in the rule as a whole being explosive.
- EightLife (B3/S238) only differs from B3/S23 in the addition of the S8 condition, which is only relevant if all nine cells in a 3x3 block are alive, making it is one of the most similar outer-totalistic rules to Life. Still, the rule contains simple predecessors for certain patterns resulting in them being disproportionately common. These include the pulsar (which evolves from a pi-heptomino here, but is somewhat less common in Life) and the honeycomb (a 12-cell still life; evolves here from a line of six cells, but is very rare in Life).
- Gems (B3457/S4568) is a rule which explodes slowly in a diamond-shaped pattern, and is best known for a relatively small spaceship which travels extremely slowly: one cell every 5,648 generations. As of March 2023, this is the only known spaceship in this rule, and the slowest known elementary (i.e. non-engineered) spaceship across the entire outer-totalistic rulespace. It has a variant in the form of Gems Minor (B34578/S456), which features similar properties including its own slow-moving spaceship at one cell every 2,068 generations.
- HighLife (B36/S23) is the most famous Life variant of all, particularly due to the "replicator", a simple pattern which after 12 generations produces two copies of itself along a diagonal line. As the replicator continues to evolve, it is seen to emulate a one-dimensional cellular automaton referred to by Stephen Wolfram as "Rule 90". Combined with other patterns, the replicator can be stabilized in a variety of ways to produce high-period oscillators and spaceships. Other notable features include two fairly common oscillators with periods 7 and 10 respectively. This ruleset was first explored in 1994 by Nathan Thompson, although the name "HighLife" was coined by Conway himself, who admitted that the game was "so rich in nice things" that he would have preferred to have found it originally as opposed to B3/S23.
- Life Without Death (B3/S012345678), as its name suggests, explores what happens if cells are never allowed to die in Conway's Game of Life. The result is patterns that tend to grow infinitely, sometimes chaotically, but sometimes in the form of "ladders" that grow in a predictable way.
- Live Free or Die (B2/S0) is a close relative of Seeds (see below) and does allow for a single still life in the form of a lone dot thanks to the S0 condition. Otherwise, it similarly exhibits highly explosive behavior. This rule once had its own wiki, although it was hosted on the now-defunct site Wikispaces.
- The "logarithmic replicator rule" (B36/S245) features a rather unusual pattern which self-replicates but, unlike the HighLife replicator, does not do so cleanly, resulting in a more chaotic form of growth.
- LongLife (B345/S5) is characterized by diamond-shaped patterns that take an unusually long time to stabilize and may end up as extremely high-period oscillators. The most famous of these oscillators is the "white whale" which, despite being only 30 cells wide and 19 cells tall, has a period of 160,000,346 generations.
- Maze (B3/S12345) is a rule that produces an infinitely growing maze-like structure. This rule itself has its own variants, including Mazectric (B3/S1234) where the corridors are somewhat longer and straighter, as well as the "Mice" rules where B7 is added to the birth conditions, resulting in small oscillating regions which can be interpreted as "mice" pacing back and forth within the maze.
- Move (B368/S245) is a rule which evolves in a similarly stable manner to Life, but contains several oscillators and spaceships that do not work in B3/S23. It also features a common puffer pattern which resembles the logarithmic replicator from the closely-related B36/S245 (see above) and can be stabilized to produce guns such as the period-404 "Jason's bow".
- Pedestrian Life (B38/S23) is named due to its relative lack of traffic lights, as their main predecessor at one point contains a dead cell surrounded by eight live cells, meaning the B8 transition comes into play. Although the rule is generally highly similar to Life otherwise, it does feature several unusual high-period patterns that occur naturally, albeit infrequently. These include:
- a rotating four-barrelled gun which produces a glider every 106 generations at a 90-degree angle from the previous glider, giving it an overall period of 424
- an oblique spaceship which travels five cells in one direction and two cells in the other every 190 generations
- orthogonal puffers which travel at 57 cells every 488 generations and 31 cells every 589 generations respectively
- a puffer that travels almost orthogonally - 101 cells in one direction, and three cells in the other direction - every 1,884 generations
- Replicator (B1357/S1357) is a rule where every pattern exhibits self-replication, with the pattern at generation 2n consisting of eight copies of the original placed increasingly far apart. Also has its own variant in the form of Fredkin (B1357/S02468), which produces nine copies instead of eight.
- Seeds (B2/S) is a highly explosive rule. The B2 condition means that any edge with two orthogonally-connected live cells will expand in that direction producing a new edge of two orthogonally-connected cells, resulting in indefinite light-speed propagation and, usually, infinite growth. The lack of any survival conditions means that no still lifes can exist, though oscillators and spaceships still can, including ones traveling slower than light speed.
- Vote (B5678/S45678) is so named because the nine cells within the neighborhood (including the center cell itself) "vote" on the state of the center cell in the next generation. The result is that random patterns rapidly stabilize into mostly stationary blobs, with the occasional period-2 oscillating region.
- The "isotropic non-totalistic
" rulespace has also received significant attention over the years. These rules differ from outer-totalistic rules in that each numerical transition is split into several different transitions where the relative arrangement of the neighbor cells is different. However, isotropic rules retain the property that they are invariant under rotation and reflection of the pattern, hence their name.- Just Friends (B2-a/S12), first described in 2000, allows cells to be born from two neighbors, except if those two cells are directly adjacent to each other. This averts the infinite growth seen in rules like Seeds and Live Free or Die (see above). This can be considered the Trope Codifiernote for isotropic non-totalistic rules, as it inspired the creation of Hensel notation which remains the most common way of representing them.
- LeapLife (B2n3/S23-q) was first considered in early 2020 as a sort of "Alternate Universe" to Life, exhibiting many of the same properties as B3/S23 while individual patterns may differ greatly. Its forum thread is one of the largest in the OCA forums, with over 1,000 replies as of 2023.
- Snowflakes (B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e) is named for a common 21-cell still life that spawns from an extremely simple two-cell predecessor. The rule also contains other small patterns that can interact with snowflakes in various ways.
- tLife (B3/S2-i34q) introduces a second extremely small spaceship in addition to the glider, that being the T-tetromino which travels one cell orthogonally every five generations. It also has its own variants such as tHighLife (B36/S2-i34q) which combines it with the changes from HighLife (see above).
- In "Generations" rules, cells that would normally "die" instead enter a state known as "aging" for a certain number of generations. In this state, they are treated as dead for the purpose of determining neighboring cells' states, but cannot be reborn until after they have died off:
- Star Wars (B2/S345/G4) is a Generations rule named for how its evolution resembles a Space Battle. It features spaceships that are referred to as "photons" due to traveling at the speed of light while the guns that produce them are referred to as "lasers".
- Brian's Brain (B2/S/G3) is often seen as resembling a neural network, with "aging" cells representating a refractory state. The rule features a large variety of rakes and spaceships, often crashing and recombining into even more objects. Unusually for a B2 rule, a small c/4 diagonal ship exists.
- "Larger than Life" rules such as Bugs (R5,C2,S33-57,B34-45,NM) feature a larger neighborhood and a range of numbers of living neighbors where cells can be born and/or survive. The "C" parameter also borrows from Generations in that it determines the total number of states the rule contains. Bugs in particular features an array of blob-shaped oscillators and spaceships.
- Symbiosis is a custom rule which, as of March 2023, has the largest forum thread out of any individual rule other than Conway's Game of Life. It features two "living" states (red and yellow) which, on their own, function identically to Life. When combined, however, any cells living or dead which contain a mixture of red and yellow neighbors will retain their state even if it would otherwise be toggled under normal Life rules. Oscillators are extremely plentiful in this rule - as of March 2023, the lowest period for which no naturally-occurring examples are known is 56 here, compared to 9 for ordinary Life.
