Editing Conway's Game of Life (section)

==Variations==
{{main|Life-like cellular automaton}}
Since the Game of Life's inception, new, similar cellular automata have been developed. The standard Game of Life is symbolized in rule-string notation as B3/S23. A cell is born if it has exactly three neighbours, survives if it has two or three living neighbours, and dies otherwise. The first number, or list of numbers, is what is required for a dead cell to be born. The second set is the requirement for a live cell to survive to the next generation. Hence B6/S16 means "a cell is born if there are six neighbours, and lives on if there are either one or six neighbours". Cellular automata on a two-dimensional grid that can be described in this way are known as [[Life-like cellular automaton|{{Not a typo|Life-like}} cellular automata]]. Another common {{Not a typo|Life-like}} automaton, [[Highlife (cellular automaton)|Highlife]], is described by the rule B36/S23, because having six neighbours, in addition to the original game's B3/S23 rule, causes a birth. HighLife is best known for its frequently occurring replicators.<ref>[http://www.tip.net.au/~dbell/articles/HighLife.zip HighLife – An Interesting Variant of Life] by David Bell (.zip file)</ref><ref>{{cite web|url=https://conwaylife.com/ref/lexicon/lex_r.htm#replicator|title=Replicator|publisher=The Life Lexicon|author=Stephen A. Silver|access-date=March 4, 2019|archive-date=March 1, 2019|archive-url=https://web.archive.org/web/20190301232016/http://www.conwaylife.com/ref/lexicon/lex_r.htm#replicator|url-status=live}}</ref>

Additional Life-like cellular automata exist. The vast majority of these 2<sup>18</sup> different rules<ref>{{cite web|url=https://conwaylife.com/wiki/Life-like#Life-like_cellular_automata|title=Life-like cellular automata - LifeWiki|publisher=Conwaylife.com|access-date=March 4, 2019|archive-date=March 6, 2019|archive-url=https://web.archive.org/web/20190306043758/http://conwaylife.com/wiki/Life-like#Life-like_cellular_automata|url-status=live}}</ref> produce universes that are either too chaotic or too desolate to be of interest, but a large subset do display interesting behaviour. A further generalization produces the ''isotropic'' rulespace, with 2<sup>102</sup> possible cellular automaton rules<ref>{{cite web|url=https://conwaylife.com/wiki/Isotropic|title=Isotropic - LifeWiki|publisher=Conwaylife.com|access-date=March 4, 2019|archive-date=March 6, 2019|archive-url=https://web.archive.org/web/20190306043649/http://conwaylife.com/wiki/Isotropic|url-status=live}}</ref> (the Game of Life again being one of them). These are rules that use the same square grid as the Life-like rules and the same eight-cell neighbourhood, and are likewise invariant under rotation and reflection. However, in isotropic rules, the positions of neighbour cells relative to each other may be taken into account in determining a cell's future state—not just the total number of those neighbours.

[[File:Oscillator.gif|right|frame|A sample of a 48-step oscillator along with 2-step and 4-step oscillators from a two-dimensional hexagonal Game of Life (rule H:B2/S34)]]

Some variations on the Game of Life modify the geometry of the universe as well as the rules. The above variations can be thought of as a two-dimensional square, because the world is two-dimensional and laid out in a square grid. One-dimensional square variations, known as [[elementary cellular automaton|elementary cellular automata]],<ref>{{cite web|url=http://mathworld.wolfram.com/ElementaryCellularAutomaton.html|publisher=Wolfram Mathworld|title=Elementary Cellular Automaton|access-date=July 12, 2009|archive-date=July 3, 2009|archive-url=https://web.archive.org/web/20090703200815/http://mathworld.wolfram.com/ElementaryCellularAutomaton.html|url-status=live}}</ref> and three-dimensional square variations have been developed, as have two-dimensional [[Regular tiling|hexagonal and triangular]] variations. A variant using [[aperiodic tiling]] grids has also been made.<ref>{{cite magazine|url=https://www.newscientist.com/article/dn22134-first-gliders-navigate-everchanging-penrose-universe.html|magazine=New Scientist|title=First gliders navigate ever-changing Penrose universe}}</ref>

Conway's rules may also be generalized such that instead of two states, ''live'' and ''dead'', there are three or more. State transitions are then determined either by a weighting system or by a table specifying separate transition rules for each state; for example, Mirek's Cellebration's multi-coloured Rules Table and Weighted Life rule families each include sample rules equivalent to the Game of Life.

Patterns relating to fractals and fractal systems may also be observed in certain {{Not a typo|Life-like}} variations. For example, the automaton B1/S12 generates four very close approximations to the [[Sierpinski triangle]] when applied to a single live cell. The Sierpinski triangle can also be observed in the Game of Life by examining the long-term growth of an infinitely long single-cell-thick line of live cells,<ref>[[Stephen Wolfram]], ''[[A New Kind of Science]]'' online, [https://www.wolframscience.com/nks/notes-6-8--structures-in-the-game-of-life/ Note (f) for structures in class 4 systems: Structures in the Game of Life]: "A simpler kind of unbounded growth occurs if one starts from an infinite line of black cells. In that case, the evolution is effectively 1D, and turns out to follow elementary rule 22"</ref> as well as in Highlife, [[Seeds (cellular automaton)|Seeds (B2/S)]], and [[Stephen Wolfram]]'s [[Rule 90]].<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=7&t=90|title=Life Imitates Sierpinski|publisher=ConwayLife.com forums|access-date=July 12, 2009}}</ref>

Immigration is a variation that is very similar to the Game of Life, except that there are two ''on'' states, often expressed as two different colours. Whenever a new cell is born, it takes on the on state that is the majority in the three cells that gave it birth. This feature can be used to examine interactions between [[spaceship (cellular automaton)|spaceships]] and other objects within the game.<ref>
{{cite web|url=https://conwaylife.com/ref/lexicon/lex_i.htm#immigration|title=Immigration|publisher=The Life Lexicon|author=Stephen A. Silver|access-date=March 4, 2019}}</ref> Another similar variation, called QuadLife, involves four different on states. When a new cell is born from three different on neighbours, it takes the fourth value, and otherwise, like Immigration, it takes the majority value.<ref>{{cite web|url=https://conwaylife.com/ref/lexicon/lex_q.htm#quadlife|title=QuadLife|publisher=The Life Lexicon|author=Stephen A. Silver|access-date=March 4, 2019}}</ref> Except for the variation among on cells, both of these variations act identically to the Game of Life.