Conway's Game of Life - Variations On Life

Variations On Life

Since Life's inception, new similar cellular automata have been developed. The standard Game of Life, in which a cell is "born" if it has exactly 3 neighbours, stays alive if it has 2 or 3 living neighbours, and dies otherwise, is symbolised as "B3/S23". 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 6 neighbours, and lives on if there are either 1 or 6 neighbours". Cellular automata on a two-dimensional grid that can be described in this way are known as Life-like cellular automata. Another common Life-like automaton, HighLife, is described by the rule B36/S23, because having 6 neighbours, in addition to the original game's B3/S23 rule, causes a birth. HighLife is best known for its frequently occurring replicators. Additional Life-like cellular automata exist, although the vast majority of them produce universes that are either too chaotic or too desolate to be of interest.

Some variations on Life modify the geometry of the universe as well as the rule. The above variations can be thought of as 2-D square, because the world is two-dimensional and laid out in a square grid. 1-D square variations (known as elementary cellular automata) and 3-D square variations have been developed, as have 2-D hexagonal and 2-D triangular variations. Variant using non-periodic tile grids has also been made.

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 Conway's Life.

Patterns relating to fractals and fractal systems may also be observed in certain Life-like variations. For example, the automaton B1/S12 generates four very close approximations to the Sierpiński triangle when applied to a single live cell. The Sierpiński triangle can also be observed in Conway's Game of Life by examining the long-term growth of a long single-cell-thick line of live cells, as well as in HighLife, Seeds (B2/S), and Wolfram's Rule 90.

Immigration is a variation that is very similar to Conway's 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 spaceships and other "objects" within the game. Another similar variation, called QuadLife, involves four different ON states. When a new cell is born from three different ON neighbours, it takes on the fourth value, and otherwise, like Immigration, it takes the majority value. Except for the variation among ON cells, both of these variations act identically to Life.