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In Conway's Game of Life
The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, meaning that its evolution is determined by its initial state, requiring no further ...
and related cellular automata
A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessel ...
, a spacefiller is a pattern that spreads out indefinitely, eventually filling the entire space with a still life
A still life (plural: still lifes) is a work of art depicting mostly wikt:inanimate, inanimate subject matter, typically commonplace objects which are either natural (food, flowers, dead animals, plants, rocks, shells, etc.) or artificiality, m ...
pattern. It typically consists of three components: stretchers that resemble spaceships at the four corners of the pattern, a growing boundary region along the edges of the pattern, and the still life in the interior pattern.
It resembles a breeder
A breeder is a person who selectively breeds carefully selected mates, normally of the same breed to sexually reproduce offspring with specific, consistently replicable qualities and characteristics. This might be as a farmer, agriculturalist, or ...
in that both types of patterns have a quadratic growth
In mathematics, a function or sequence is said to exhibit quadratic growth when its values are proportional to the square of the function argument or sequence position. "Quadratic growth" often means more generally "quadratic growth in the limit", ...
rate in their numbers of live cells, and in both having a three-component architecture. However, in a breeder the moving part of the breeder (corresponding to the stretcher) leaves behind a fixed sequence of glider guns which fill space with gliders, moving objects (gliders or spaceships) rather than still life patterns. With a spacefiller, unlike a breeder, every point in the space eventually becomes part of the space-filling still life pattern.
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