In
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 ...
such as
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 ...
, a breeder is a pattern that exhibits
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" ...
, by generating multiple copies of a secondary pattern, each of which then generates multiple copies of a tertiary pattern.
Classification
Breeders can be classed by the relative motion of the patterns. The classes are denoted by three-letter codes, which denote whether the primary, secondary and tertiary elements respectively are moving (M) or stationary (S). The four basic types are:
# SMM – A
gun
A gun is a ranged weapon designed to use a shooting tube (gun barrel) to launch projectiles. The projectiles are typically solid, but can also be pressurized liquid (e.g. in water guns/cannons, spray guns for painting or pressure washing, p ...
that fires out
rakes.
# MSM – A
puffer that leaves guns in its wake.
# MMS – A rake that fires out puffers.
# MMM – A rake that fires out more rakes, such that there are no stationary elements.
A
spacefiller
In Conway's Game of Life and related cellular automata, a spacefiller is a pattern that spreads out indefinitely, eventually filling the entire space with a still life pattern. It typically consists of three components: stretchers that resem ...
(which also undergoes quadratic growth) may be thought of as a fifth class of breeder. However it differs from a true breeder in that it expands a single island of cells, rather than creating independent objects.
References
{{Conway's Game of Life
Cellular automaton patterns