In Conway's Game of Life

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....

, a breeder is a pattern that exhibits quadratic growth

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, in the limit as the argument or sequence position goes to infinity...

, 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 four basic types are:

• A gun that fires out rakes. (The primary pattern is stationary, whilst both the secondary and tertiary patterns move.)
• A puffer that leaves guns in its wake. (The secondary patterns are stationary, whilst both the primary and tertiary patterns move.)
• A rake that fires out puffers. (The tertiary patterns are stationary, whilst the primary and secondary patterns move.)
• A rake that fires out more rakes. (All the patterns move.)

A spacefiller

Spacefiller

A spacefiller is a life pattern that grows quadratically by filling space with still life. It can be thought of as a fifth class of breeder in which the primary and secondary patterns move and tertiary patterns are stationary ....

(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.