A rake in a cellular automaton

Cellular automaton

A cellular automaton is a discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modeling. It consists of a regular grid of cells, each in one of a finite number of states, such as "On" and "Off"...

 is a puffer that, instead of leaving behind a trail of debris, emits a stream of spaceships

Spaceship (CA)

In a cellular automaton, a finite pattern is called a spaceship if it reappears after a certain number of generations in the same orientation but in a different position...

. 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....

, the discovery of rakes was one of the key components needed to form the breeder

Breeder (cellular automaton)

In Conway's Game of Life, a breeder is a pattern that exhibits quadratic growth, by generating multiple copies of a secondary pattern, each of which then generates multiple copies of a tertiary pattern.-Classification:...

, the first known patterns in Life in which the number of live cells 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...

. A breeder is formed by arranging several rakes so that the gliders they generate interact to form a sequence of glider guns, the gliders from which fill a growing triangle of the plane. More generally, when a rake exists for a cellular automaton rule, one can often construct puffers which leave trails of many other kinds of objects, by colliding the streams of spaceships emitted by multiple rakes moving in parallel. As David Bell writes,
The first rake to be discovered, in the early 1970s, was the "space rake", which moves with speed c/2, emitting a glider every 20 steps. For Life, rakes are now known that move orthogonally with speeds c/2, c/3, c/4, c/5, 2c/5, and 17c/45, and diagonally with speeds c/4 and c/12, with many different periods. Rakes are also known for some other Life-like cellular automata including HighLife

HighLife

HighLife is a cellular automaton similar to Conway's Game of Life. It was devised in 1994 by Nathan Thompson. It is a two-dimensional, two-state cellular automaton in the "Life family" and is described by the rule B36/S23; that is, a cell is born if it has 3 or 6 neighbors and survives if it has 2...

, Day & Night

Day & Night

Day & Night is a cellular automaton rule in the same family as Game of Life. It is defined by rule notation B3678/S34678, meaning that a dead cell becomes live if it has 3, 6, 7, or 8 live neighbors, and a live cell remains alive if it has 3, 4, 6, 7, or 8 live neighbors, out of the eight...

, and Seeds.

Gotts (1980) shows that the space rake in Life can be formed by a "standard collision sequence" in which a single glider interacts with a widely separated set of 3-cell initial seeds (blinkers and blocks). As a consequence, he finds lower bounds on the probability that these patterns form in any sufficiently sparse and sufficiently large random initial condition for Life. This result leads to standard collision sequences for many other patterns such as breeders.