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Rake (cellular automaton)
A rake, in the lexicon of cellular automata, is a type of ''puffer train'', which is an automaton that leaves behind a trail of debris. In the case of a rake, however, the debris left behind is a stream of spaceships,〔(Rake, Life lexicon ). (Rake, E. Weisstein ).〕 which are automata that "travel" by looping through a short series of iterations and end up in a new location after each cycle returns to the original configuration.
In Conway's Game of Life, the discovery of rakes was one of the key components needed to form the ''breeder'', the first known pattern in Life in which the number of live cells exhibits quadratic growth. A breeder is formed by arranging several rakes so that the ''gliders''—the smallest possible spaceships—they generate interact to form a sequence of ''glider guns'', patterns which emit gliders. The emitted gliders fill a growing triangle of the plane of the game. More generally, when a rake exists for a cellular automaton rule (a mathematical function defining the next iteration to be derived from a particular configuration of live and dead cells), 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.〔For this reason, (Jason Summers' life status page ) describes a rake as a "versatile puffer", and collects data on the existence of rakes for various speeds and periods of puffers.〕 As David Bell writes:
The first rake to be discovered, in the early 1970s, was the "space rake", which moves with speed ''c''/2 (or one unit every two steps), emitting a glider every twenty steps.〔(Space rake, Life lexicon ). (Space rake, E. Weisstein ). The first published description of the space rake was in Lifeline, a newsletter published by R. Wainwright in the early 1970s, issue 3.6 ((index )).〕 For Life, rakes are now known that move orthogonally with speeds ''c''/2, ''c''/3, ''c''/4, ''c''/5, 2''c''/5, and 17''c''/45, and diagonally with speeds ''c''/4 and ''c''/12, with many different periods.〔(Jason Summers' life status page ).〕 Rakes are also known for some other Highlife,〔David I. Bell, (HighLife - An Interesting Variant of Life ), 1994.〕 Day & Night,〔David I. Bell, (Day & Night - An Interesting Variant of Life ), 1997.〕 and Seeds.〔(Patterns for the Seeds rule ), collected by Jason Summers.〕
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.〔cite journal|author = Gotts, N. M.|title=Emergent phenomena in large sparse random arrays of Conway's ‘Game of Life’|journal=International Journal of Systems Science|volume=31|issue=7|pages=873–894|doi=10.1080/002077200406598|year=2000}}〕
==References==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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