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| [[Image:Animated spaceships.gif|right|frame|Orthogonal spaceships in [[Conway's Game of Life]] of varying speeds. Note some spaceships “overtake” others due to speed differences.]]
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| 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. The smallest such number of generations is called the '''period''' of the spaceship.
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| The speed of a spaceship is often expressed in terms of ''c'', the metaphorical [[speed of light (cellular automaton)|speed of light]] (one cell per generation) which in many cellular automata is the fastest that an effect can spread. For example, a [[Glider (Conway's Life)|glider]] in [[Conway's Game of Life]] is said to have a speed of <math>c/4</math>, as it takes four generations for a given state to be translated by one cell. Similarly, the ''lightweight spaceship'' is said to have a speed of <math>c/2</math>, as it takes four generations for a given state to be translated by two cells. More generally, if a spaceship in a 2D automaton is translated by <math>(x, y)</math> after <math>n</math> generations, then the speed <math>v</math> is defined as:
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| <center><math>v=\frac{\max\left(|x|,|y|\right)}{n}\,c</math></center>
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| This notation can be readily generalised to cellular automata with dimensionality other than two.
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| A '''tagalong''' is a pattern that is not a spaceship in itself but that can be attached to the back of a spaceship to form a larger spaceship. Similarly, a '''pushalong''' is placed at the front.
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| A pattern that, when a spaceship is input, outputs a copy of the spaceship travelling in a different direction is called a [[Reflector (cellular automaton)|reflector]].
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| Spaceships are important because they can sometimes be modified to produce [[Puffer train (cellular automaton)|puffer]]s. Spaceships can also be used to transmit [[information]]. For example, in [[Conway's Game of Life]], the ability of the [[glider (Conway's Life)|glider]] (Life's simplest spaceship) to transmit information is part of a proof that Life is [[Turing-complete]].
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| ==External links==
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| * [http://www.j-paine.org/dobbs/life.html Spaceships in Conway's Game of Life] by David I. Bell
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| * [http://www.ics.uci.edu/~eppstein/ca/ Gliders in "Life"-Like Cellular Automata] by [[David Eppstein]]
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| {{Conway's Game of Life}}
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| [[Category:Cellular automaton patterns]]
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I like my hobby Painting. Seems boring? Not!
I try tо learn Swedish іn my spare time.
Review mʏ homeƿage - free moshi monster code