en>NottNott: Reverted edits by 119.154.3.73 (talk): editing tests (HG)

2014-10-11T18:08:28Z

Reverted edits by 119.154.3.73 (talk): editing tests (HG)

← Older revision		Revision as of 20:08, 11 October 2014
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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.]]~~		I like my hobby Painting. Seems boring? Not!<br>I try tо learn Swedish іn my spare time.<br><br>Review mʏ homeƿage - [http://free-moshi-monster-codes.webnode.com/ free moshi monster code]

	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.

	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:~~

	~~<center><math>v=\frac{\max\left(\|x\|,\|y\|\right)}{n}\,c~~<~~/math~~><~~/center~~>

	~~This notation can be readily generalised to cellular automata with dimensionality other than two.~~

	~~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.~~

	~~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]].~~

	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]].~~

	~~==External links==~~
	* [http://~~www.j~~-~~paine.org/dobbs/life.html Spaceships in Conway's Game of Life] by David I. Bell~~
	* [http://www.ics.~~uci~~.~~edu/~eppstein/ca~~/ ~~Gliders in "Life"-Like Cellular Automata] by [[David Eppstein]]~~


	~~{{Conway's Game of Life}}~~

	~~[[Category:Cellular automaton patterns]~~]

en>Myasuda: /* Canonical and non-canonical consequences of NOR gates */ sp

2013-10-20T18:09:28Z

Canonical and non-canonical consequences of NOR gates: sp

New page

[[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.]]

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.

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:

<center><math>v=\frac{\max\left(|x|,|y|\right)}{n}\,c</math></center>

This notation can be readily generalised to cellular automata with dimensionality other than two.

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.

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]].

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]].

==External links==
* [http://www.j-paine.org/dobbs/life.html Spaceships in Conway's Game of Life] by David I. Bell
* [http://www.ics.uci.edu/~eppstein/ca/ Gliders in "Life"-Like Cellular Automata] by [[David Eppstein]]

{{Conway's Game of Life}}

[[Category:Cellular automaton patterns]]

Canonical normal form - Revision history

en>NottNott: Reverted edits by 119.154.3.73 (talk): editing tests (HG)

en>Myasuda: /* Canonical and non-canonical consequences of NOR gates */ sp