One-cell-thick pattern - Revision history

ElijahKen: /* Spaceships and oscillators */ Correcting a tiny spelling error

2026-11-15T06:48:08Z

Spaceships and oscillators: Correcting a tiny spelling error

← Older revision		Revision as of 06:48, 15 November 2026
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	== Spaceships and oscillators ==		== Spaceships and oscillators ==
	The [[blinker]] is the only explicit ''finite'' [[oscillator]] that is one cell thick in one or more of its phases (tiling the plane with {{headerlessRLE\|oooooo..}} gives an infinite period-9 oscillator based on the [[worker bee]]; also see note 2), and in April {{year\|1992}}, [[Allan Wechsler]] used a search program to show that there are no oscillators of period 3, 5 or 7 that are one cell thick.<ref>E-mail sent from Allan Wechsler to LifeList</ref> In December 2025, [[Keith Amling]] verified that there are no one cell thick oscillators of periods 3 through 11.<ref name="post222829" /> The situation is technically unknown for other periods, though the existence of high-period examples is implied via the existence of the unidimensional spaceship{{refn\|group=note\|Since the unidimensional spaceship is a periodic pattern which programs its own reconstruction in a different place via a universal constructor, a unidimensional self-constructing pattern only has to program its universal constructor to either rebuild itself in the same place or rebuild itself flipped 180 degrees to become a unidimensional oscillator. The latter scenario would also provide an example of an oscillator that is unidimensional in more than one phase.}}. ~~Interstingly~~, the [[pentadecathlon]] has a simple one cell thick predecessor, namely a 10-cell line, and the oscillator's evolution sequence involves it evolving into a pattern that is almost 1 cell thick.		The [[blinker]] is the only explicit ''finite'' [[oscillator]] that is one cell thick in one or more of its phases (tiling the plane with {{headerlessRLE\|oooooo..}} gives an infinite period-9 oscillator based on the [[worker bee]]; also see note 2), and in April {{year\|1992}}, [[Allan Wechsler]] used a search program to show that there are no oscillators of period 3, 5 or 7 that are one cell thick.<ref>E-mail sent from Allan Wechsler to LifeList</ref> In December 2025, [[Keith Amling]] verified that there are no one cell thick oscillators of periods 3 through 11.<ref name="post222829" /> The situation is technically unknown for other periods, though the existence of high-period examples is implied via the existence of the unidimensional spaceship{{refn\|group=note\|Since the unidimensional spaceship is a periodic pattern which programs its own reconstruction in a different place via a universal constructor, a unidimensional self-constructing pattern only has to program its universal constructor to either rebuild itself in the same place or rebuild itself flipped 180 degrees to become a unidimensional oscillator. The latter scenario would also provide an example of an oscillator that is unidimensional in more than one phase.}}. Interestingly, the [[pentadecathlon]] has a simple one cell thick predecessor, namely a 10-cell line, and the oscillator's evolution sequence involves it evolving into a pattern that is almost 1 cell thick.

	Since 2016, there has been research into the existence of a unidimensional spaceship.<ref name="post27410" /> This project was successful when user [[Hippo.69]] completed a 2c/1330767555768 spaceship on December 2, {{year\|2025}}. This ship, [[Unidimensional spaceship 1]], has a {{times\|3707300605\|1}} bounding box in one phase.<ref name="post222136" />. This ship consists of a unidimensional pattern that is a predecessor to a [[universal constructor]]. The process of creating a unidimensional universal constructor predecessor was the relatively simple part of the design; having the universal constructor then resynthesize the unidimensional pattern was much more difficult, as all sparks had to disappear before the ship entered its unidimensional phase. Due to symmetry, any one-cell-thick spaceship must move in the direction its length points in.		Since 2016, there has been research into the existence of a unidimensional spaceship.<ref name="post27410" /> This project was successful when user [[Hippo.69]] completed a 2c/1330767555768 spaceship on December 2, {{year\|2025}}. This ship, [[Unidimensional spaceship 1]], has a {{times\|3707300605\|1}} bounding box in one phase.<ref name="post222136" />. This ship consists of a unidimensional pattern that is a predecessor to a [[universal constructor]]. The process of creating a unidimensional universal constructor predecessor was the relatively simple part of the design; having the universal constructor then resynthesize the unidimensional pattern was much more difficult, as all sparks had to disappear before the ship entered its unidimensional phase. Due to symmetry, any one-cell-thick spaceship must move in the direction its length points in.

Hotcrystal0 at 14:24, 16 August 2026

2026-08-16T14:24:35Z

← Older revision		Revision as of 14:24, 16 August 2026
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	\|title = Re: Soup search results		\|title = Re: Soup search results
	\|p = 64642		\|p = 64642
	\|author = ~~wwei23~~		\|author = Aleph
	\|date = October 11, 2018		\|date = October 11, 2018
	}}</ref>		}}</ref>

WhiteHawk: /* Spaceships and oscillators */ unidimensional spaceship implies "infinite" finite unidimensional oscillators that construct & destroy self-constructing circuitry

2026-04-24T01:48:23Z

Spaceships and oscillators: unidimensional spaceship implies "infinite" finite unidimensional oscillators that construct & destroy self-constructing circuitry

← Older revision		Revision as of 01:48, 24 April 2026
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	== Spaceships and oscillators ==		== Spaceships and oscillators ==
	The [[blinker]] is the only ~~known~~ ''finite'' [[oscillator]] that is one cell thick in one or more of its phases (tiling the plane with {{headerlessRLE\|oooooo..}} gives an infinite period-9 oscillator based on the [[worker bee]]; also see note 2), and in April {{year\|1992}}, [[Allan Wechsler]] used a search program to show that there are no oscillators of period 3, 5 or 7 that are one cell thick.<ref>E-mail sent from Allan Wechsler to LifeList</ref> In December 2025, [[Keith Amling]] verified that there are no one cell thick oscillators of periods 3 through 11.<ref name="post222829" /> The situation is technically unknown for other periods, though the existence of high-period examples is implied via the existence of the unidimensional spaceship{{refn\|group=note\|Since the unidimensional spaceship is a periodic pattern which programs its own reconstruction in a different place via a universal constructor, a unidimensional self-constructing pattern only has to program its universal constructor to either rebuild itself in the same place or rebuild itself flipped 180 degrees to become a unidimensional oscillator. The latter scenario would also provide an example of an oscillator that is unidimensional in more than one phase.}}. Interstingly, the [[pentadecathlon]] has a simple one cell thick predecessor, namely a 10-cell line, and the oscillator's evolution sequence involves it evolving into a pattern that is almost 1 cell thick.		The [[blinker]] is the only explicit ''finite'' [[oscillator]] that is one cell thick in one or more of its phases (tiling the plane with {{headerlessRLE\|oooooo..}} gives an infinite period-9 oscillator based on the [[worker bee]]; also see note 2), and in April {{year\|1992}}, [[Allan Wechsler]] used a search program to show that there are no oscillators of period 3, 5 or 7 that are one cell thick.<ref>E-mail sent from Allan Wechsler to LifeList</ref> In December 2025, [[Keith Amling]] verified that there are no one cell thick oscillators of periods 3 through 11.<ref name="post222829" /> The situation is technically unknown for other periods, though the existence of high-period examples is implied via the existence of the unidimensional spaceship{{refn\|group=note\|Since the unidimensional spaceship is a periodic pattern which programs its own reconstruction in a different place via a universal constructor, a unidimensional self-constructing pattern only has to program its universal constructor to either rebuild itself in the same place or rebuild itself flipped 180 degrees to become a unidimensional oscillator. The latter scenario would also provide an example of an oscillator that is unidimensional in more than one phase.}}. Interstingly, the [[pentadecathlon]] has a simple one cell thick predecessor, namely a 10-cell line, and the oscillator's evolution sequence involves it evolving into a pattern that is almost 1 cell thick.

	Since 2016, there has been research into the existence of a unidimensional spaceship.<ref name="post27410" /> This project was successful when user [[Hippo.69]] completed a 2c/1330767555768 spaceship on December 2, {{year\|2025}}. This ship, [[Unidimensional spaceship 1]], has a {{times\|3707300605\|1}} bounding box in one phase.<ref name="post222136" />. This ship consists of a unidimensional pattern that is a predecessor to a [[universal constructor]]. The process of creating a unidimensional universal constructor predecessor was the relatively simple part of the design; having the universal constructor then resynthesize the unidimensional pattern was much more difficult, as all sparks had to disappear before the ship entered its unidimensional phase. Due to symmetry, any one-cell-thick spaceship must move in the direction its length points in.		Since 2016, there has been research into the existence of a unidimensional spaceship.<ref name="post27410" /> This project was successful when user [[Hippo.69]] completed a 2c/1330767555768 spaceship on December 2, {{year\|2025}}. This ship, [[Unidimensional spaceship 1]], has a {{times\|3707300605\|1}} bounding box in one phase.<ref name="post222136" />. This ship consists of a unidimensional pattern that is a predecessor to a [[universal constructor]]. The process of creating a unidimensional universal constructor predecessor was the relatively simple part of the design; having the universal constructor then resynthesize the unidimensional pattern was much more difficult, as all sparks had to disappear before the ship entered its unidimensional phase. Due to symmetry, any one-cell-thick spaceship must move in the direction its length points in.

Neocaridina: /* One cell thick patterns evolving into one cell thick patterns */

2026-02-17T15:04:51Z

One cell thick patterns evolving into one cell thick patterns

← Older revision		Revision as of 15:04, 17 February 2026
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	== One cell thick patterns evolving into one cell thick patterns ==		== One cell thick patterns evolving into one cell thick patterns ==
	A weaker problem is to find a unidimensional pattern that is the predecessor of another non-trivial unidimensional pattern. Non-trivial means that it must contain at least one line that is not the [[blinker]], a [[spark]], or a ~~hypothetical~~ one-cell-thick spaceship. For example, this rules out the pattern {{headerlessRLE\|oo.o.oo.ooo}}, which becomes a single blinker without any of the separate line segments ever having the opportunity to interact. By contrast, the pattern {{headerlessRLE\|ooooo.ooo}} also produces a single blinker, but the interaction between the two segments makes it a non-trivial unidimensional pattern.		A weaker problem is to find a unidimensional pattern that is the predecessor of another non-trivial unidimensional pattern. Non-trivial means that it must contain at least one line that is not the [[blinker]], a [[spark]], or a one-cell-thick spaceship. For example, this rules out the pattern {{headerlessRLE\|oo.o.oo.ooo}}, which becomes a single blinker without any of the separate line segments ever having the opportunity to interact. By contrast, the pattern {{headerlessRLE\|ooooo.ooo}} also produces a single blinker, but the interaction between the two segments makes it a non-trivial unidimensional pattern.

	In August 2016, toroidalet presented a unidimensional predecessor of a unidimensional pattern;<ref name="post33987" /> it evolves into a different one cell thick pattern in generation 9, and into two [[beehive]]s in generation 22:		In August 2016, toroidalet presented a unidimensional predecessor of a unidimensional pattern;<ref name="post33987" /> it evolves into a different one cell thick pattern in generation 9, and into two [[beehive]]s in generation 22:

Sokwe: /* Spaceships and oscillators */ clarification of Amling's result

2025-12-17T10:56:27Z

Spaceships and oscillators: clarification of Amling's result

← Older revision		Revision as of 10:56, 17 December 2025
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	== Spaceships and oscillators ==		== Spaceships and oscillators ==
	The [[blinker]] is the only known ''finite'' [[oscillator]] that is one cell thick in one or more of its phases (tiling the plane with {{headerlessRLE\|oooooo..}} gives an infinite period-9 oscillator based on the [[worker bee]]; also see note 2), and in April {{year\|1992}}, [[Allan Wechsler]] used a search program to show that there are no oscillators of period 3, 5 or 7 that are one cell thick.<ref>E-mail sent from Allan Wechsler to LifeList</ref> In December 2025, [[Keith Amling]] ~~also~~ verified that there are no one cell thick oscillators of periods ~~9 and~~ 11.<ref name="post222829" /> The situation is technically unknown for other periods, though the existence of high-period examples is implied via the existence of the unidimensional spaceship{{refn\|group=note\|Since the unidimensional spaceship is a periodic pattern which programs its own reconstruction in a different place via a universal constructor, a unidimensional self-constructing pattern only has to program its universal constructor to either rebuild itself in the same place or rebuild itself flipped 180 degrees to become a unidimensional oscillator. The latter scenario would also provide an example of an oscillator that is unidimensional in more than one phase.}}. Interstingly, the [[pentadecathlon]] has a simple one cell thick predecessor, namely a 10-cell line, and the oscillator's evolution sequence involves it evolving into a pattern that is almost 1 cell thick.		The [[blinker]] is the only known ''finite'' [[oscillator]] that is one cell thick in one or more of its phases (tiling the plane with {{headerlessRLE\|oooooo..}} gives an infinite period-9 oscillator based on the [[worker bee]]; also see note 2), and in April {{year\|1992}}, [[Allan Wechsler]] used a search program to show that there are no oscillators of period 3, 5 or 7 that are one cell thick.<ref>E-mail sent from Allan Wechsler to LifeList</ref> In December 2025, [[Keith Amling]] verified that there are no one cell thick oscillators of periods 3 through 11.<ref name="post222829" /> The situation is technically unknown for other periods, though the existence of high-period examples is implied via the existence of the unidimensional spaceship{{refn\|group=note\|Since the unidimensional spaceship is a periodic pattern which programs its own reconstruction in a different place via a universal constructor, a unidimensional self-constructing pattern only has to program its universal constructor to either rebuild itself in the same place or rebuild itself flipped 180 degrees to become a unidimensional oscillator. The latter scenario would also provide an example of an oscillator that is unidimensional in more than one phase.}}. Interstingly, the [[pentadecathlon]] has a simple one cell thick predecessor, namely a 10-cell line, and the oscillator's evolution sequence involves it evolving into a pattern that is almost 1 cell thick.

	Since 2016, there has been research into the existence of a unidimensional spaceship.<ref name="post27410" /> This project was successful when user [[Hippo.69]] completed a 2c/1330767555768 spaceship on December 2, {{year\|2025}}. This ship, [[Unidimensional spaceship 1]], has a {{times\|3707300605\|1}} bounding box in one phase.<ref name="post222136" />. This ship consists of a unidimensional pattern that is a predecessor to a [[universal constructor]]. The process of creating a unidimensional universal constructor predecessor was the relatively simple part of the design; having the universal constructor then resynthesize the unidimensional pattern was much more difficult, as all sparks had to disappear before the ship entered its unidimensional phase. Due to symmetry, any one-cell-thick spaceship must move in the direction its length points in.		Since 2016, there has been research into the existence of a unidimensional spaceship.<ref name="post27410" /> This project was successful when user [[Hippo.69]] completed a 2c/1330767555768 spaceship on December 2, {{year\|2025}}. This ship, [[Unidimensional spaceship 1]], has a {{times\|3707300605\|1}} bounding box in one phase.<ref name="post222136" />. This ship consists of a unidimensional pattern that is a predecessor to a [[universal constructor]]. The process of creating a unidimensional universal constructor predecessor was the relatively simple part of the design; having the universal constructor then resynthesize the unidimensional pattern was much more difficult, as all sparks had to disappear before the ship entered its unidimensional phase. Due to symmetry, any one-cell-thick spaceship must move in the direction its length points in.

Qqd: Slight rearrangement

2025-12-17T06:07:10Z

Slight rearrangement

← Older revision		Revision as of 06:07, 17 December 2025
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	== Spaceships and oscillators ==		== Spaceships and oscillators ==
	The [[blinker]] is the only known ''finite'' [[oscillator]] that is one cell thick in one or more of its phases (tiling the plane with {{headerlessRLE\|oooooo..}} gives an infinite period-9 oscillator based on the [[worker bee]]; also see note 2), and in April {{year\|1992}}, [[Allan Wechsler]] used a search program to show that there are no oscillators of period 3, 5 or 7 that are one cell thick. In December 2025, [[Keith Amling]] also ~~proved~~ that there are no one cell thick oscillators of periods 9 and 11.<ref name="post222829" /> The situation is technically unknown for other periods,~~<ref>E-mail sent from Allan Wechsler to LifeList</ref>~~ though the existence of high-period examples is implied via the existence of the unidimensional spaceship{{refn\|group=note\|Since the unidimensional spaceship is a periodic pattern which programs its own reconstruction in a different place via a universal constructor, a unidimensional self-constructing pattern only has to program its universal constructor to either rebuild itself in the same place or rebuild itself flipped 180 degrees to become a unidimensional oscillator. The latter scenario would also provide an example of an oscillator that is unidimensional in more than one phase.}}. Interstingly, the [[pentadecathlon]] has a simple one cell thick predecessor, namely a 10-cell line, and the oscillator's evolution sequence involves it evolving into a pattern that is almost 1 cell thick.		The [[blinker]] is the only known ''finite'' [[oscillator]] that is one cell thick in one or more of its phases (tiling the plane with {{headerlessRLE\|oooooo..}} gives an infinite period-9 oscillator based on the [[worker bee]]; also see note 2), and in April {{year\|1992}}, [[Allan Wechsler]] used a search program to show that there are no oscillators of period 3, 5 or 7 that are one cell thick.<ref>E-mail sent from Allan Wechsler to LifeList</ref> In December 2025, [[Keith Amling]] also verified that there are no one cell thick oscillators of periods 9 and 11.<ref name="post222829" /> The situation is technically unknown for other periods, though the existence of high-period examples is implied via the existence of the unidimensional spaceship{{refn\|group=note\|Since the unidimensional spaceship is a periodic pattern which programs its own reconstruction in a different place via a universal constructor, a unidimensional self-constructing pattern only has to program its universal constructor to either rebuild itself in the same place or rebuild itself flipped 180 degrees to become a unidimensional oscillator. The latter scenario would also provide an example of an oscillator that is unidimensional in more than one phase.}}. Interstingly, the [[pentadecathlon]] has a simple one cell thick predecessor, namely a 10-cell line, and the oscillator's evolution sequence involves it evolving into a pattern that is almost 1 cell thick.

	Since 2016, there has been research into the existence of a unidimensional spaceship.<ref name="post27410" /> This project was successful when user [[Hippo.69]] completed a 2c/1330767555768 spaceship on December 2, {{year\|2025}}. This ship, [[Unidimensional spaceship 1]], has a {{times\|3707300605\|1}} bounding box in one phase.<ref name="post222136" />. This ship consists of a unidimensional pattern that is a predecessor to a [[universal constructor]]. The process of creating a unidimensional universal constructor predecessor was the relatively simple part of the design; having the universal constructor then resynthesize the unidimensional pattern was much more difficult, as all sparks had to disappear before the ship entered its unidimensional phase. Due to symmetry, any one-cell-thick spaceship must move in the direction its length points in.		Since 2016, there has been research into the existence of a unidimensional spaceship.<ref name="post27410" /> This project was successful when user [[Hippo.69]] completed a 2c/1330767555768 spaceship on December 2, {{year\|2025}}. This ship, [[Unidimensional spaceship 1]], has a {{times\|3707300605\|1}} bounding box in one phase.<ref name="post222136" />. This ship consists of a unidimensional pattern that is a predecessor to a [[universal constructor]]. The process of creating a unidimensional universal constructor predecessor was the relatively simple part of the design; having the universal constructor then resynthesize the unidimensional pattern was much more difficult, as all sparks had to disappear before the ship entered its unidimensional phase. Due to symmetry, any one-cell-thick spaceship must move in the direction its length points in.

Qqd: Added a statement regarding the existence of p9 or p11 one cell thick oscillators

2025-12-17T06:05:20Z

Added a statement regarding the existence of p9 or p11 one cell thick oscillators

← Older revision		Revision as of 06:05, 17 December 2025
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	== Spaceships and oscillators ==		== Spaceships and oscillators ==
	The [[blinker]] is the only known ''finite'' [[oscillator]] that is one cell thick in one or more of its phases (tiling the plane with {{headerlessRLE\|oooooo..}} gives an infinite period-9 oscillator based on the [[worker bee]]; also see note 2), and in April {{year\|1992}}, [[Allan Wechsler]] used a search program to show that there are no oscillators of period 3, 5 or 7 that are one cell thick. The situation is technically unknown for other periods,<ref>E-mail sent from Allan Wechsler to LifeList</ref> though the existence of high-period examples is implied via the existence of the unidimensional spaceship{{refn\|group=note\|Since the unidimensional spaceship is a periodic pattern which programs its own reconstruction in a different place via a universal constructor, a unidimensional self-constructing pattern only has to program its universal constructor to either rebuild itself in the same place or rebuild itself flipped 180 degrees to become a unidimensional oscillator. The latter scenario would also provide an example of an oscillator that is unidimensional in more than one phase.}}. Interstingly, the [[pentadecathlon]] has a simple one cell thick predecessor, namely a 10-cell line, and the oscillator's evolution sequence involves it evolving into a pattern that is almost 1 cell thick.		The [[blinker]] is the only known ''finite'' [[oscillator]] that is one cell thick in one or more of its phases (tiling the plane with {{headerlessRLE\|oooooo..}} gives an infinite period-9 oscillator based on the [[worker bee]]; also see note 2), and in April {{year\|1992}}, [[Allan Wechsler]] used a search program to show that there are no oscillators of period 3, 5 or 7 that are one cell thick. In December 2025, [[Keith Amling]] also proved that there are no one cell thick oscillators of periods 9 and 11.<ref name="post222829" /> The situation is technically unknown for other periods,<ref>E-mail sent from Allan Wechsler to LifeList</ref> though the existence of high-period examples is implied via the existence of the unidimensional spaceship{{refn\|group=note\|Since the unidimensional spaceship is a periodic pattern which programs its own reconstruction in a different place via a universal constructor, a unidimensional self-constructing pattern only has to program its universal constructor to either rebuild itself in the same place or rebuild itself flipped 180 degrees to become a unidimensional oscillator. The latter scenario would also provide an example of an oscillator that is unidimensional in more than one phase.}}. Interstingly, the [[pentadecathlon]] has a simple one cell thick predecessor, namely a 10-cell line, and the oscillator's evolution sequence involves it evolving into a pattern that is almost 1 cell thick.

	Since 2016, there has been research into the existence of a unidimensional spaceship.<ref name="post27410" /> This project was successful when user [[Hippo.69]] completed a 2c/1330767555768 spaceship on December 2, {{year\|2025}}. This ship, [[Unidimensional spaceship 1]], has a {{times\|3707300605\|1}} bounding box in one phase.<ref name="post222136" />. This ship consists of a unidimensional pattern that is a predecessor to a [[universal constructor]]. The process of creating a unidimensional universal constructor predecessor was the relatively simple part of the design; having the universal constructor then resynthesize the unidimensional pattern was much more difficult, as all sparks had to disappear before the ship entered its unidimensional phase. Due to symmetry, any one-cell-thick spaceship must move in the direction its length points in.		Since 2016, there has been research into the existence of a unidimensional spaceship.<ref name="post27410" /> This project was successful when user [[Hippo.69]] completed a 2c/1330767555768 spaceship on December 2, {{year\|2025}}. This ship, [[Unidimensional spaceship 1]], has a {{times\|3707300605\|1}} bounding box in one phase.<ref name="post222136" />. This ship consists of a unidimensional pattern that is a predecessor to a [[universal constructor]]. The process of creating a unidimensional universal constructor predecessor was the relatively simple part of the design; having the universal constructor then resynthesize the unidimensional pattern was much more difficult, as all sparks had to disappear before the ship entered its unidimensional phase. Due to symmetry, any one-cell-thick spaceship must move in the direction its length points in.
Line 139:		Line 139:
	== References ==		== References ==
	<references>		<references>
			<ref name="post222829">{{LinkForumThread
			\|format = ref
			\|title = Re: Oscillator Discussion Thread
			\|p = 222829
			\|author = Keith Amling
			\|date = December 17, 2025
			}}</ref>
	<ref name="post155087">{{LinkForumThread		<ref name="post155087">{{LinkForumThread
	\|format = ref		\|format = ref

WhiteHawk: /* Spaceships and oscillators */ Fixing some syntax and elaborating on note 2

2025-12-14T00:00:34Z

Spaceships and oscillators: Fixing some syntax and elaborating on note 2

← Older revision		Revision as of 00:00, 14 December 2025
Line 6:		Line 6:

	== Spaceships and oscillators ==		== Spaceships and oscillators ==
	The [[blinker]] is the only known ''finite'' [[oscillator]] that is one cell thick in one or more of its phases (tiling the plane with {{headerlessRLE\|oooooo..}} gives an infinite period-9 oscillator based on the [[worker bee]]), and in April {{year\|1992}}, [[Allan Wechsler]] used a search program to show that there are no oscillators of period 3, 5 or 7 that are one cell thick. The situation is technically unknown for other periods,<ref>E-mail sent from Allan Wechsler to LifeList</ref> though the existence of high-period examples is implied via the existence of the unidimensional spaceship{{refn\|group=note\|Since the unidimensional spaceship is a periodic pattern which programs its ~~rebuilding~~ in a different place via a universal constructor, a unidimensional ~~oscillator~~ only has to program its universal constructor to either rebuild itself in the same place or rebuild itself flipped 180 degrees}}. Interstingly, the [[pentadecathlon]] has a simple one cell thick predecessor, namely a 10-cell line, and the oscillator's evolution sequence involves it evolving into a pattern that is almost 1 cell thick.		The [[blinker]] is the only known ''finite'' [[oscillator]] that is one cell thick in one or more of its phases (tiling the plane with {{headerlessRLE\|oooooo..}} gives an infinite period-9 oscillator based on the [[worker bee]]; also see note 2), and in April {{year\|1992}}, [[Allan Wechsler]] used a search program to show that there are no oscillators of period 3, 5 or 7 that are one cell thick. The situation is technically unknown for other periods,<ref>E-mail sent from Allan Wechsler to LifeList</ref> though the existence of high-period examples is implied via the existence of the unidimensional spaceship{{refn\|group=note\|Since the unidimensional spaceship is a periodic pattern which programs its own reconstruction in a different place via a universal constructor, a unidimensional self-constructing pattern only has to program its universal constructor to either rebuild itself in the same place or rebuild itself flipped 180 degrees to become a unidimensional oscillator. The latter scenario would also provide an example of an oscillator that is unidimensional in more than one phase.}}. Interstingly, the [[pentadecathlon]] has a simple one cell thick predecessor, namely a 10-cell line, and the oscillator's evolution sequence involves it evolving into a pattern that is almost 1 cell thick.

	Since 2016, there has been research into the existence of a unidimensional spaceship.<ref name="post27410" /> This project was successful when user [[Hippo.69]] completed a 2c/1330767555768 spaceship on December 2, {{year\|2025}}. This ship, [[Unidimensional spaceship 1]], has a {{times\|3707300605\|1}} bounding box in one phase.<ref name="post222136" />. This ship consists of a unidimensional pattern that is a predecessor to a [[universal constructor]]. The process of creating a unidimensional universal constructor predecessor was the relatively simple part of the design; having the universal constructor then resynthesize the unidimensional pattern was much more difficult, as all sparks had to disappear before the ship entered its unidimensional phase. Due to symmetry, any one-cell-thick spaceship must move in the direction its length points in.		Since 2016, there has been research into the existence of a unidimensional spaceship.<ref name="post27410" /> This project was successful when user [[Hippo.69]] completed a 2c/1330767555768 spaceship on December 2, {{year\|2025}}. This ship, [[Unidimensional spaceship 1]], has a {{times\|3707300605\|1}} bounding box in one phase.<ref name="post222136" />. This ship consists of a unidimensional pattern that is a predecessor to a [[universal constructor]]. The process of creating a unidimensional universal constructor predecessor was the relatively simple part of the design; having the universal constructor then resynthesize the unidimensional pattern was much more difficult, as all sparks had to disappear before the ship entered its unidimensional phase. Due to symmetry, any one-cell-thick spaceship must move in the direction its length points in.

WhiteHawk: /* Spaceships and oscillators */ Fixing some syntax

2025-12-13T23:53:26Z

Spaceships and oscillators: Fixing some syntax

← Older revision		Revision as of 23:53, 13 December 2025
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	== Spaceships and oscillators ==		== Spaceships and oscillators ==
	The [[blinker]] is the only known ''finite'' [[oscillator]] that is one cell thick in one or more of its phases (tiling the plane with {{headerlessRLE\|oooooo..}} gives an infinite period-9 oscillator based on the [[worker bee]]), and in April {{year\|1992}}, [[Allan Wechsler]] used a search program to show that there are no oscillators of period 3, 5 or 7 that are one cell thick. The situation is technically unknown for other periods, <ref>E-mail sent from Allan Wechsler to LifeList</ref>, though the existence of high-period examples is implied via the existence of the unidimensional spaceship{{refn\|group=note\|Since the unidimensional spaceship is a periodic pattern which programs its rebuilding in a different place via a universal constructor, a unidimensional oscillator only has to program its universal constructor to either rebuild itself in the same place or rebuild itself flipped 180 degrees}}. Interstingly, the [[pentadecathlon]] has a simple one cell thick predecessor, namely a 10-cell line, and the oscillator's evolution sequence involves it evolving into a pattern that is almost 1 cell thick.		The [[blinker]] is the only known ''finite'' [[oscillator]] that is one cell thick in one or more of its phases (tiling the plane with {{headerlessRLE\|oooooo..}} gives an infinite period-9 oscillator based on the [[worker bee]]), and in April {{year\|1992}}, [[Allan Wechsler]] used a search program to show that there are no oscillators of period 3, 5 or 7 that are one cell thick. The situation is technically unknown for other periods,<ref>E-mail sent from Allan Wechsler to LifeList</ref> though the existence of high-period examples is implied via the existence of the unidimensional spaceship{{refn\|group=note\|Since the unidimensional spaceship is a periodic pattern which programs its rebuilding in a different place via a universal constructor, a unidimensional oscillator only has to program its universal constructor to either rebuild itself in the same place or rebuild itself flipped 180 degrees}}. Interstingly, the [[pentadecathlon]] has a simple one cell thick predecessor, namely a 10-cell line, and the oscillator's evolution sequence involves it evolving into a pattern that is almost 1 cell thick.

	Since 2016, there has been research into the existence of a unidimensional spaceship.<ref name="post27410" /> This project was successful when user [[Hippo.69]] completed a 2c/1330767555768 spaceship on December 2, {{year\|2025}}. This ship, [[Unidimensional spaceship 1]], has a {{times\|3707300605\|1}} bounding box in one phase.<ref name="post222136" />. This ship consists of a unidimensional pattern that is a predecessor to a [[universal constructor]]. The process of creating a unidimensional universal constructor predecessor was the relatively simple part of the design; having the universal constructor then resynthesize the unidimensional pattern was much more difficult, as all sparks had to disappear before the ship entered its unidimensional phase. Due to symmetry, any one-cell-thick spaceship must move in the direction its length points in.		Since 2016, there has been research into the existence of a unidimensional spaceship.<ref name="post27410" /> This project was successful when user [[Hippo.69]] completed a 2c/1330767555768 spaceship on December 2, {{year\|2025}}. This ship, [[Unidimensional spaceship 1]], has a {{times\|3707300605\|1}} bounding box in one phase.<ref name="post222136" />. This ship consists of a unidimensional pattern that is a predecessor to a [[universal constructor]]. The process of creating a unidimensional universal constructor predecessor was the relatively simple part of the design; having the universal constructor then resynthesize the unidimensional pattern was much more difficult, as all sparks had to disappear before the ship entered its unidimensional phase. Due to symmetry, any one-cell-thick spaceship must move in the direction its length points in.

WhiteHawk: /* Spaceships and oscillators */

2025-12-13T23:52:41Z

Spaceships and oscillators

← Older revision		Revision as of 23:52, 13 December 2025
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	The [[blinker]] is the only known ''finite'' [[oscillator]] that is one cell thick in one or more of its phases (tiling the plane with {{headerlessRLE\|oooooo..}} gives an infinite period-9 oscillator based on the [[worker bee]]), and in April {{year\|1992}}, [[Allan Wechsler]] used a search program to show that there are no oscillators of period 3, 5 or 7 that are one cell thick. The situation is technically unknown for other periods, <ref>E-mail sent from Allan Wechsler to LifeList</ref>, though the existence of high-period examples is implied via the existence of the unidimensional spaceship{{refn\|group=note\|Since the unidimensional spaceship is a periodic pattern which programs its rebuilding in a different place via a universal constructor, a unidimensional oscillator only has to program its universal constructor to either rebuild itself in the same place or rebuild itself flipped 180 degrees}}. Interstingly, the [[pentadecathlon]] has a simple one cell thick predecessor, namely a 10-cell line, and the oscillator's evolution sequence involves it evolving into a pattern that is almost 1 cell thick.		The [[blinker]] is the only known ''finite'' [[oscillator]] that is one cell thick in one or more of its phases (tiling the plane with {{headerlessRLE\|oooooo..}} gives an infinite period-9 oscillator based on the [[worker bee]]), and in April {{year\|1992}}, [[Allan Wechsler]] used a search program to show that there are no oscillators of period 3, 5 or 7 that are one cell thick. The situation is technically unknown for other periods, <ref>E-mail sent from Allan Wechsler to LifeList</ref>, though the existence of high-period examples is implied via the existence of the unidimensional spaceship{{refn\|group=note\|Since the unidimensional spaceship is a periodic pattern which programs its rebuilding in a different place via a universal constructor, a unidimensional oscillator only has to program its universal constructor to either rebuild itself in the same place or rebuild itself flipped 180 degrees}}. Interstingly, the [[pentadecathlon]] has a simple one cell thick predecessor, namely a 10-cell line, and the oscillator's evolution sequence involves it evolving into a pattern that is almost 1 cell thick.

	Since 2016, there has been research into the existence of a unidimensional spaceship.<ref name="post27410" /> This ~~porject~~ was successful when user [[Hippo.69]] completed a 2c/1330767555768 spaceship on December 2, {{year\|2025}}. This ship, [[Unidimensional spaceship 1]], has a {{times\|3707300605\|1}} bounding box in one phase.<ref name="post222136" />. This ship consists of a unidimensional pattern that is a predecessor to a [[universal constructor]]. The process of creating a unidimensional universal constructor predecessor was the relatively simple part of the design; having the universal constructor then resynthesize the unidimensional pattern was much more difficult, as all sparks had to disappear before the ship entered its unidimensional phase. Due to symmetry, any one-cell-thick spaceship must move in the direction its length points in.		Since 2016, there has been research into the existence of a unidimensional spaceship.<ref name="post27410" /> This project was successful when user [[Hippo.69]] completed a 2c/1330767555768 spaceship on December 2, {{year\|2025}}. This ship, [[Unidimensional spaceship 1]], has a {{times\|3707300605\|1}} bounding box in one phase.<ref name="post222136" />. This ship consists of a unidimensional pattern that is a predecessor to a [[universal constructor]]. The process of creating a unidimensional universal constructor predecessor was the relatively simple part of the design; having the universal constructor then resynthesize the unidimensional pattern was much more difficult, as all sparks had to disappear before the ship entered its unidimensional phase. Due to symmetry, any one-cell-thick spaceship must move in the direction its length points in.

	== Infinite growth ==		== Infinite growth ==