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A pattern is said to be '''stable''' if it is a [[still life]] or consists of still lifes; in other words, it is a [[parent]] of itself. For example, a [[stable reflector]] is a [[reflector]] that is a period-1 pattern.<ref>{{CiteLexicon|file=lex_s.htm#stable|name=Stable}}</ref><ref>{{CiteLexicon|file=lex_r.htm#reflector|name=Reflector}}</ref> | A pattern is said to be '''stable''' if it is a [[still life]] or consists of still lifes; in other words, it is a [[parent]] of itself. For example, a [[stable reflector]] is a [[reflector]] that is a period-1 pattern.<ref>{{CiteLexicon|file=lex_s.htm#stable|name=Stable}}</ref><ref>{{CiteLexicon|file=lex_r.htm#reflector|name=Reflector}}</ref> | ||
Period 1 is often abbreviated '''p1''' connoting stable. In the context of logic [[circuitry]], this tends to mean that a mechanism is constructed from [[ | Period 1 is often abbreviated '''p1''' connoting stable. In the context of logic [[circuitry]], this tends to mean that a mechanism is constructed from [[conduit]]s that contain only [[still life]]s as [[catalyst]]s.<ref>{{CiteLexicon|file=lex_p.htm#p1|name=p1}}</ref> | ||
==Stability and methuselahs== | |||
{{related|Unknown fate|Methuselah|Infinite growth|Conway's Game of Life: Mathematics and Construction}} | |||
A pattern | A [[pattern]] can be said to '''stabilize (at time T)''' when the pattern settles (at time T) into non-interacting still lifes, oscillators and spaceships. A pattern that takes exceptionally long to stabilize, relative to other similarly sized patterns, is called a [[methuselah]].<ref>[[Conway's Game of Life: Mathematics and Construction]] 1.6 Methuselahs and Stability: "We will see shortly that properly defining what it means for a pattern to "stabilize" is very troublesome, but for now it just means that the pattern has broken down into non-interacting still lifes, oscillators, and spaceships."</ref> | ||
Sometimes an [[Infinite growth|indefinitely growing]] pattern can still be said to stabilize ''at some point'' in its evolution (even though it never settles into non-interacting stationary objects and escaping spaceships), when the pattern starts growing in a regular and predictable way; for example, the [[BLSE]] and the [[GPSE]] can be said to stabilize once they enter the periodic portion of evolution.<ref>Conway's Game of Life: Mathematics and Construction 1.6 Methuselahs and Stability</ref> | |||
==Stabilizing an unstable pattern== | |||
A pattern P2 is said to '''stabilize''' an unstable pattern P1 if, when P1 and P2 are properly positioned, the resulting pattern is stable. This is known as a '''stabilization''' of P1.<ref>Conway's Game of Life: Mathematics and Construction 1.4 The B-Heptomino and Twin Bees: "In order to stabilize the twin bees, we take a cue from the queen bee and try placing blocks in such a way as to eat the mess that is left behind."</ref> For example, a [[shillelagh]] (P2) stabilizes an unstable [[house]] (P1), producing the [[house siamese shillelagh]] still life, which is a stabilization of house. | |||
==References== | ==References== | ||
<references /> | <references /> | ||
== | ==Links and further reading== | ||
* [[Conway's Game of Life: Mathematics and Construction]] | |||
* {{LinkForumThread | * {{LinkForumThread | ||
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Latest revision as of 03:45, 29 September 2023
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A pattern is said to be stable if it is a still life or consists of still lifes; in other words, it is a parent of itself. For example, a stable reflector is a reflector that is a period-1 pattern.[1][2]
Period 1 is often abbreviated p1 connoting stable. In the context of logic circuitry, this tends to mean that a mechanism is constructed from conduits that contain only still lifes as catalysts.[3]
Stability and methuselahs
- See also: Unknown fate, Methuselah, Infinite growth, Conway's Game of Life: Mathematics and Construction
A pattern can be said to stabilize (at time T) when the pattern settles (at time T) into non-interacting still lifes, oscillators and spaceships. A pattern that takes exceptionally long to stabilize, relative to other similarly sized patterns, is called a methuselah.[4]
Sometimes an indefinitely growing pattern can still be said to stabilize at some point in its evolution (even though it never settles into non-interacting stationary objects and escaping spaceships), when the pattern starts growing in a regular and predictable way; for example, the BLSE and the GPSE can be said to stabilize once they enter the periodic portion of evolution.[5]
Stabilizing an unstable pattern
A pattern P2 is said to stabilize an unstable pattern P1 if, when P1 and P2 are properly positioned, the resulting pattern is stable. This is known as a stabilization of P1.[6] For example, a shillelagh (P2) stabilizes an unstable house (P1), producing the house siamese shillelagh still life, which is a stabilization of house.
References
- ↑ "Stable". The Life Lexicon. Stephen Silver.
- ↑ "Reflector". The Life Lexicon. Stephen Silver.
- ↑ "p1". The Life Lexicon. Stephen Silver.
- ↑ Conway's Game of Life: Mathematics and Construction 1.6 Methuselahs and Stability: "We will see shortly that properly defining what it means for a pattern to "stabilize" is very troublesome, but for now it just means that the pattern has broken down into non-interacting still lifes, oscillators, and spaceships."
- ↑ Conway's Game of Life: Mathematics and Construction 1.6 Methuselahs and Stability
- ↑ Conway's Game of Life: Mathematics and Construction 1.4 The B-Heptomino and Twin Bees: "In order to stabilize the twin bees, we take a cue from the queen bee and try placing blocks in such a way as to eat the mess that is left behind."
Links and further reading
- Conway's Game of Life: Mathematics and Construction
- Dave Greene (August 19, 2022). Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums