Stable: Difference between revisions
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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> | ||
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Revision as of 19:13, 19 August 2022
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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]
Alternatively, a pattern is stable if all future generations can be predicted without evolving the pattern any further (trivially, a still life fits this definition). This includes patterns which evolve to stationary ash and optional spaceships escaping to infinity on non-interacting paths.[3]
A pattern becomes stable at time T if it conforms to the above definition at time T.[3]
A pattern is unstable if it does not fit the above definition.
Pattern B (the stabilizer) is said to stabilize unstable pattern A if, when A and B are properly positioned, the resulting pattern is stable. This is known as a stabilization of A. For example, a shillelagh (B) stabilizes an unstable house (A), producing the house siamese shillelagh still life, which is a stabilzation of house.
References
- ↑ "Stable". The Life Lexicon. Stephen Silver.
- ↑ "Reflector". The Life Lexicon. Stephen Silver.
- ↑ 3.0 3.1 Dave Greene (August 19, 2022). Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums