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Stable

The term stable is used in several contexts. The most general is as follows:

A stable pattern is a periodic pattern for which all future generations can be predicted accurately after one full period without evolving the pattern any further. This includes still lifes, oscillators, spaceships and guns.

A stable pattern may also be a pattern composed of one or more stable patterns that do not interfere with each other. This includes patterns which have evolved to stationary ash and optional spaceships escaping to infinity on non-interacting paths.

• An object or pattern becomes stable at time T if it conforms to the above definition at time T but not before. Such a pattern is said to stabilize at time T. A pattern that takes exceptionally long to stabilize, relative to other similarly sized patterns, is called a methuselah.
• 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. For example, a shillelagh (P2) stabilizes an unstable house (P1), producing the house siamese shillelagh still life, which is a stabilization of house.

History

The concept of a stable pattern was first formalized in the following table which appeared in the March 1971 publication of Lifeline Volume 1:

A CLASSIFICATION SYSTEM FOR 'LIFE' OBJECTS
OBJECTS	Characteristics of Life History				Class	Age	Example
	Stable	Inactive			Class I Still Lifes	∞	block
		Active	Stationary		Class II Oscillators	∞	blinker
			Moving	Constant Bits	Class III Spaceships	∞	glider
				Increasing Bits	Class IV Glider Guns	∞	Glider Gun
	Unstable	Predictable			Class V All Objects Not In Above (Known)	varies	n-ominoes
		Unpredictable			Class VI All Objects Not In Above	?	broths

While this classification system would be expanded--for example, the glider guns class became spaceship guns--the fundamental notion of what constituted a stable pattern was established.

Other contexts

• Period 1 is often abbreviated p1 connoting stable. Thus stable is sometimes used as a synonym for still life.
• A stable reflector is a reflector that is a p1 pattern.
• In the context of logic circuitry, p1 or stable tends to mean that a mechanism is constructed from Herschel conduits that contain only still lifes as catalysts.
• A p1 slow salvo is a slow salvo in which the intermediate settled-down stages are all period 1 and may be referred to as stable.
• 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.

Further reading

• Conway's Game of Life: Mathematics and Construction