Problem

An open problem is a problem for which no solution has been found. An example is "Do oscillators of all periods exist in Conway's Game of Life?".

Unsolved problems can be subdivided into several basic categories:

• Periods: Do oscillators, spaceships, guns or puffers exist of a particular period?
• Unusual-growth patterns: What is the long-term effect of a predefined pattern? For example, it is unknown whether the Fermat prime calculator grows indefinitely.
• Solvable problems: Some problems are known to have a solution, but as yet no pattern has been built. For instance, no adjustable-speed diagonal spaceship has been built to date, but a workable blueprint is available, and no new technical problems would have to be overcome to complete the construction.
• Construction and destruction problems: These include finding the smallest Garden of Eden, building a stable eater that can absorb any single glider aimed at it, determining whether a particular object has a glider synthesis, or discovering an unstoppable-growth pattern.
• Spatial minimization problems: Find an object that satisfies some criterion that fits within a certain bounding box. Examples include Mike Playle's prize for a small stable reflector.
• Temporal minimization problems: As above, but concentrating on speed rather than size.

List of problems

Open and previously open problems include:

Problem	Status	Year posed	Posed by	Year solved	Solved by
Description
Coolout Conjecture	solved	<1992	Richard Schroeppel	2001	Richard Schroeppel
The question “given a partial Life pattern that's internally consistent with being part of a still life (stable pattern), is there always a way to add a stabilizing boundary?” was answered in the negative.
Garden of Eden	solved	?	?	<1970	Edward Moore
The existence of a Garden of Eden in Life was known from the start because of a theorem by Edward Moore that guarantees their existence in a wide class of cellular automata.
Grandfather problem	solved	1972	John Conway	2016	mtve
The question “is there a configuration which has a father but no grandfather?” was answered in the affirmative.
Omniperiodicity	open	?	?	—	—
The question “do oscillators of all periods exist?” remains open for Life; no oscillators are known are periods 19, 23, 38 and 41, and no non-trivial oscillators are known for period 34.
Replicators	solved	?	?	1982	Elwyn R. Berlekamp, John Conway, Richard K. Guy
The question “do replicators exist in Life?” was answered in the affirmative.
Unique father problem	open	1972	John Conway	—	—
The question “is there a stable configuration whose only father is itself?” remains open.
Universal computer / Universal constructor	solved	?	John Conway	1982	Elwyn R. Berlekamp, John Conway, Richard K. Guy
The question “does Life support universal computation and universal construction?” was answered in the affirmative.