Problem

An open problem is a problem for which no solution has been found. An example is 'Do oscillators of all periods exist?'

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 replicator has been built, but they are known to exist. Spiral growth is another example.
• 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 minimisation problems: Find an object that satisfies some criterion that fits within a certain bounding box. Examples include Dave Greene's prize for a small stable reflector.
• Temporal minimisation problems: As above, but concentrating on speed rather than size.