User:Tropylium/Lively
This draft page documents a terminological proposal for general use in Life or wider cellular automaton research.
A cellular automaton pattern is lively if all of its live cells satisfy the survival conditions of the rule.[1] Birth of new cells may or may not occur.
All still lifes are lively patterns, and thus, a rule can have still lifes if and only if it has lively patterns. As no reference is made to birth conditions, determining whether a pattern is lively is computationally simpler than determining if it is a still life.
A lively pattern that is not a still life, but can be stabilized into a still life by the addition of further clusters of live cells outside its boundary (can be satisfied) is a still life component. An inductee is a connected, satisfiable lively pattern that can exist as a singular island within a still life.
The Coolout Conjecture with its generalizations asks whether a lively pattern that locally appears to be satisfiable might be regardless not overall satisfiable.