For any given rule of evolution, some cells will retain their existing state, while others change; generally there is no correlation between the two alternatives, giving the automaton a different appearance from generation to generation. Still, it could happen that there are particular combinations which remain immobile. One such, deliberately included in Conway's choice of a rule, is that if a cell and all its neighbors are dead, it remains dead. Automata which follow this requirement are said to have a quiescent state; live cells cannot appear spontaneously, but only near other live cells.
A quiescent state is not usually considered to be a still life; the latter term is reserved for collections of live cells for which cells neither die nor are born with succeeding generations.
It is curious that the simplest possible approach, if managed properly, suffices to enumerate the still lifes for an automaton. To begin with, neighborhoods can be classified as ``good'' or ``bad'' according to how their cell evolves. For the moment, a good neighborhood is one whose cell remains fixed; a cell that changes state is in a bad neighborhood. Obviously we are only interested in good neighborhoods.
The next step checks the neighborhoods of the neighbors; but not all pairs of neighborhoods overlap consistently. Only good neighborhoods that overlap well need be considered. The direct approach procedes along some path, fitting good neighborhoods together until an inconsistency results. By backtracking and considering alternative neighborhoods, it might be possible to generate a whole region which is unaffected by evolution. Trying again and again until all the possibilities are exhausted would eventually produce a complete list of static regions.
The whole plane can never be covered by this process; but it would be possible to stop when a quiescent border was reached, or even if the region began to repeat itself after a certain distance. So, at the very least, it should be possible to find all the still lifes covering a fixed area. Of course, the quantity of computation required grows exponentially with the area to be covered.
Giving first priority to the compatibility of overlapping neighborhoods, later rejecting those whose evolution is not satisfactory, places the computation on a firmer foundation. In either case, there is a simple diagram from which the compatibility of neighborhoods can be ascertained.