Bounding box
The bounding box of a pattern is the smallest rectangular array of cells that contains the entire pattern.
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Stationary objects
The bounding box of a still life is the bounding box which contains the pattern in its only phase. The bounding box of an oscillator is sometimes considered in one phase, but is most often expanded so as to include the entire oscillator in all of its phases. A gun's bounding box is similar to that of an oscillator but it does not include any outgoing streams of spaceships.
Other life-like cellular automata
The same definitions of bounding box also apply in other life-like cellular automata, and the rules for these cellular automata determine bounding box properties. For example, it is quite simple to show that a rule with no births cannot contain any oscillators or moving patterns because patterns are unable to expand in any direction.
Spaceships
The nonexistence of spaceships in life-like cellular automata can often be determined by simple patterns in the rulestrings, which affect the changes in a patterns bounding box. For an object to be considered a spaceship it must return to its initial phase (but in a different location), thus ensuring that the bounding box returns to a fixed size. For cellular automata with rules that include a birth with only one live neighbour, the bounding box of all patterns (excluding the pattern with no on cells) expands at the speed of light in every direction. Spaceships also cannot exist in rules with survival at zero, one, two, and three cells, as the trailing edge of a moving pattern could never completely die. For rules that do not have births at one, two, or three cells, the pattern can never expand beyond its initial bounding box, preventing any spaceships from existing. Such a rule can have oscillators however (provided it has births), but these oscillators will never leave their initial bounding box, and so their bounding boxes can be treated in the same way as those of still lifes.
Notes
External links
"bounding box" at the Life Lexicon