Is there any relationship between the bounding box and the period of an oscillator in the Conway's Game of Life? Is there any relationship between the bounding box and the period of an oscillator in the Conway's Game of Life?
In particular I am interested in this case: what is the maximum period for an oscillator contained in a bounding box of area $A$?
 A: The only way to be sure what types of patterns exist at some given size is to try them all.  This is impractical above extremely small sizes, and at larger sizes, it is theoretically undecidable even to determine whether a pattern is an oscillator.  In practice, people use a combination of computer searches and ingenuity to create oscillators or other interesting patterns.
Some examples of small oscillators can be found here:
periods 10-25,
periods 26-50,
periods 52-168.
To get a high-period oscillator in a small bounding box, you can combine several smaller oscillators having relatively prime periods.  Or you could take another approach, like adding an eater to turn this
period 149730 gun
into an oscillator.
If you have a lot more space, you can implement a Turing machine and then write a Turing machine program to count up to some large number before getting back to the initial state, achieving a periodicity which is exponential in the bounding box size.  Since only exponentially many patterns exist, there cannot be a super-exponential period.
