Since patterns in Conway’s Game can grow exponentially and without limit, I doubt there are any useful conservation principles that hold in all cases. There are probably specific pattern sets that obey conservation of certain properties, but not the ruleset as a whole.
I’m not sure what you mean by “grow exponentially” here—they certainly can’t add dimension or number of live cells exponentially with respect to time; dimension is only ever added one cell per time-slice and is thus O(n) while number of cells contained within the maximum dimensions is O(n^2) and thus so is the number of live cells.
Since patterns in Conway’s Game can grow exponentially and without limit, I doubt there are any useful conservation principles that hold in all cases. There are probably specific pattern sets that obey conservation of certain properties, but not the ruleset as a whole.
I’m not sure what you mean by “grow exponentially” here—they certainly can’t add dimension or number of live cells exponentially with respect to time; dimension is only ever added one cell per time-slice and is thus O(n) while number of cells contained within the maximum dimensions is O(n^2) and thus so is the number of live cells.