why it matters
A NOT gate plus a way to merge two streams (a second collision that kills a clock glider if either input is present) gives NOR, and NOR alone builds every Boolean circuit. Add memory from glider loops or stable blocks, and the board holds a computer. Berlekamp, Conway and Guy sketched this in Winning Ways (1982); Paul Rendell built a working Turing machine in Life in 2000. The same story plays out in one dimension: Matthew Cook's proof thatRule 110 is universal uses gliders colliding against a periodic background.
The complexity stamp says P because evaluating a Boolean circuit is P-complete: this gate is the unit of that problem. The board it runs on is not so tame. Ask what a large Life pattern will eventually do and you are asking what a computer will eventually do. That question lives in RE.
Geometry found by exhaustive search and checked on random bit strings: scripts/find-not-gate.mts, scripts/verify-not-gate.mts.